ScalarEvolution.cpp revision fcb4356dee96563def584fe38eeafb3eb63c5cd8
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/InstructionSimplify.h" 73#include "llvm/Analysis/LoopInfo.h" 74#include "llvm/Analysis/ValueTracking.h" 75#include "llvm/Assembly/Writer.h" 76#include "llvm/Target/TargetData.h" 77#include "llvm/Support/CommandLine.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/Debug.h" 80#include "llvm/Support/ErrorHandling.h" 81#include "llvm/Support/GetElementPtrTypeIterator.h" 82#include "llvm/Support/InstIterator.h" 83#include "llvm/Support/MathExtras.h" 84#include "llvm/Support/raw_ostream.h" 85#include "llvm/ADT/Statistic.h" 86#include "llvm/ADT/STLExtras.h" 87#include "llvm/ADT/SmallPtrSet.h" 88#include <algorithm> 89using namespace llvm; 90 91STATISTIC(NumArrayLenItCounts, 92 "Number of trip counts computed with array length"); 93STATISTIC(NumTripCountsComputed, 94 "Number of loops with predictable loop counts"); 95STATISTIC(NumTripCountsNotComputed, 96 "Number of loops without predictable loop counts"); 97STATISTIC(NumBruteForceTripCountsComputed, 98 "Number of loops with trip counts computed by force"); 99 100static cl::opt<unsigned> 101MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 102 cl::desc("Maximum number of iterations SCEV will " 103 "symbolically execute a constant " 104 "derived loop"), 105 cl::init(100)); 106 107INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 108 "Scalar Evolution Analysis", false, true) 109INITIALIZE_PASS_DEPENDENCY(LoopInfo) 110INITIALIZE_PASS_DEPENDENCY(DominatorTree) 111INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 112 "Scalar Evolution Analysis", false, true) 113char ScalarEvolution::ID = 0; 114 115//===----------------------------------------------------------------------===// 116// SCEV class definitions 117//===----------------------------------------------------------------------===// 118 119//===----------------------------------------------------------------------===// 120// Implementation of the SCEV class. 121// 122 123void SCEV::dump() const { 124 print(dbgs()); 125 dbgs() << '\n'; 126} 127 128void SCEV::print(raw_ostream &OS) const { 129 switch (getSCEVType()) { 130 case scConstant: 131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 132 return; 133 case scTruncate: { 134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 135 const SCEV *Op = Trunc->getOperand(); 136 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 137 << *Trunc->getType() << ")"; 138 return; 139 } 140 case scZeroExtend: { 141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 142 const SCEV *Op = ZExt->getOperand(); 143 OS << "(zext " << *Op->getType() << " " << *Op << " to " 144 << *ZExt->getType() << ")"; 145 return; 146 } 147 case scSignExtend: { 148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 149 const SCEV *Op = SExt->getOperand(); 150 OS << "(sext " << *Op->getType() << " " << *Op << " to " 151 << *SExt->getType() << ")"; 152 return; 153 } 154 case scAddRecExpr: { 155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 156 OS << "{" << *AR->getOperand(0); 157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 158 OS << ",+," << *AR->getOperand(i); 159 OS << "}<"; 160 if (AR->getNoWrapFlags(FlagNUW)) 161 OS << "nuw><"; 162 if (AR->getNoWrapFlags(FlagNSW)) 163 OS << "nsw><"; 164 if (AR->getNoWrapFlags(FlagNW) && 165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 166 OS << "nw><"; 167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 168 OS << ">"; 169 return; 170 } 171 case scAddExpr: 172 case scMulExpr: 173 case scUMaxExpr: 174 case scSMaxExpr: { 175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 176 const char *OpStr = 0; 177 switch (NAry->getSCEVType()) { 178 case scAddExpr: OpStr = " + "; break; 179 case scMulExpr: OpStr = " * "; break; 180 case scUMaxExpr: OpStr = " umax "; break; 181 case scSMaxExpr: OpStr = " smax "; break; 182 } 183 OS << "("; 184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 185 I != E; ++I) { 186 OS << **I; 187 if (llvm::next(I) != E) 188 OS << OpStr; 189 } 190 OS << ")"; 191 return; 192 } 193 case scUDivExpr: { 194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 196 return; 197 } 198 case scUnknown: { 199 const SCEVUnknown *U = cast<SCEVUnknown>(this); 200 Type *AllocTy; 201 if (U->isSizeOf(AllocTy)) { 202 OS << "sizeof(" << *AllocTy << ")"; 203 return; 204 } 205 if (U->isAlignOf(AllocTy)) { 206 OS << "alignof(" << *AllocTy << ")"; 207 return; 208 } 209 210 Type *CTy; 211 Constant *FieldNo; 212 if (U->isOffsetOf(CTy, FieldNo)) { 213 OS << "offsetof(" << *CTy << ", "; 214 WriteAsOperand(OS, FieldNo, false); 215 OS << ")"; 216 return; 217 } 218 219 // Otherwise just print it normally. 220 WriteAsOperand(OS, U->getValue(), false); 221 return; 222 } 223 case scCouldNotCompute: 224 OS << "***COULDNOTCOMPUTE***"; 225 return; 226 default: break; 227 } 228 llvm_unreachable("Unknown SCEV kind!"); 229} 230 231Type *SCEV::getType() const { 232 switch (getSCEVType()) { 233 case scConstant: 234 return cast<SCEVConstant>(this)->getType(); 235 case scTruncate: 236 case scZeroExtend: 237 case scSignExtend: 238 return cast<SCEVCastExpr>(this)->getType(); 239 case scAddRecExpr: 240 case scMulExpr: 241 case scUMaxExpr: 242 case scSMaxExpr: 243 return cast<SCEVNAryExpr>(this)->getType(); 244 case scAddExpr: 245 return cast<SCEVAddExpr>(this)->getType(); 246 case scUDivExpr: 247 return cast<SCEVUDivExpr>(this)->getType(); 248 case scUnknown: 249 return cast<SCEVUnknown>(this)->getType(); 250 case scCouldNotCompute: 251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 252 return 0; 253 default: break; 254 } 255 llvm_unreachable("Unknown SCEV kind!"); 256 return 0; 257} 258 259bool SCEV::isZero() const { 260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 261 return SC->getValue()->isZero(); 262 return false; 263} 264 265bool SCEV::isOne() const { 266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 267 return SC->getValue()->isOne(); 268 return false; 269} 270 271bool SCEV::isAllOnesValue() const { 272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 273 return SC->getValue()->isAllOnesValue(); 274 return false; 275} 276 277SCEVCouldNotCompute::SCEVCouldNotCompute() : 278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 279 280bool SCEVCouldNotCompute::classof(const SCEV *S) { 281 return S->getSCEVType() == scCouldNotCompute; 282} 283 284const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 285 FoldingSetNodeID ID; 286 ID.AddInteger(scConstant); 287 ID.AddPointer(V); 288 void *IP = 0; 289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 291 UniqueSCEVs.InsertNode(S, IP); 292 return S; 293} 294 295const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 296 return getConstant(ConstantInt::get(getContext(), Val)); 297} 298 299const SCEV * 300ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 301 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 302 return getConstant(ConstantInt::get(ITy, V, isSigned)); 303} 304 305SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 306 unsigned SCEVTy, const SCEV *op, Type *ty) 307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 308 309SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 310 const SCEV *op, Type *ty) 311 : SCEVCastExpr(ID, scTruncate, op, ty) { 312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 313 (Ty->isIntegerTy() || Ty->isPointerTy()) && 314 "Cannot truncate non-integer value!"); 315} 316 317SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 318 const SCEV *op, Type *ty) 319 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 321 (Ty->isIntegerTy() || Ty->isPointerTy()) && 322 "Cannot zero extend non-integer value!"); 323} 324 325SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 326 const SCEV *op, Type *ty) 327 : SCEVCastExpr(ID, scSignExtend, op, ty) { 328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 329 (Ty->isIntegerTy() || Ty->isPointerTy()) && 330 "Cannot sign extend non-integer value!"); 331} 332 333void SCEVUnknown::deleted() { 334 // Clear this SCEVUnknown from various maps. 335 SE->forgetMemoizedResults(this); 336 337 // Remove this SCEVUnknown from the uniquing map. 338 SE->UniqueSCEVs.RemoveNode(this); 339 340 // Release the value. 341 setValPtr(0); 342} 343 344void SCEVUnknown::allUsesReplacedWith(Value *New) { 345 // Clear this SCEVUnknown from various maps. 346 SE->forgetMemoizedResults(this); 347 348 // Remove this SCEVUnknown from the uniquing map. 349 SE->UniqueSCEVs.RemoveNode(this); 350 351 // Update this SCEVUnknown to point to the new value. This is needed 352 // because there may still be outstanding SCEVs which still point to 353 // this SCEVUnknown. 354 setValPtr(New); 355} 356 357bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 359 if (VCE->getOpcode() == Instruction::PtrToInt) 360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 361 if (CE->getOpcode() == Instruction::GetElementPtr && 362 CE->getOperand(0)->isNullValue() && 363 CE->getNumOperands() == 2) 364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 365 if (CI->isOne()) { 366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 367 ->getElementType(); 368 return true; 369 } 370 371 return false; 372} 373 374bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 376 if (VCE->getOpcode() == Instruction::PtrToInt) 377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 378 if (CE->getOpcode() == Instruction::GetElementPtr && 379 CE->getOperand(0)->isNullValue()) { 380 Type *Ty = 381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 382 if (StructType *STy = dyn_cast<StructType>(Ty)) 383 if (!STy->isPacked() && 384 CE->getNumOperands() == 3 && 385 CE->getOperand(1)->isNullValue()) { 386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 387 if (CI->isOne() && 388 STy->getNumElements() == 2 && 389 STy->getElementType(0)->isIntegerTy(1)) { 390 AllocTy = STy->getElementType(1); 391 return true; 392 } 393 } 394 } 395 396 return false; 397} 398 399bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 401 if (VCE->getOpcode() == Instruction::PtrToInt) 402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 403 if (CE->getOpcode() == Instruction::GetElementPtr && 404 CE->getNumOperands() == 3 && 405 CE->getOperand(0)->isNullValue() && 406 CE->getOperand(1)->isNullValue()) { 407 Type *Ty = 408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 409 // Ignore vector types here so that ScalarEvolutionExpander doesn't 410 // emit getelementptrs that index into vectors. 411 if (Ty->isStructTy() || Ty->isArrayTy()) { 412 CTy = Ty; 413 FieldNo = CE->getOperand(2); 414 return true; 415 } 416 } 417 418 return false; 419} 420 421//===----------------------------------------------------------------------===// 422// SCEV Utilities 423//===----------------------------------------------------------------------===// 424 425namespace { 426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 427 /// than the complexity of the RHS. This comparator is used to canonicalize 428 /// expressions. 429 class SCEVComplexityCompare { 430 const LoopInfo *const LI; 431 public: 432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 433 434 // Return true or false if LHS is less than, or at least RHS, respectively. 435 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 436 return compare(LHS, RHS) < 0; 437 } 438 439 // Return negative, zero, or positive, if LHS is less than, equal to, or 440 // greater than RHS, respectively. A three-way result allows recursive 441 // comparisons to be more efficient. 442 int compare(const SCEV *LHS, const SCEV *RHS) const { 443 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 444 if (LHS == RHS) 445 return 0; 446 447 // Primarily, sort the SCEVs by their getSCEVType(). 448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 449 if (LType != RType) 450 return (int)LType - (int)RType; 451 452 // Aside from the getSCEVType() ordering, the particular ordering 453 // isn't very important except that it's beneficial to be consistent, 454 // so that (a + b) and (b + a) don't end up as different expressions. 455 switch (LType) { 456 case scUnknown: { 457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 459 460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 461 // not as complete as it could be. 462 const Value *LV = LU->getValue(), *RV = RU->getValue(); 463 464 // Order pointer values after integer values. This helps SCEVExpander 465 // form GEPs. 466 bool LIsPointer = LV->getType()->isPointerTy(), 467 RIsPointer = RV->getType()->isPointerTy(); 468 if (LIsPointer != RIsPointer) 469 return (int)LIsPointer - (int)RIsPointer; 470 471 // Compare getValueID values. 472 unsigned LID = LV->getValueID(), 473 RID = RV->getValueID(); 474 if (LID != RID) 475 return (int)LID - (int)RID; 476 477 // Sort arguments by their position. 478 if (const Argument *LA = dyn_cast<Argument>(LV)) { 479 const Argument *RA = cast<Argument>(RV); 480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 481 return (int)LArgNo - (int)RArgNo; 482 } 483 484 // For instructions, compare their loop depth, and their operand 485 // count. This is pretty loose. 486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 487 const Instruction *RInst = cast<Instruction>(RV); 488 489 // Compare loop depths. 490 const BasicBlock *LParent = LInst->getParent(), 491 *RParent = RInst->getParent(); 492 if (LParent != RParent) { 493 unsigned LDepth = LI->getLoopDepth(LParent), 494 RDepth = LI->getLoopDepth(RParent); 495 if (LDepth != RDepth) 496 return (int)LDepth - (int)RDepth; 497 } 498 499 // Compare the number of operands. 500 unsigned LNumOps = LInst->getNumOperands(), 501 RNumOps = RInst->getNumOperands(); 502 return (int)LNumOps - (int)RNumOps; 503 } 504 505 return 0; 506 } 507 508 case scConstant: { 509 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 510 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 511 512 // Compare constant values. 513 const APInt &LA = LC->getValue()->getValue(); 514 const APInt &RA = RC->getValue()->getValue(); 515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 516 if (LBitWidth != RBitWidth) 517 return (int)LBitWidth - (int)RBitWidth; 518 return LA.ult(RA) ? -1 : 1; 519 } 520 521 case scAddRecExpr: { 522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 524 525 // Compare addrec loop depths. 526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 527 if (LLoop != RLoop) { 528 unsigned LDepth = LLoop->getLoopDepth(), 529 RDepth = RLoop->getLoopDepth(); 530 if (LDepth != RDepth) 531 return (int)LDepth - (int)RDepth; 532 } 533 534 // Addrec complexity grows with operand count. 535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 536 if (LNumOps != RNumOps) 537 return (int)LNumOps - (int)RNumOps; 538 539 // Lexicographically compare. 540 for (unsigned i = 0; i != LNumOps; ++i) { 541 long X = compare(LA->getOperand(i), RA->getOperand(i)); 542 if (X != 0) 543 return X; 544 } 545 546 return 0; 547 } 548 549 case scAddExpr: 550 case scMulExpr: 551 case scSMaxExpr: 552 case scUMaxExpr: { 553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 555 556 // Lexicographically compare n-ary expressions. 557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 558 for (unsigned i = 0; i != LNumOps; ++i) { 559 if (i >= RNumOps) 560 return 1; 561 long X = compare(LC->getOperand(i), RC->getOperand(i)); 562 if (X != 0) 563 return X; 564 } 565 return (int)LNumOps - (int)RNumOps; 566 } 567 568 case scUDivExpr: { 569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 571 572 // Lexicographically compare udiv expressions. 573 long X = compare(LC->getLHS(), RC->getLHS()); 574 if (X != 0) 575 return X; 576 return compare(LC->getRHS(), RC->getRHS()); 577 } 578 579 case scTruncate: 580 case scZeroExtend: 581 case scSignExtend: { 582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 584 585 // Compare cast expressions by operand. 586 return compare(LC->getOperand(), RC->getOperand()); 587 } 588 589 default: 590 break; 591 } 592 593 llvm_unreachable("Unknown SCEV kind!"); 594 return 0; 595 } 596 }; 597} 598 599/// GroupByComplexity - Given a list of SCEV objects, order them by their 600/// complexity, and group objects of the same complexity together by value. 601/// When this routine is finished, we know that any duplicates in the vector are 602/// consecutive and that complexity is monotonically increasing. 603/// 604/// Note that we go take special precautions to ensure that we get deterministic 605/// results from this routine. In other words, we don't want the results of 606/// this to depend on where the addresses of various SCEV objects happened to 607/// land in memory. 608/// 609static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 610 LoopInfo *LI) { 611 if (Ops.size() < 2) return; // Noop 612 if (Ops.size() == 2) { 613 // This is the common case, which also happens to be trivially simple. 614 // Special case it. 615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 616 if (SCEVComplexityCompare(LI)(RHS, LHS)) 617 std::swap(LHS, RHS); 618 return; 619 } 620 621 // Do the rough sort by complexity. 622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 623 624 // Now that we are sorted by complexity, group elements of the same 625 // complexity. Note that this is, at worst, N^2, but the vector is likely to 626 // be extremely short in practice. Note that we take this approach because we 627 // do not want to depend on the addresses of the objects we are grouping. 628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 629 const SCEV *S = Ops[i]; 630 unsigned Complexity = S->getSCEVType(); 631 632 // If there are any objects of the same complexity and same value as this 633 // one, group them. 634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 635 if (Ops[j] == S) { // Found a duplicate. 636 // Move it to immediately after i'th element. 637 std::swap(Ops[i+1], Ops[j]); 638 ++i; // no need to rescan it. 639 if (i == e-2) return; // Done! 640 } 641 } 642 } 643} 644 645 646 647//===----------------------------------------------------------------------===// 648// Simple SCEV method implementations 649//===----------------------------------------------------------------------===// 650 651/// BinomialCoefficient - Compute BC(It, K). The result has width W. 652/// Assume, K > 0. 653static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 654 ScalarEvolution &SE, 655 Type* ResultTy) { 656 // Handle the simplest case efficiently. 657 if (K == 1) 658 return SE.getTruncateOrZeroExtend(It, ResultTy); 659 660 // We are using the following formula for BC(It, K): 661 // 662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 663 // 664 // Suppose, W is the bitwidth of the return value. We must be prepared for 665 // overflow. Hence, we must assure that the result of our computation is 666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 667 // safe in modular arithmetic. 668 // 669 // However, this code doesn't use exactly that formula; the formula it uses 670 // is something like the following, where T is the number of factors of 2 in 671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 672 // exponentiation: 673 // 674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 675 // 676 // This formula is trivially equivalent to the previous formula. However, 677 // this formula can be implemented much more efficiently. The trick is that 678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 679 // arithmetic. To do exact division in modular arithmetic, all we have 680 // to do is multiply by the inverse. Therefore, this step can be done at 681 // width W. 682 // 683 // The next issue is how to safely do the division by 2^T. The way this 684 // is done is by doing the multiplication step at a width of at least W + T 685 // bits. This way, the bottom W+T bits of the product are accurate. Then, 686 // when we perform the division by 2^T (which is equivalent to a right shift 687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 688 // truncated out after the division by 2^T. 689 // 690 // In comparison to just directly using the first formula, this technique 691 // is much more efficient; using the first formula requires W * K bits, 692 // but this formula less than W + K bits. Also, the first formula requires 693 // a division step, whereas this formula only requires multiplies and shifts. 694 // 695 // It doesn't matter whether the subtraction step is done in the calculation 696 // width or the input iteration count's width; if the subtraction overflows, 697 // the result must be zero anyway. We prefer here to do it in the width of 698 // the induction variable because it helps a lot for certain cases; CodeGen 699 // isn't smart enough to ignore the overflow, which leads to much less 700 // efficient code if the width of the subtraction is wider than the native 701 // register width. 702 // 703 // (It's possible to not widen at all by pulling out factors of 2 before 704 // the multiplication; for example, K=2 can be calculated as 705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 706 // extra arithmetic, so it's not an obvious win, and it gets 707 // much more complicated for K > 3.) 708 709 // Protection from insane SCEVs; this bound is conservative, 710 // but it probably doesn't matter. 711 if (K > 1000) 712 return SE.getCouldNotCompute(); 713 714 unsigned W = SE.getTypeSizeInBits(ResultTy); 715 716 // Calculate K! / 2^T and T; we divide out the factors of two before 717 // multiplying for calculating K! / 2^T to avoid overflow. 718 // Other overflow doesn't matter because we only care about the bottom 719 // W bits of the result. 720 APInt OddFactorial(W, 1); 721 unsigned T = 1; 722 for (unsigned i = 3; i <= K; ++i) { 723 APInt Mult(W, i); 724 unsigned TwoFactors = Mult.countTrailingZeros(); 725 T += TwoFactors; 726 Mult = Mult.lshr(TwoFactors); 727 OddFactorial *= Mult; 728 } 729 730 // We need at least W + T bits for the multiplication step 731 unsigned CalculationBits = W + T; 732 733 // Calculate 2^T, at width T+W. 734 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 735 736 // Calculate the multiplicative inverse of K! / 2^T; 737 // this multiplication factor will perform the exact division by 738 // K! / 2^T. 739 APInt Mod = APInt::getSignedMinValue(W+1); 740 APInt MultiplyFactor = OddFactorial.zext(W+1); 741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 742 MultiplyFactor = MultiplyFactor.trunc(W); 743 744 // Calculate the product, at width T+W 745 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 746 CalculationBits); 747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 748 for (unsigned i = 1; i != K; ++i) { 749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 750 Dividend = SE.getMulExpr(Dividend, 751 SE.getTruncateOrZeroExtend(S, CalculationTy)); 752 } 753 754 // Divide by 2^T 755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 756 757 // Truncate the result, and divide by K! / 2^T. 758 759 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 760 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 761} 762 763/// evaluateAtIteration - Return the value of this chain of recurrences at 764/// the specified iteration number. We can evaluate this recurrence by 765/// multiplying each element in the chain by the binomial coefficient 766/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 767/// 768/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 769/// 770/// where BC(It, k) stands for binomial coefficient. 771/// 772const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 773 ScalarEvolution &SE) const { 774 const SCEV *Result = getStart(); 775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 776 // The computation is correct in the face of overflow provided that the 777 // multiplication is performed _after_ the evaluation of the binomial 778 // coefficient. 779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 780 if (isa<SCEVCouldNotCompute>(Coeff)) 781 return Coeff; 782 783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 784 } 785 return Result; 786} 787 788//===----------------------------------------------------------------------===// 789// SCEV Expression folder implementations 790//===----------------------------------------------------------------------===// 791 792const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 793 Type *Ty) { 794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 795 "This is not a truncating conversion!"); 796 assert(isSCEVable(Ty) && 797 "This is not a conversion to a SCEVable type!"); 798 Ty = getEffectiveSCEVType(Ty); 799 800 FoldingSetNodeID ID; 801 ID.AddInteger(scTruncate); 802 ID.AddPointer(Op); 803 ID.AddPointer(Ty); 804 void *IP = 0; 805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 806 807 // Fold if the operand is constant. 808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 809 return getConstant( 810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 811 getEffectiveSCEVType(Ty)))); 812 813 // trunc(trunc(x)) --> trunc(x) 814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 815 return getTruncateExpr(ST->getOperand(), Ty); 816 817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 819 return getTruncateOrSignExtend(SS->getOperand(), Ty); 820 821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 824 825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 826 // eliminate all the truncates. 827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 828 SmallVector<const SCEV *, 4> Operands; 829 bool hasTrunc = false; 830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 832 hasTrunc = isa<SCEVTruncateExpr>(S); 833 Operands.push_back(S); 834 } 835 if (!hasTrunc) 836 return getAddExpr(Operands); 837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 838 } 839 840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 841 // eliminate all the truncates. 842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 843 SmallVector<const SCEV *, 4> Operands; 844 bool hasTrunc = false; 845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 847 hasTrunc = isa<SCEVTruncateExpr>(S); 848 Operands.push_back(S); 849 } 850 if (!hasTrunc) 851 return getMulExpr(Operands); 852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 853 } 854 855 // If the input value is a chrec scev, truncate the chrec's operands. 856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 857 SmallVector<const SCEV *, 4> Operands; 858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 861 } 862 863 // As a special case, fold trunc(undef) to undef. We don't want to 864 // know too much about SCEVUnknowns, but this special case is handy 865 // and harmless. 866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 867 if (isa<UndefValue>(U->getValue())) 868 return getSCEV(UndefValue::get(Ty)); 869 870 // The cast wasn't folded; create an explicit cast node. We can reuse 871 // the existing insert position since if we get here, we won't have 872 // made any changes which would invalidate it. 873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 874 Op, Ty); 875 UniqueSCEVs.InsertNode(S, IP); 876 return S; 877} 878 879const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 880 Type *Ty) { 881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 882 "This is not an extending conversion!"); 883 assert(isSCEVable(Ty) && 884 "This is not a conversion to a SCEVable type!"); 885 Ty = getEffectiveSCEVType(Ty); 886 887 // Fold if the operand is constant. 888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 889 return getConstant( 890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 891 getEffectiveSCEVType(Ty)))); 892 893 // zext(zext(x)) --> zext(x) 894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 895 return getZeroExtendExpr(SZ->getOperand(), Ty); 896 897 // Before doing any expensive analysis, check to see if we've already 898 // computed a SCEV for this Op and Ty. 899 FoldingSetNodeID ID; 900 ID.AddInteger(scZeroExtend); 901 ID.AddPointer(Op); 902 ID.AddPointer(Ty); 903 void *IP = 0; 904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 905 906 // zext(trunc(x)) --> zext(x) or x or trunc(x) 907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 908 // It's possible the bits taken off by the truncate were all zero bits. If 909 // so, we should be able to simplify this further. 910 const SCEV *X = ST->getOperand(); 911 ConstantRange CR = getUnsignedRange(X); 912 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 913 unsigned NewBits = getTypeSizeInBits(Ty); 914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 915 CR.zextOrTrunc(NewBits))) 916 return getTruncateOrZeroExtend(X, Ty); 917 } 918 919 // If the input value is a chrec scev, and we can prove that the value 920 // did not overflow the old, smaller, value, we can zero extend all of the 921 // operands (often constants). This allows analysis of something like 922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 924 if (AR->isAffine()) { 925 const SCEV *Start = AR->getStart(); 926 const SCEV *Step = AR->getStepRecurrence(*this); 927 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 928 const Loop *L = AR->getLoop(); 929 930 // If we have special knowledge that this addrec won't overflow, 931 // we don't need to do any further analysis. 932 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 933 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 934 getZeroExtendExpr(Step, Ty), 935 L, AR->getNoWrapFlags()); 936 937 // Check whether the backedge-taken count is SCEVCouldNotCompute. 938 // Note that this serves two purposes: It filters out loops that are 939 // simply not analyzable, and it covers the case where this code is 940 // being called from within backedge-taken count analysis, such that 941 // attempting to ask for the backedge-taken count would likely result 942 // in infinite recursion. In the later case, the analysis code will 943 // cope with a conservative value, and it will take care to purge 944 // that value once it has finished. 945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 947 // Manually compute the final value for AR, checking for 948 // overflow. 949 950 // Check whether the backedge-taken count can be losslessly casted to 951 // the addrec's type. The count is always unsigned. 952 const SCEV *CastedMaxBECount = 953 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 954 const SCEV *RecastedMaxBECount = 955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 956 if (MaxBECount == RecastedMaxBECount) { 957 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 958 // Check whether Start+Step*MaxBECount has no unsigned overflow. 959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 960 const SCEV *Add = getAddExpr(Start, ZMul); 961 const SCEV *OperandExtendedAdd = 962 getAddExpr(getZeroExtendExpr(Start, WideTy), 963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 964 getZeroExtendExpr(Step, WideTy))); 965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 966 // Cache knowledge of AR NUW, which is propagated to this AddRec. 967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 968 // Return the expression with the addrec on the outside. 969 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 970 getZeroExtendExpr(Step, Ty), 971 L, AR->getNoWrapFlags()); 972 } 973 // Similar to above, only this time treat the step value as signed. 974 // This covers loops that count down. 975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 976 Add = getAddExpr(Start, SMul); 977 OperandExtendedAdd = 978 getAddExpr(getZeroExtendExpr(Start, WideTy), 979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 980 getSignExtendExpr(Step, WideTy))); 981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 982 // Cache knowledge of AR NW, which is propagated to this AddRec. 983 // Negative step causes unsigned wrap, but it still can't self-wrap. 984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 985 // Return the expression with the addrec on the outside. 986 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 987 getSignExtendExpr(Step, Ty), 988 L, AR->getNoWrapFlags()); 989 } 990 } 991 992 // If the backedge is guarded by a comparison with the pre-inc value 993 // the addrec is safe. Also, if the entry is guarded by a comparison 994 // with the start value and the backedge is guarded by a comparison 995 // with the post-inc value, the addrec is safe. 996 if (isKnownPositive(Step)) { 997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 998 getUnsignedRange(Step).getUnsignedMax()); 999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1002 AR->getPostIncExpr(*this), N))) { 1003 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1005 // Return the expression with the addrec on the outside. 1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1007 getZeroExtendExpr(Step, Ty), 1008 L, AR->getNoWrapFlags()); 1009 } 1010 } else if (isKnownNegative(Step)) { 1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1012 getSignedRange(Step).getSignedMin()); 1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1016 AR->getPostIncExpr(*this), N))) { 1017 // Cache knowledge of AR NW, which is propagated to this AddRec. 1018 // Negative step causes unsigned wrap, but it still can't self-wrap. 1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1020 // Return the expression with the addrec on the outside. 1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1022 getSignExtendExpr(Step, Ty), 1023 L, AR->getNoWrapFlags()); 1024 } 1025 } 1026 } 1027 } 1028 1029 // The cast wasn't folded; create an explicit cast node. 1030 // Recompute the insert position, as it may have been invalidated. 1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1033 Op, Ty); 1034 UniqueSCEVs.InsertNode(S, IP); 1035 return S; 1036} 1037 1038// Get the limit of a recurrence such that incrementing by Step cannot cause 1039// signed overflow as long as the value of the recurrence within the loop does 1040// not exceed this limit before incrementing. 1041static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1042 ICmpInst::Predicate *Pred, 1043 ScalarEvolution *SE) { 1044 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1045 if (SE->isKnownPositive(Step)) { 1046 *Pred = ICmpInst::ICMP_SLT; 1047 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1048 SE->getSignedRange(Step).getSignedMax()); 1049 } 1050 if (SE->isKnownNegative(Step)) { 1051 *Pred = ICmpInst::ICMP_SGT; 1052 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1053 SE->getSignedRange(Step).getSignedMin()); 1054 } 1055 return 0; 1056} 1057 1058// The recurrence AR has been shown to have no signed wrap. Typically, if we can 1059// prove NSW for AR, then we can just as easily prove NSW for its preincrement 1060// or postincrement sibling. This allows normalizing a sign extended AddRec as 1061// such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a 1062// result, the expression "Step + sext(PreIncAR)" is congruent with 1063// "sext(PostIncAR)" 1064static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR, 1065 Type *Ty, 1066 ScalarEvolution *SE) { 1067 const Loop *L = AR->getLoop(); 1068 const SCEV *Start = AR->getStart(); 1069 const SCEV *Step = AR->getStepRecurrence(*SE); 1070 1071 // Check for a simple looking step prior to loop entry. 1072 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1073 if (!SA || SA->getNumOperands() != 2 || SA->getOperand(0) != Step) 1074 return 0; 1075 1076 // This is a postinc AR. Check for overflow on the preinc recurrence using the 1077 // same three conditions that getSignExtendedExpr checks. 1078 1079 // 1. NSW flags on the step increment. 1080 const SCEV *PreStart = SA->getOperand(1); 1081 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1082 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1083 1084 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW)) 1085 return PreStart; 1086 1087 // 2. Direct overflow check on the step operation's expression. 1088 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1089 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1090 const SCEV *OperandExtendedStart = 1091 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy), 1092 SE->getSignExtendExpr(Step, WideTy)); 1093 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) { 1094 // Cache knowledge of PreAR NSW. 1095 if (PreAR) 1096 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW); 1097 // FIXME: this optimization needs a unit test 1098 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n"); 1099 return PreStart; 1100 } 1101 1102 // 3. Loop precondition. 1103 ICmpInst::Predicate Pred; 1104 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE); 1105 1106 if (OverflowLimit && 1107 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1108 return PreStart; 1109 } 1110 return 0; 1111} 1112 1113// Get the normalized sign-extended expression for this AddRec's Start. 1114static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR, 1115 Type *Ty, 1116 ScalarEvolution *SE) { 1117 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE); 1118 if (!PreStart) 1119 return SE->getSignExtendExpr(AR->getStart(), Ty); 1120 1121 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty), 1122 SE->getSignExtendExpr(PreStart, Ty)); 1123} 1124 1125const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1126 Type *Ty) { 1127 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1128 "This is not an extending conversion!"); 1129 assert(isSCEVable(Ty) && 1130 "This is not a conversion to a SCEVable type!"); 1131 Ty = getEffectiveSCEVType(Ty); 1132 1133 // Fold if the operand is constant. 1134 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1135 return getConstant( 1136 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1137 getEffectiveSCEVType(Ty)))); 1138 1139 // sext(sext(x)) --> sext(x) 1140 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1141 return getSignExtendExpr(SS->getOperand(), Ty); 1142 1143 // sext(zext(x)) --> zext(x) 1144 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1145 return getZeroExtendExpr(SZ->getOperand(), Ty); 1146 1147 // Before doing any expensive analysis, check to see if we've already 1148 // computed a SCEV for this Op and Ty. 1149 FoldingSetNodeID ID; 1150 ID.AddInteger(scSignExtend); 1151 ID.AddPointer(Op); 1152 ID.AddPointer(Ty); 1153 void *IP = 0; 1154 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1155 1156 // If the input value is provably positive, build a zext instead. 1157 if (isKnownNonNegative(Op)) 1158 return getZeroExtendExpr(Op, Ty); 1159 1160 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1161 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1162 // It's possible the bits taken off by the truncate were all sign bits. If 1163 // so, we should be able to simplify this further. 1164 const SCEV *X = ST->getOperand(); 1165 ConstantRange CR = getSignedRange(X); 1166 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1167 unsigned NewBits = getTypeSizeInBits(Ty); 1168 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1169 CR.sextOrTrunc(NewBits))) 1170 return getTruncateOrSignExtend(X, Ty); 1171 } 1172 1173 // If the input value is a chrec scev, and we can prove that the value 1174 // did not overflow the old, smaller, value, we can sign extend all of the 1175 // operands (often constants). This allows analysis of something like 1176 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1177 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1178 if (AR->isAffine()) { 1179 const SCEV *Start = AR->getStart(); 1180 const SCEV *Step = AR->getStepRecurrence(*this); 1181 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1182 const Loop *L = AR->getLoop(); 1183 1184 // If we have special knowledge that this addrec won't overflow, 1185 // we don't need to do any further analysis. 1186 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1187 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1188 getSignExtendExpr(Step, Ty), 1189 L, SCEV::FlagNSW); 1190 1191 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1192 // Note that this serves two purposes: It filters out loops that are 1193 // simply not analyzable, and it covers the case where this code is 1194 // being called from within backedge-taken count analysis, such that 1195 // attempting to ask for the backedge-taken count would likely result 1196 // in infinite recursion. In the later case, the analysis code will 1197 // cope with a conservative value, and it will take care to purge 1198 // that value once it has finished. 1199 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1200 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1201 // Manually compute the final value for AR, checking for 1202 // overflow. 1203 1204 // Check whether the backedge-taken count can be losslessly casted to 1205 // the addrec's type. The count is always unsigned. 1206 const SCEV *CastedMaxBECount = 1207 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1208 const SCEV *RecastedMaxBECount = 1209 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1210 if (MaxBECount == RecastedMaxBECount) { 1211 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1212 // Check whether Start+Step*MaxBECount has no signed overflow. 1213 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1214 const SCEV *Add = getAddExpr(Start, SMul); 1215 const SCEV *OperandExtendedAdd = 1216 getAddExpr(getSignExtendExpr(Start, WideTy), 1217 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1218 getSignExtendExpr(Step, WideTy))); 1219 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1220 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1221 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1222 // Return the expression with the addrec on the outside. 1223 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1224 getSignExtendExpr(Step, Ty), 1225 L, AR->getNoWrapFlags()); 1226 } 1227 // Similar to above, only this time treat the step value as unsigned. 1228 // This covers loops that count up with an unsigned step. 1229 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1230 Add = getAddExpr(Start, UMul); 1231 OperandExtendedAdd = 1232 getAddExpr(getSignExtendExpr(Start, WideTy), 1233 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1234 getZeroExtendExpr(Step, WideTy))); 1235 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1236 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1237 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1238 // Return the expression with the addrec on the outside. 1239 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1240 getZeroExtendExpr(Step, Ty), 1241 L, AR->getNoWrapFlags()); 1242 } 1243 } 1244 1245 // If the backedge is guarded by a comparison with the pre-inc value 1246 // the addrec is safe. Also, if the entry is guarded by a comparison 1247 // with the start value and the backedge is guarded by a comparison 1248 // with the post-inc value, the addrec is safe. 1249 ICmpInst::Predicate Pred; 1250 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this); 1251 if (OverflowLimit && 1252 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1253 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1254 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1255 OverflowLimit)))) { 1256 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1259 getSignExtendExpr(Step, Ty), 1260 L, AR->getNoWrapFlags()); 1261 } 1262 } 1263 } 1264 1265 // The cast wasn't folded; create an explicit cast node. 1266 // Recompute the insert position, as it may have been invalidated. 1267 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1268 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1269 Op, Ty); 1270 UniqueSCEVs.InsertNode(S, IP); 1271 return S; 1272} 1273 1274/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1275/// unspecified bits out to the given type. 1276/// 1277const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1278 Type *Ty) { 1279 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1280 "This is not an extending conversion!"); 1281 assert(isSCEVable(Ty) && 1282 "This is not a conversion to a SCEVable type!"); 1283 Ty = getEffectiveSCEVType(Ty); 1284 1285 // Sign-extend negative constants. 1286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1287 if (SC->getValue()->getValue().isNegative()) 1288 return getSignExtendExpr(Op, Ty); 1289 1290 // Peel off a truncate cast. 1291 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1292 const SCEV *NewOp = T->getOperand(); 1293 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1294 return getAnyExtendExpr(NewOp, Ty); 1295 return getTruncateOrNoop(NewOp, Ty); 1296 } 1297 1298 // Next try a zext cast. If the cast is folded, use it. 1299 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1300 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1301 return ZExt; 1302 1303 // Next try a sext cast. If the cast is folded, use it. 1304 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1305 if (!isa<SCEVSignExtendExpr>(SExt)) 1306 return SExt; 1307 1308 // Force the cast to be folded into the operands of an addrec. 1309 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1310 SmallVector<const SCEV *, 4> Ops; 1311 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1312 I != E; ++I) 1313 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1314 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1315 } 1316 1317 // As a special case, fold anyext(undef) to undef. We don't want to 1318 // know too much about SCEVUnknowns, but this special case is handy 1319 // and harmless. 1320 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1321 if (isa<UndefValue>(U->getValue())) 1322 return getSCEV(UndefValue::get(Ty)); 1323 1324 // If the expression is obviously signed, use the sext cast value. 1325 if (isa<SCEVSMaxExpr>(Op)) 1326 return SExt; 1327 1328 // Absent any other information, use the zext cast value. 1329 return ZExt; 1330} 1331 1332/// CollectAddOperandsWithScales - Process the given Ops list, which is 1333/// a list of operands to be added under the given scale, update the given 1334/// map. This is a helper function for getAddRecExpr. As an example of 1335/// what it does, given a sequence of operands that would form an add 1336/// expression like this: 1337/// 1338/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1339/// 1340/// where A and B are constants, update the map with these values: 1341/// 1342/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1343/// 1344/// and add 13 + A*B*29 to AccumulatedConstant. 1345/// This will allow getAddRecExpr to produce this: 1346/// 1347/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1348/// 1349/// This form often exposes folding opportunities that are hidden in 1350/// the original operand list. 1351/// 1352/// Return true iff it appears that any interesting folding opportunities 1353/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1354/// the common case where no interesting opportunities are present, and 1355/// is also used as a check to avoid infinite recursion. 1356/// 1357static bool 1358CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1359 SmallVector<const SCEV *, 8> &NewOps, 1360 APInt &AccumulatedConstant, 1361 const SCEV *const *Ops, size_t NumOperands, 1362 const APInt &Scale, 1363 ScalarEvolution &SE) { 1364 bool Interesting = false; 1365 1366 // Iterate over the add operands. They are sorted, with constants first. 1367 unsigned i = 0; 1368 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1369 ++i; 1370 // Pull a buried constant out to the outside. 1371 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1372 Interesting = true; 1373 AccumulatedConstant += Scale * C->getValue()->getValue(); 1374 } 1375 1376 // Next comes everything else. We're especially interested in multiplies 1377 // here, but they're in the middle, so just visit the rest with one loop. 1378 for (; i != NumOperands; ++i) { 1379 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1380 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1381 APInt NewScale = 1382 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1383 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1384 // A multiplication of a constant with another add; recurse. 1385 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1386 Interesting |= 1387 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1388 Add->op_begin(), Add->getNumOperands(), 1389 NewScale, SE); 1390 } else { 1391 // A multiplication of a constant with some other value. Update 1392 // the map. 1393 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1394 const SCEV *Key = SE.getMulExpr(MulOps); 1395 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1396 M.insert(std::make_pair(Key, NewScale)); 1397 if (Pair.second) { 1398 NewOps.push_back(Pair.first->first); 1399 } else { 1400 Pair.first->second += NewScale; 1401 // The map already had an entry for this value, which may indicate 1402 // a folding opportunity. 1403 Interesting = true; 1404 } 1405 } 1406 } else { 1407 // An ordinary operand. Update the map. 1408 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1409 M.insert(std::make_pair(Ops[i], Scale)); 1410 if (Pair.second) { 1411 NewOps.push_back(Pair.first->first); 1412 } else { 1413 Pair.first->second += Scale; 1414 // The map already had an entry for this value, which may indicate 1415 // a folding opportunity. 1416 Interesting = true; 1417 } 1418 } 1419 } 1420 1421 return Interesting; 1422} 1423 1424namespace { 1425 struct APIntCompare { 1426 bool operator()(const APInt &LHS, const APInt &RHS) const { 1427 return LHS.ult(RHS); 1428 } 1429 }; 1430} 1431 1432/// getAddExpr - Get a canonical add expression, or something simpler if 1433/// possible. 1434const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1435 SCEV::NoWrapFlags Flags) { 1436 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1437 "only nuw or nsw allowed"); 1438 assert(!Ops.empty() && "Cannot get empty add!"); 1439 if (Ops.size() == 1) return Ops[0]; 1440#ifndef NDEBUG 1441 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1442 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1443 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1444 "SCEVAddExpr operand types don't match!"); 1445#endif 1446 1447 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1448 // And vice-versa. 1449 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1450 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1451 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1452 bool All = true; 1453 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1454 E = Ops.end(); I != E; ++I) 1455 if (!isKnownNonNegative(*I)) { 1456 All = false; 1457 break; 1458 } 1459 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1460 } 1461 1462 // Sort by complexity, this groups all similar expression types together. 1463 GroupByComplexity(Ops, LI); 1464 1465 // If there are any constants, fold them together. 1466 unsigned Idx = 0; 1467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1468 ++Idx; 1469 assert(Idx < Ops.size()); 1470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1471 // We found two constants, fold them together! 1472 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1473 RHSC->getValue()->getValue()); 1474 if (Ops.size() == 2) return Ops[0]; 1475 Ops.erase(Ops.begin()+1); // Erase the folded element 1476 LHSC = cast<SCEVConstant>(Ops[0]); 1477 } 1478 1479 // If we are left with a constant zero being added, strip it off. 1480 if (LHSC->getValue()->isZero()) { 1481 Ops.erase(Ops.begin()); 1482 --Idx; 1483 } 1484 1485 if (Ops.size() == 1) return Ops[0]; 1486 } 1487 1488 // Okay, check to see if the same value occurs in the operand list more than 1489 // once. If so, merge them together into an multiply expression. Since we 1490 // sorted the list, these values are required to be adjacent. 1491 Type *Ty = Ops[0]->getType(); 1492 bool FoundMatch = false; 1493 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1494 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1495 // Scan ahead to count how many equal operands there are. 1496 unsigned Count = 2; 1497 while (i+Count != e && Ops[i+Count] == Ops[i]) 1498 ++Count; 1499 // Merge the values into a multiply. 1500 const SCEV *Scale = getConstant(Ty, Count); 1501 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1502 if (Ops.size() == Count) 1503 return Mul; 1504 Ops[i] = Mul; 1505 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1506 --i; e -= Count - 1; 1507 FoundMatch = true; 1508 } 1509 if (FoundMatch) 1510 return getAddExpr(Ops, Flags); 1511 1512 // Check for truncates. If all the operands are truncated from the same 1513 // type, see if factoring out the truncate would permit the result to be 1514 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1515 // if the contents of the resulting outer trunc fold to something simple. 1516 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1517 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1518 Type *DstType = Trunc->getType(); 1519 Type *SrcType = Trunc->getOperand()->getType(); 1520 SmallVector<const SCEV *, 8> LargeOps; 1521 bool Ok = true; 1522 // Check all the operands to see if they can be represented in the 1523 // source type of the truncate. 1524 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1525 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1526 if (T->getOperand()->getType() != SrcType) { 1527 Ok = false; 1528 break; 1529 } 1530 LargeOps.push_back(T->getOperand()); 1531 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1532 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1533 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1534 SmallVector<const SCEV *, 8> LargeMulOps; 1535 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1536 if (const SCEVTruncateExpr *T = 1537 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1538 if (T->getOperand()->getType() != SrcType) { 1539 Ok = false; 1540 break; 1541 } 1542 LargeMulOps.push_back(T->getOperand()); 1543 } else if (const SCEVConstant *C = 1544 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1545 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1546 } else { 1547 Ok = false; 1548 break; 1549 } 1550 } 1551 if (Ok) 1552 LargeOps.push_back(getMulExpr(LargeMulOps)); 1553 } else { 1554 Ok = false; 1555 break; 1556 } 1557 } 1558 if (Ok) { 1559 // Evaluate the expression in the larger type. 1560 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1561 // If it folds to something simple, use it. Otherwise, don't. 1562 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1563 return getTruncateExpr(Fold, DstType); 1564 } 1565 } 1566 1567 // Skip past any other cast SCEVs. 1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1569 ++Idx; 1570 1571 // If there are add operands they would be next. 1572 if (Idx < Ops.size()) { 1573 bool DeletedAdd = false; 1574 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1575 // If we have an add, expand the add operands onto the end of the operands 1576 // list. 1577 Ops.erase(Ops.begin()+Idx); 1578 Ops.append(Add->op_begin(), Add->op_end()); 1579 DeletedAdd = true; 1580 } 1581 1582 // If we deleted at least one add, we added operands to the end of the list, 1583 // and they are not necessarily sorted. Recurse to resort and resimplify 1584 // any operands we just acquired. 1585 if (DeletedAdd) 1586 return getAddExpr(Ops); 1587 } 1588 1589 // Skip over the add expression until we get to a multiply. 1590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1591 ++Idx; 1592 1593 // Check to see if there are any folding opportunities present with 1594 // operands multiplied by constant values. 1595 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1596 uint64_t BitWidth = getTypeSizeInBits(Ty); 1597 DenseMap<const SCEV *, APInt> M; 1598 SmallVector<const SCEV *, 8> NewOps; 1599 APInt AccumulatedConstant(BitWidth, 0); 1600 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1601 Ops.data(), Ops.size(), 1602 APInt(BitWidth, 1), *this)) { 1603 // Some interesting folding opportunity is present, so its worthwhile to 1604 // re-generate the operands list. Group the operands by constant scale, 1605 // to avoid multiplying by the same constant scale multiple times. 1606 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1607 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1608 E = NewOps.end(); I != E; ++I) 1609 MulOpLists[M.find(*I)->second].push_back(*I); 1610 // Re-generate the operands list. 1611 Ops.clear(); 1612 if (AccumulatedConstant != 0) 1613 Ops.push_back(getConstant(AccumulatedConstant)); 1614 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1615 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1616 if (I->first != 0) 1617 Ops.push_back(getMulExpr(getConstant(I->first), 1618 getAddExpr(I->second))); 1619 if (Ops.empty()) 1620 return getConstant(Ty, 0); 1621 if (Ops.size() == 1) 1622 return Ops[0]; 1623 return getAddExpr(Ops); 1624 } 1625 } 1626 1627 // If we are adding something to a multiply expression, make sure the 1628 // something is not already an operand of the multiply. If so, merge it into 1629 // the multiply. 1630 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1631 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1632 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1633 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1634 if (isa<SCEVConstant>(MulOpSCEV)) 1635 continue; 1636 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1637 if (MulOpSCEV == Ops[AddOp]) { 1638 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1639 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1640 if (Mul->getNumOperands() != 2) { 1641 // If the multiply has more than two operands, we must get the 1642 // Y*Z term. 1643 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1644 Mul->op_begin()+MulOp); 1645 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1646 InnerMul = getMulExpr(MulOps); 1647 } 1648 const SCEV *One = getConstant(Ty, 1); 1649 const SCEV *AddOne = getAddExpr(One, InnerMul); 1650 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1651 if (Ops.size() == 2) return OuterMul; 1652 if (AddOp < Idx) { 1653 Ops.erase(Ops.begin()+AddOp); 1654 Ops.erase(Ops.begin()+Idx-1); 1655 } else { 1656 Ops.erase(Ops.begin()+Idx); 1657 Ops.erase(Ops.begin()+AddOp-1); 1658 } 1659 Ops.push_back(OuterMul); 1660 return getAddExpr(Ops); 1661 } 1662 1663 // Check this multiply against other multiplies being added together. 1664 for (unsigned OtherMulIdx = Idx+1; 1665 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1666 ++OtherMulIdx) { 1667 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1668 // If MulOp occurs in OtherMul, we can fold the two multiplies 1669 // together. 1670 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1671 OMulOp != e; ++OMulOp) 1672 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1673 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1674 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1675 if (Mul->getNumOperands() != 2) { 1676 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1677 Mul->op_begin()+MulOp); 1678 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1679 InnerMul1 = getMulExpr(MulOps); 1680 } 1681 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1682 if (OtherMul->getNumOperands() != 2) { 1683 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1684 OtherMul->op_begin()+OMulOp); 1685 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1686 InnerMul2 = getMulExpr(MulOps); 1687 } 1688 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1689 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1690 if (Ops.size() == 2) return OuterMul; 1691 Ops.erase(Ops.begin()+Idx); 1692 Ops.erase(Ops.begin()+OtherMulIdx-1); 1693 Ops.push_back(OuterMul); 1694 return getAddExpr(Ops); 1695 } 1696 } 1697 } 1698 } 1699 1700 // If there are any add recurrences in the operands list, see if any other 1701 // added values are loop invariant. If so, we can fold them into the 1702 // recurrence. 1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1704 ++Idx; 1705 1706 // Scan over all recurrences, trying to fold loop invariants into them. 1707 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1708 // Scan all of the other operands to this add and add them to the vector if 1709 // they are loop invariant w.r.t. the recurrence. 1710 SmallVector<const SCEV *, 8> LIOps; 1711 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1712 const Loop *AddRecLoop = AddRec->getLoop(); 1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1714 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1715 LIOps.push_back(Ops[i]); 1716 Ops.erase(Ops.begin()+i); 1717 --i; --e; 1718 } 1719 1720 // If we found some loop invariants, fold them into the recurrence. 1721 if (!LIOps.empty()) { 1722 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1723 LIOps.push_back(AddRec->getStart()); 1724 1725 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1726 AddRec->op_end()); 1727 AddRecOps[0] = getAddExpr(LIOps); 1728 1729 // Build the new addrec. Propagate the NUW and NSW flags if both the 1730 // outer add and the inner addrec are guaranteed to have no overflow. 1731 // Always propagate NW. 1732 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1733 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1734 1735 // If all of the other operands were loop invariant, we are done. 1736 if (Ops.size() == 1) return NewRec; 1737 1738 // Otherwise, add the folded AddRec by the non-liv parts. 1739 for (unsigned i = 0;; ++i) 1740 if (Ops[i] == AddRec) { 1741 Ops[i] = NewRec; 1742 break; 1743 } 1744 return getAddExpr(Ops); 1745 } 1746 1747 // Okay, if there weren't any loop invariants to be folded, check to see if 1748 // there are multiple AddRec's with the same loop induction variable being 1749 // added together. If so, we can fold them. 1750 for (unsigned OtherIdx = Idx+1; 1751 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1752 ++OtherIdx) 1753 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1754 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1755 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1756 AddRec->op_end()); 1757 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1758 ++OtherIdx) 1759 if (const SCEVAddRecExpr *OtherAddRec = 1760 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1761 if (OtherAddRec->getLoop() == AddRecLoop) { 1762 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1763 i != e; ++i) { 1764 if (i >= AddRecOps.size()) { 1765 AddRecOps.append(OtherAddRec->op_begin()+i, 1766 OtherAddRec->op_end()); 1767 break; 1768 } 1769 AddRecOps[i] = getAddExpr(AddRecOps[i], 1770 OtherAddRec->getOperand(i)); 1771 } 1772 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1773 } 1774 // Step size has changed, so we cannot guarantee no self-wraparound. 1775 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1776 return getAddExpr(Ops); 1777 } 1778 1779 // Otherwise couldn't fold anything into this recurrence. Move onto the 1780 // next one. 1781 } 1782 1783 // Okay, it looks like we really DO need an add expr. Check to see if we 1784 // already have one, otherwise create a new one. 1785 FoldingSetNodeID ID; 1786 ID.AddInteger(scAddExpr); 1787 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1788 ID.AddPointer(Ops[i]); 1789 void *IP = 0; 1790 SCEVAddExpr *S = 1791 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1792 if (!S) { 1793 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1794 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1795 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1796 O, Ops.size()); 1797 UniqueSCEVs.InsertNode(S, IP); 1798 } 1799 S->setNoWrapFlags(Flags); 1800 return S; 1801} 1802 1803/// getMulExpr - Get a canonical multiply expression, or something simpler if 1804/// possible. 1805const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1806 SCEV::NoWrapFlags Flags) { 1807 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1808 "only nuw or nsw allowed"); 1809 assert(!Ops.empty() && "Cannot get empty mul!"); 1810 if (Ops.size() == 1) return Ops[0]; 1811#ifndef NDEBUG 1812 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1813 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1814 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1815 "SCEVMulExpr operand types don't match!"); 1816#endif 1817 1818 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1819 // And vice-versa. 1820 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1821 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1822 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1823 bool All = true; 1824 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1825 E = Ops.end(); I != E; ++I) 1826 if (!isKnownNonNegative(*I)) { 1827 All = false; 1828 break; 1829 } 1830 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1831 } 1832 1833 // Sort by complexity, this groups all similar expression types together. 1834 GroupByComplexity(Ops, LI); 1835 1836 // If there are any constants, fold them together. 1837 unsigned Idx = 0; 1838 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1839 1840 // C1*(C2+V) -> C1*C2 + C1*V 1841 if (Ops.size() == 2) 1842 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1843 if (Add->getNumOperands() == 2 && 1844 isa<SCEVConstant>(Add->getOperand(0))) 1845 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1846 getMulExpr(LHSC, Add->getOperand(1))); 1847 1848 ++Idx; 1849 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1850 // We found two constants, fold them together! 1851 ConstantInt *Fold = ConstantInt::get(getContext(), 1852 LHSC->getValue()->getValue() * 1853 RHSC->getValue()->getValue()); 1854 Ops[0] = getConstant(Fold); 1855 Ops.erase(Ops.begin()+1); // Erase the folded element 1856 if (Ops.size() == 1) return Ops[0]; 1857 LHSC = cast<SCEVConstant>(Ops[0]); 1858 } 1859 1860 // If we are left with a constant one being multiplied, strip it off. 1861 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1862 Ops.erase(Ops.begin()); 1863 --Idx; 1864 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1865 // If we have a multiply of zero, it will always be zero. 1866 return Ops[0]; 1867 } else if (Ops[0]->isAllOnesValue()) { 1868 // If we have a mul by -1 of an add, try distributing the -1 among the 1869 // add operands. 1870 if (Ops.size() == 2) { 1871 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1872 SmallVector<const SCEV *, 4> NewOps; 1873 bool AnyFolded = false; 1874 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1875 E = Add->op_end(); I != E; ++I) { 1876 const SCEV *Mul = getMulExpr(Ops[0], *I); 1877 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1878 NewOps.push_back(Mul); 1879 } 1880 if (AnyFolded) 1881 return getAddExpr(NewOps); 1882 } 1883 else if (const SCEVAddRecExpr * 1884 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1885 // Negation preserves a recurrence's no self-wrap property. 1886 SmallVector<const SCEV *, 4> Operands; 1887 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1888 E = AddRec->op_end(); I != E; ++I) { 1889 Operands.push_back(getMulExpr(Ops[0], *I)); 1890 } 1891 return getAddRecExpr(Operands, AddRec->getLoop(), 1892 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1893 } 1894 } 1895 } 1896 1897 if (Ops.size() == 1) 1898 return Ops[0]; 1899 } 1900 1901 // Skip over the add expression until we get to a multiply. 1902 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1903 ++Idx; 1904 1905 // If there are mul operands inline them all into this expression. 1906 if (Idx < Ops.size()) { 1907 bool DeletedMul = false; 1908 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1909 // If we have an mul, expand the mul operands onto the end of the operands 1910 // list. 1911 Ops.erase(Ops.begin()+Idx); 1912 Ops.append(Mul->op_begin(), Mul->op_end()); 1913 DeletedMul = true; 1914 } 1915 1916 // If we deleted at least one mul, we added operands to the end of the list, 1917 // and they are not necessarily sorted. Recurse to resort and resimplify 1918 // any operands we just acquired. 1919 if (DeletedMul) 1920 return getMulExpr(Ops); 1921 } 1922 1923 // If there are any add recurrences in the operands list, see if any other 1924 // added values are loop invariant. If so, we can fold them into the 1925 // recurrence. 1926 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1927 ++Idx; 1928 1929 // Scan over all recurrences, trying to fold loop invariants into them. 1930 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1931 // Scan all of the other operands to this mul and add them to the vector if 1932 // they are loop invariant w.r.t. the recurrence. 1933 SmallVector<const SCEV *, 8> LIOps; 1934 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1935 const Loop *AddRecLoop = AddRec->getLoop(); 1936 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1937 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1938 LIOps.push_back(Ops[i]); 1939 Ops.erase(Ops.begin()+i); 1940 --i; --e; 1941 } 1942 1943 // If we found some loop invariants, fold them into the recurrence. 1944 if (!LIOps.empty()) { 1945 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1946 SmallVector<const SCEV *, 4> NewOps; 1947 NewOps.reserve(AddRec->getNumOperands()); 1948 const SCEV *Scale = getMulExpr(LIOps); 1949 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1950 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1951 1952 // Build the new addrec. Propagate the NUW and NSW flags if both the 1953 // outer mul and the inner addrec are guaranteed to have no overflow. 1954 // 1955 // No self-wrap cannot be guaranteed after changing the step size, but 1956 // will be inferred if either NUW or NSW is true. 1957 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 1958 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 1959 1960 // If all of the other operands were loop invariant, we are done. 1961 if (Ops.size() == 1) return NewRec; 1962 1963 // Otherwise, multiply the folded AddRec by the non-liv parts. 1964 for (unsigned i = 0;; ++i) 1965 if (Ops[i] == AddRec) { 1966 Ops[i] = NewRec; 1967 break; 1968 } 1969 return getMulExpr(Ops); 1970 } 1971 1972 // Okay, if there weren't any loop invariants to be folded, check to see if 1973 // there are multiple AddRec's with the same loop induction variable being 1974 // multiplied together. If so, we can fold them. 1975 for (unsigned OtherIdx = Idx+1; 1976 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1977 ++OtherIdx) 1978 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1979 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1980 // {A*C,+,F*D + G*B + B*D}<L> 1981 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1982 ++OtherIdx) 1983 if (const SCEVAddRecExpr *OtherAddRec = 1984 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1985 if (OtherAddRec->getLoop() == AddRecLoop) { 1986 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1987 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1988 const SCEV *B = F->getStepRecurrence(*this); 1989 const SCEV *D = G->getStepRecurrence(*this); 1990 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1991 getMulExpr(G, B), 1992 getMulExpr(B, D)); 1993 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1994 F->getLoop(), 1995 SCEV::FlagAnyWrap); 1996 if (Ops.size() == 2) return NewAddRec; 1997 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1998 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1999 } 2000 return getMulExpr(Ops); 2001 } 2002 2003 // Otherwise couldn't fold anything into this recurrence. Move onto the 2004 // next one. 2005 } 2006 2007 // Okay, it looks like we really DO need an mul expr. Check to see if we 2008 // already have one, otherwise create a new one. 2009 FoldingSetNodeID ID; 2010 ID.AddInteger(scMulExpr); 2011 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2012 ID.AddPointer(Ops[i]); 2013 void *IP = 0; 2014 SCEVMulExpr *S = 2015 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2016 if (!S) { 2017 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2018 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2019 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2020 O, Ops.size()); 2021 UniqueSCEVs.InsertNode(S, IP); 2022 } 2023 S->setNoWrapFlags(Flags); 2024 return S; 2025} 2026 2027/// getUDivExpr - Get a canonical unsigned division expression, or something 2028/// simpler if possible. 2029const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2030 const SCEV *RHS) { 2031 assert(getEffectiveSCEVType(LHS->getType()) == 2032 getEffectiveSCEVType(RHS->getType()) && 2033 "SCEVUDivExpr operand types don't match!"); 2034 2035 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2036 if (RHSC->getValue()->equalsInt(1)) 2037 return LHS; // X udiv 1 --> x 2038 // If the denominator is zero, the result of the udiv is undefined. Don't 2039 // try to analyze it, because the resolution chosen here may differ from 2040 // the resolution chosen in other parts of the compiler. 2041 if (!RHSC->getValue()->isZero()) { 2042 // Determine if the division can be folded into the operands of 2043 // its operands. 2044 // TODO: Generalize this to non-constants by using known-bits information. 2045 Type *Ty = LHS->getType(); 2046 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2047 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2048 // For non-power-of-two values, effectively round the value up to the 2049 // nearest power of two. 2050 if (!RHSC->getValue()->getValue().isPowerOf2()) 2051 ++MaxShiftAmt; 2052 IntegerType *ExtTy = 2053 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2054 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2055 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2056 if (const SCEVConstant *Step = 2057 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 2058 if (!Step->getValue()->getValue() 2059 .urem(RHSC->getValue()->getValue()) && 2060 getZeroExtendExpr(AR, ExtTy) == 2061 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2062 getZeroExtendExpr(Step, ExtTy), 2063 AR->getLoop(), SCEV::FlagAnyWrap)) { 2064 SmallVector<const SCEV *, 4> Operands; 2065 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2066 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2067 return getAddRecExpr(Operands, AR->getLoop(), 2068 SCEV::FlagNW); 2069 } 2070 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2071 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2072 SmallVector<const SCEV *, 4> Operands; 2073 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2074 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2075 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2076 // Find an operand that's safely divisible. 2077 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2078 const SCEV *Op = M->getOperand(i); 2079 const SCEV *Div = getUDivExpr(Op, RHSC); 2080 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2081 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2082 M->op_end()); 2083 Operands[i] = Div; 2084 return getMulExpr(Operands); 2085 } 2086 } 2087 } 2088 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2089 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2090 SmallVector<const SCEV *, 4> Operands; 2091 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2092 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2093 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2094 Operands.clear(); 2095 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2096 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2097 if (isa<SCEVUDivExpr>(Op) || 2098 getMulExpr(Op, RHS) != A->getOperand(i)) 2099 break; 2100 Operands.push_back(Op); 2101 } 2102 if (Operands.size() == A->getNumOperands()) 2103 return getAddExpr(Operands); 2104 } 2105 } 2106 2107 // Fold if both operands are constant. 2108 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2109 Constant *LHSCV = LHSC->getValue(); 2110 Constant *RHSCV = RHSC->getValue(); 2111 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2112 RHSCV))); 2113 } 2114 } 2115 } 2116 2117 FoldingSetNodeID ID; 2118 ID.AddInteger(scUDivExpr); 2119 ID.AddPointer(LHS); 2120 ID.AddPointer(RHS); 2121 void *IP = 0; 2122 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2123 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2124 LHS, RHS); 2125 UniqueSCEVs.InsertNode(S, IP); 2126 return S; 2127} 2128 2129 2130/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2131/// Simplify the expression as much as possible. 2132const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2133 const Loop *L, 2134 SCEV::NoWrapFlags Flags) { 2135 SmallVector<const SCEV *, 4> Operands; 2136 Operands.push_back(Start); 2137 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2138 if (StepChrec->getLoop() == L) { 2139 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2140 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2141 } 2142 2143 Operands.push_back(Step); 2144 return getAddRecExpr(Operands, L, Flags); 2145} 2146 2147/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2148/// Simplify the expression as much as possible. 2149const SCEV * 2150ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2151 const Loop *L, SCEV::NoWrapFlags Flags) { 2152 if (Operands.size() == 1) return Operands[0]; 2153#ifndef NDEBUG 2154 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2155 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2156 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2157 "SCEVAddRecExpr operand types don't match!"); 2158 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2159 assert(isLoopInvariant(Operands[i], L) && 2160 "SCEVAddRecExpr operand is not loop-invariant!"); 2161#endif 2162 2163 if (Operands.back()->isZero()) { 2164 Operands.pop_back(); 2165 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2166 } 2167 2168 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2169 // use that information to infer NUW and NSW flags. However, computing a 2170 // BE count requires calling getAddRecExpr, so we may not yet have a 2171 // meaningful BE count at this point (and if we don't, we'd be stuck 2172 // with a SCEVCouldNotCompute as the cached BE count). 2173 2174 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2175 // And vice-versa. 2176 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2177 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2178 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2179 bool All = true; 2180 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2181 E = Operands.end(); I != E; ++I) 2182 if (!isKnownNonNegative(*I)) { 2183 All = false; 2184 break; 2185 } 2186 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2187 } 2188 2189 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2190 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2191 const Loop *NestedLoop = NestedAR->getLoop(); 2192 if (L->contains(NestedLoop) ? 2193 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2194 (!NestedLoop->contains(L) && 2195 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2196 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2197 NestedAR->op_end()); 2198 Operands[0] = NestedAR->getStart(); 2199 // AddRecs require their operands be loop-invariant with respect to their 2200 // loops. Don't perform this transformation if it would break this 2201 // requirement. 2202 bool AllInvariant = true; 2203 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2204 if (!isLoopInvariant(Operands[i], L)) { 2205 AllInvariant = false; 2206 break; 2207 } 2208 if (AllInvariant) { 2209 // Create a recurrence for the outer loop with the same step size. 2210 // 2211 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2212 // inner recurrence has the same property. 2213 SCEV::NoWrapFlags OuterFlags = 2214 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2215 2216 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2217 AllInvariant = true; 2218 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2219 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2220 AllInvariant = false; 2221 break; 2222 } 2223 if (AllInvariant) { 2224 // Ok, both add recurrences are valid after the transformation. 2225 // 2226 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2227 // the outer recurrence has the same property. 2228 SCEV::NoWrapFlags InnerFlags = 2229 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2230 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2231 } 2232 } 2233 // Reset Operands to its original state. 2234 Operands[0] = NestedAR; 2235 } 2236 } 2237 2238 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2239 // already have one, otherwise create a new one. 2240 FoldingSetNodeID ID; 2241 ID.AddInteger(scAddRecExpr); 2242 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2243 ID.AddPointer(Operands[i]); 2244 ID.AddPointer(L); 2245 void *IP = 0; 2246 SCEVAddRecExpr *S = 2247 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2248 if (!S) { 2249 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2250 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2251 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2252 O, Operands.size(), L); 2253 UniqueSCEVs.InsertNode(S, IP); 2254 } 2255 S->setNoWrapFlags(Flags); 2256 return S; 2257} 2258 2259const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2260 const SCEV *RHS) { 2261 SmallVector<const SCEV *, 2> Ops; 2262 Ops.push_back(LHS); 2263 Ops.push_back(RHS); 2264 return getSMaxExpr(Ops); 2265} 2266 2267const SCEV * 2268ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2269 assert(!Ops.empty() && "Cannot get empty smax!"); 2270 if (Ops.size() == 1) return Ops[0]; 2271#ifndef NDEBUG 2272 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2273 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2274 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2275 "SCEVSMaxExpr operand types don't match!"); 2276#endif 2277 2278 // Sort by complexity, this groups all similar expression types together. 2279 GroupByComplexity(Ops, LI); 2280 2281 // If there are any constants, fold them together. 2282 unsigned Idx = 0; 2283 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2284 ++Idx; 2285 assert(Idx < Ops.size()); 2286 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2287 // We found two constants, fold them together! 2288 ConstantInt *Fold = ConstantInt::get(getContext(), 2289 APIntOps::smax(LHSC->getValue()->getValue(), 2290 RHSC->getValue()->getValue())); 2291 Ops[0] = getConstant(Fold); 2292 Ops.erase(Ops.begin()+1); // Erase the folded element 2293 if (Ops.size() == 1) return Ops[0]; 2294 LHSC = cast<SCEVConstant>(Ops[0]); 2295 } 2296 2297 // If we are left with a constant minimum-int, strip it off. 2298 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2299 Ops.erase(Ops.begin()); 2300 --Idx; 2301 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2302 // If we have an smax with a constant maximum-int, it will always be 2303 // maximum-int. 2304 return Ops[0]; 2305 } 2306 2307 if (Ops.size() == 1) return Ops[0]; 2308 } 2309 2310 // Find the first SMax 2311 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2312 ++Idx; 2313 2314 // Check to see if one of the operands is an SMax. If so, expand its operands 2315 // onto our operand list, and recurse to simplify. 2316 if (Idx < Ops.size()) { 2317 bool DeletedSMax = false; 2318 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2319 Ops.erase(Ops.begin()+Idx); 2320 Ops.append(SMax->op_begin(), SMax->op_end()); 2321 DeletedSMax = true; 2322 } 2323 2324 if (DeletedSMax) 2325 return getSMaxExpr(Ops); 2326 } 2327 2328 // Okay, check to see if the same value occurs in the operand list twice. If 2329 // so, delete one. Since we sorted the list, these values are required to 2330 // be adjacent. 2331 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2332 // X smax Y smax Y --> X smax Y 2333 // X smax Y --> X, if X is always greater than Y 2334 if (Ops[i] == Ops[i+1] || 2335 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2336 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2337 --i; --e; 2338 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2339 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2340 --i; --e; 2341 } 2342 2343 if (Ops.size() == 1) return Ops[0]; 2344 2345 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2346 2347 // Okay, it looks like we really DO need an smax expr. Check to see if we 2348 // already have one, otherwise create a new one. 2349 FoldingSetNodeID ID; 2350 ID.AddInteger(scSMaxExpr); 2351 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2352 ID.AddPointer(Ops[i]); 2353 void *IP = 0; 2354 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2355 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2356 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2357 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2358 O, Ops.size()); 2359 UniqueSCEVs.InsertNode(S, IP); 2360 return S; 2361} 2362 2363const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2364 const SCEV *RHS) { 2365 SmallVector<const SCEV *, 2> Ops; 2366 Ops.push_back(LHS); 2367 Ops.push_back(RHS); 2368 return getUMaxExpr(Ops); 2369} 2370 2371const SCEV * 2372ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2373 assert(!Ops.empty() && "Cannot get empty umax!"); 2374 if (Ops.size() == 1) return Ops[0]; 2375#ifndef NDEBUG 2376 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2377 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2378 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2379 "SCEVUMaxExpr operand types don't match!"); 2380#endif 2381 2382 // Sort by complexity, this groups all similar expression types together. 2383 GroupByComplexity(Ops, LI); 2384 2385 // If there are any constants, fold them together. 2386 unsigned Idx = 0; 2387 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2388 ++Idx; 2389 assert(Idx < Ops.size()); 2390 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2391 // We found two constants, fold them together! 2392 ConstantInt *Fold = ConstantInt::get(getContext(), 2393 APIntOps::umax(LHSC->getValue()->getValue(), 2394 RHSC->getValue()->getValue())); 2395 Ops[0] = getConstant(Fold); 2396 Ops.erase(Ops.begin()+1); // Erase the folded element 2397 if (Ops.size() == 1) return Ops[0]; 2398 LHSC = cast<SCEVConstant>(Ops[0]); 2399 } 2400 2401 // If we are left with a constant minimum-int, strip it off. 2402 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2403 Ops.erase(Ops.begin()); 2404 --Idx; 2405 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2406 // If we have an umax with a constant maximum-int, it will always be 2407 // maximum-int. 2408 return Ops[0]; 2409 } 2410 2411 if (Ops.size() == 1) return Ops[0]; 2412 } 2413 2414 // Find the first UMax 2415 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2416 ++Idx; 2417 2418 // Check to see if one of the operands is a UMax. If so, expand its operands 2419 // onto our operand list, and recurse to simplify. 2420 if (Idx < Ops.size()) { 2421 bool DeletedUMax = false; 2422 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2423 Ops.erase(Ops.begin()+Idx); 2424 Ops.append(UMax->op_begin(), UMax->op_end()); 2425 DeletedUMax = true; 2426 } 2427 2428 if (DeletedUMax) 2429 return getUMaxExpr(Ops); 2430 } 2431 2432 // Okay, check to see if the same value occurs in the operand list twice. If 2433 // so, delete one. Since we sorted the list, these values are required to 2434 // be adjacent. 2435 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2436 // X umax Y umax Y --> X umax Y 2437 // X umax Y --> X, if X is always greater than Y 2438 if (Ops[i] == Ops[i+1] || 2439 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2440 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2441 --i; --e; 2442 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2443 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2444 --i; --e; 2445 } 2446 2447 if (Ops.size() == 1) return Ops[0]; 2448 2449 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2450 2451 // Okay, it looks like we really DO need a umax expr. Check to see if we 2452 // already have one, otherwise create a new one. 2453 FoldingSetNodeID ID; 2454 ID.AddInteger(scUMaxExpr); 2455 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2456 ID.AddPointer(Ops[i]); 2457 void *IP = 0; 2458 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2459 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2460 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2461 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2462 O, Ops.size()); 2463 UniqueSCEVs.InsertNode(S, IP); 2464 return S; 2465} 2466 2467const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2468 const SCEV *RHS) { 2469 // ~smax(~x, ~y) == smin(x, y). 2470 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2471} 2472 2473const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2474 const SCEV *RHS) { 2475 // ~umax(~x, ~y) == umin(x, y) 2476 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2477} 2478 2479const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) { 2480 // If we have TargetData, we can bypass creating a target-independent 2481 // constant expression and then folding it back into a ConstantInt. 2482 // This is just a compile-time optimization. 2483 if (TD) 2484 return getConstant(TD->getIntPtrType(getContext()), 2485 TD->getTypeAllocSize(AllocTy)); 2486 2487 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2488 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2489 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2490 C = Folded; 2491 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2492 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2493} 2494 2495const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) { 2496 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2497 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2498 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2499 C = Folded; 2500 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2501 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2502} 2503 2504const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, 2505 unsigned FieldNo) { 2506 // If we have TargetData, we can bypass creating a target-independent 2507 // constant expression and then folding it back into a ConstantInt. 2508 // This is just a compile-time optimization. 2509 if (TD) 2510 return getConstant(TD->getIntPtrType(getContext()), 2511 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2512 2513 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2514 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2515 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2516 C = Folded; 2517 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2518 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2519} 2520 2521const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy, 2522 Constant *FieldNo) { 2523 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2524 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2525 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2526 C = Folded; 2527 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2528 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2529} 2530 2531const SCEV *ScalarEvolution::getUnknown(Value *V) { 2532 // Don't attempt to do anything other than create a SCEVUnknown object 2533 // here. createSCEV only calls getUnknown after checking for all other 2534 // interesting possibilities, and any other code that calls getUnknown 2535 // is doing so in order to hide a value from SCEV canonicalization. 2536 2537 FoldingSetNodeID ID; 2538 ID.AddInteger(scUnknown); 2539 ID.AddPointer(V); 2540 void *IP = 0; 2541 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2542 assert(cast<SCEVUnknown>(S)->getValue() == V && 2543 "Stale SCEVUnknown in uniquing map!"); 2544 return S; 2545 } 2546 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2547 FirstUnknown); 2548 FirstUnknown = cast<SCEVUnknown>(S); 2549 UniqueSCEVs.InsertNode(S, IP); 2550 return S; 2551} 2552 2553//===----------------------------------------------------------------------===// 2554// Basic SCEV Analysis and PHI Idiom Recognition Code 2555// 2556 2557/// isSCEVable - Test if values of the given type are analyzable within 2558/// the SCEV framework. This primarily includes integer types, and it 2559/// can optionally include pointer types if the ScalarEvolution class 2560/// has access to target-specific information. 2561bool ScalarEvolution::isSCEVable(Type *Ty) const { 2562 // Integers and pointers are always SCEVable. 2563 return Ty->isIntegerTy() || Ty->isPointerTy(); 2564} 2565 2566/// getTypeSizeInBits - Return the size in bits of the specified type, 2567/// for which isSCEVable must return true. 2568uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 2569 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2570 2571 // If we have a TargetData, use it! 2572 if (TD) 2573 return TD->getTypeSizeInBits(Ty); 2574 2575 // Integer types have fixed sizes. 2576 if (Ty->isIntegerTy()) 2577 return Ty->getPrimitiveSizeInBits(); 2578 2579 // The only other support type is pointer. Without TargetData, conservatively 2580 // assume pointers are 64-bit. 2581 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2582 return 64; 2583} 2584 2585/// getEffectiveSCEVType - Return a type with the same bitwidth as 2586/// the given type and which represents how SCEV will treat the given 2587/// type, for which isSCEVable must return true. For pointer types, 2588/// this is the pointer-sized integer type. 2589Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 2590 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2591 2592 if (Ty->isIntegerTy()) 2593 return Ty; 2594 2595 // The only other support type is pointer. 2596 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2597 if (TD) return TD->getIntPtrType(getContext()); 2598 2599 // Without TargetData, conservatively assume pointers are 64-bit. 2600 return Type::getInt64Ty(getContext()); 2601} 2602 2603const SCEV *ScalarEvolution::getCouldNotCompute() { 2604 return &CouldNotCompute; 2605} 2606 2607/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2608/// expression and create a new one. 2609const SCEV *ScalarEvolution::getSCEV(Value *V) { 2610 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2611 2612 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2613 if (I != ValueExprMap.end()) return I->second; 2614 const SCEV *S = createSCEV(V); 2615 2616 // The process of creating a SCEV for V may have caused other SCEVs 2617 // to have been created, so it's necessary to insert the new entry 2618 // from scratch, rather than trying to remember the insert position 2619 // above. 2620 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2621 return S; 2622} 2623 2624/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2625/// 2626const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2627 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2628 return getConstant( 2629 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2630 2631 Type *Ty = V->getType(); 2632 Ty = getEffectiveSCEVType(Ty); 2633 return getMulExpr(V, 2634 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2635} 2636 2637/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2638const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2639 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2640 return getConstant( 2641 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2642 2643 Type *Ty = V->getType(); 2644 Ty = getEffectiveSCEVType(Ty); 2645 const SCEV *AllOnes = 2646 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2647 return getMinusSCEV(AllOnes, V); 2648} 2649 2650/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2651const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2652 SCEV::NoWrapFlags Flags) { 2653 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2654 2655 // Fast path: X - X --> 0. 2656 if (LHS == RHS) 2657 return getConstant(LHS->getType(), 0); 2658 2659 // X - Y --> X + -Y 2660 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2661} 2662 2663/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2664/// input value to the specified type. If the type must be extended, it is zero 2665/// extended. 2666const SCEV * 2667ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 2668 Type *SrcTy = V->getType(); 2669 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2670 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2671 "Cannot truncate or zero extend with non-integer arguments!"); 2672 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2673 return V; // No conversion 2674 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2675 return getTruncateExpr(V, Ty); 2676 return getZeroExtendExpr(V, Ty); 2677} 2678 2679/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2680/// input value to the specified type. If the type must be extended, it is sign 2681/// extended. 2682const SCEV * 2683ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2684 Type *Ty) { 2685 Type *SrcTy = V->getType(); 2686 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2687 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2688 "Cannot truncate or zero extend with non-integer arguments!"); 2689 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2690 return V; // No conversion 2691 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2692 return getTruncateExpr(V, Ty); 2693 return getSignExtendExpr(V, Ty); 2694} 2695 2696/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2697/// input value to the specified type. If the type must be extended, it is zero 2698/// extended. The conversion must not be narrowing. 2699const SCEV * 2700ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 2701 Type *SrcTy = V->getType(); 2702 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2703 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2704 "Cannot noop or zero extend with non-integer arguments!"); 2705 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2706 "getNoopOrZeroExtend cannot truncate!"); 2707 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2708 return V; // No conversion 2709 return getZeroExtendExpr(V, Ty); 2710} 2711 2712/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2713/// input value to the specified type. If the type must be extended, it is sign 2714/// extended. The conversion must not be narrowing. 2715const SCEV * 2716ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 2717 Type *SrcTy = V->getType(); 2718 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2719 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2720 "Cannot noop or sign extend with non-integer arguments!"); 2721 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2722 "getNoopOrSignExtend cannot truncate!"); 2723 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2724 return V; // No conversion 2725 return getSignExtendExpr(V, Ty); 2726} 2727 2728/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2729/// the input value to the specified type. If the type must be extended, 2730/// it is extended with unspecified bits. The conversion must not be 2731/// narrowing. 2732const SCEV * 2733ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 2734 Type *SrcTy = V->getType(); 2735 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2736 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2737 "Cannot noop or any extend with non-integer arguments!"); 2738 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2739 "getNoopOrAnyExtend cannot truncate!"); 2740 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2741 return V; // No conversion 2742 return getAnyExtendExpr(V, Ty); 2743} 2744 2745/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2746/// input value to the specified type. The conversion must not be widening. 2747const SCEV * 2748ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 2749 Type *SrcTy = V->getType(); 2750 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2751 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2752 "Cannot truncate or noop with non-integer arguments!"); 2753 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2754 "getTruncateOrNoop cannot extend!"); 2755 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2756 return V; // No conversion 2757 return getTruncateExpr(V, Ty); 2758} 2759 2760/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2761/// the types using zero-extension, and then perform a umax operation 2762/// with them. 2763const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2764 const SCEV *RHS) { 2765 const SCEV *PromotedLHS = LHS; 2766 const SCEV *PromotedRHS = RHS; 2767 2768 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2769 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2770 else 2771 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2772 2773 return getUMaxExpr(PromotedLHS, PromotedRHS); 2774} 2775 2776/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2777/// the types using zero-extension, and then perform a umin operation 2778/// with them. 2779const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2780 const SCEV *RHS) { 2781 const SCEV *PromotedLHS = LHS; 2782 const SCEV *PromotedRHS = RHS; 2783 2784 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2785 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2786 else 2787 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2788 2789 return getUMinExpr(PromotedLHS, PromotedRHS); 2790} 2791 2792/// getPointerBase - Transitively follow the chain of pointer-type operands 2793/// until reaching a SCEV that does not have a single pointer operand. This 2794/// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2795/// but corner cases do exist. 2796const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2797 // A pointer operand may evaluate to a nonpointer expression, such as null. 2798 if (!V->getType()->isPointerTy()) 2799 return V; 2800 2801 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2802 return getPointerBase(Cast->getOperand()); 2803 } 2804 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2805 const SCEV *PtrOp = 0; 2806 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2807 I != E; ++I) { 2808 if ((*I)->getType()->isPointerTy()) { 2809 // Cannot find the base of an expression with multiple pointer operands. 2810 if (PtrOp) 2811 return V; 2812 PtrOp = *I; 2813 } 2814 } 2815 if (!PtrOp) 2816 return V; 2817 return getPointerBase(PtrOp); 2818 } 2819 return V; 2820} 2821 2822/// PushDefUseChildren - Push users of the given Instruction 2823/// onto the given Worklist. 2824static void 2825PushDefUseChildren(Instruction *I, 2826 SmallVectorImpl<Instruction *> &Worklist) { 2827 // Push the def-use children onto the Worklist stack. 2828 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2829 UI != UE; ++UI) 2830 Worklist.push_back(cast<Instruction>(*UI)); 2831} 2832 2833/// ForgetSymbolicValue - This looks up computed SCEV values for all 2834/// instructions that depend on the given instruction and removes them from 2835/// the ValueExprMapType map if they reference SymName. This is used during PHI 2836/// resolution. 2837void 2838ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2839 SmallVector<Instruction *, 16> Worklist; 2840 PushDefUseChildren(PN, Worklist); 2841 2842 SmallPtrSet<Instruction *, 8> Visited; 2843 Visited.insert(PN); 2844 while (!Worklist.empty()) { 2845 Instruction *I = Worklist.pop_back_val(); 2846 if (!Visited.insert(I)) continue; 2847 2848 ValueExprMapType::iterator It = 2849 ValueExprMap.find(static_cast<Value *>(I)); 2850 if (It != ValueExprMap.end()) { 2851 const SCEV *Old = It->second; 2852 2853 // Short-circuit the def-use traversal if the symbolic name 2854 // ceases to appear in expressions. 2855 if (Old != SymName && !hasOperand(Old, SymName)) 2856 continue; 2857 2858 // SCEVUnknown for a PHI either means that it has an unrecognized 2859 // structure, it's a PHI that's in the progress of being computed 2860 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2861 // additional loop trip count information isn't going to change anything. 2862 // In the second case, createNodeForPHI will perform the necessary 2863 // updates on its own when it gets to that point. In the third, we do 2864 // want to forget the SCEVUnknown. 2865 if (!isa<PHINode>(I) || 2866 !isa<SCEVUnknown>(Old) || 2867 (I != PN && Old == SymName)) { 2868 forgetMemoizedResults(Old); 2869 ValueExprMap.erase(It); 2870 } 2871 } 2872 2873 PushDefUseChildren(I, Worklist); 2874 } 2875} 2876 2877/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2878/// a loop header, making it a potential recurrence, or it doesn't. 2879/// 2880const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2881 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2882 if (L->getHeader() == PN->getParent()) { 2883 // The loop may have multiple entrances or multiple exits; we can analyze 2884 // this phi as an addrec if it has a unique entry value and a unique 2885 // backedge value. 2886 Value *BEValueV = 0, *StartValueV = 0; 2887 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2888 Value *V = PN->getIncomingValue(i); 2889 if (L->contains(PN->getIncomingBlock(i))) { 2890 if (!BEValueV) { 2891 BEValueV = V; 2892 } else if (BEValueV != V) { 2893 BEValueV = 0; 2894 break; 2895 } 2896 } else if (!StartValueV) { 2897 StartValueV = V; 2898 } else if (StartValueV != V) { 2899 StartValueV = 0; 2900 break; 2901 } 2902 } 2903 if (BEValueV && StartValueV) { 2904 // While we are analyzing this PHI node, handle its value symbolically. 2905 const SCEV *SymbolicName = getUnknown(PN); 2906 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2907 "PHI node already processed?"); 2908 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2909 2910 // Using this symbolic name for the PHI, analyze the value coming around 2911 // the back-edge. 2912 const SCEV *BEValue = getSCEV(BEValueV); 2913 2914 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2915 // has a special value for the first iteration of the loop. 2916 2917 // If the value coming around the backedge is an add with the symbolic 2918 // value we just inserted, then we found a simple induction variable! 2919 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2920 // If there is a single occurrence of the symbolic value, replace it 2921 // with a recurrence. 2922 unsigned FoundIndex = Add->getNumOperands(); 2923 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2924 if (Add->getOperand(i) == SymbolicName) 2925 if (FoundIndex == e) { 2926 FoundIndex = i; 2927 break; 2928 } 2929 2930 if (FoundIndex != Add->getNumOperands()) { 2931 // Create an add with everything but the specified operand. 2932 SmallVector<const SCEV *, 8> Ops; 2933 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2934 if (i != FoundIndex) 2935 Ops.push_back(Add->getOperand(i)); 2936 const SCEV *Accum = getAddExpr(Ops); 2937 2938 // This is not a valid addrec if the step amount is varying each 2939 // loop iteration, but is not itself an addrec in this loop. 2940 if (isLoopInvariant(Accum, L) || 2941 (isa<SCEVAddRecExpr>(Accum) && 2942 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2943 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 2944 2945 // If the increment doesn't overflow, then neither the addrec nor 2946 // the post-increment will overflow. 2947 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2948 if (OBO->hasNoUnsignedWrap()) 2949 Flags = setFlags(Flags, SCEV::FlagNUW); 2950 if (OBO->hasNoSignedWrap()) 2951 Flags = setFlags(Flags, SCEV::FlagNSW); 2952 } else if (const GEPOperator *GEP = 2953 dyn_cast<GEPOperator>(BEValueV)) { 2954 // If the increment is an inbounds GEP, then we know the address 2955 // space cannot be wrapped around. We cannot make any guarantee 2956 // about signed or unsigned overflow because pointers are 2957 // unsigned but we may have a negative index from the base 2958 // pointer. 2959 if (GEP->isInBounds()) 2960 Flags = setFlags(Flags, SCEV::FlagNW); 2961 } 2962 2963 const SCEV *StartVal = getSCEV(StartValueV); 2964 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 2965 2966 // Since the no-wrap flags are on the increment, they apply to the 2967 // post-incremented value as well. 2968 if (isLoopInvariant(Accum, L)) 2969 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2970 Accum, L, Flags); 2971 2972 // Okay, for the entire analysis of this edge we assumed the PHI 2973 // to be symbolic. We now need to go back and purge all of the 2974 // entries for the scalars that use the symbolic expression. 2975 ForgetSymbolicName(PN, SymbolicName); 2976 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2977 return PHISCEV; 2978 } 2979 } 2980 } else if (const SCEVAddRecExpr *AddRec = 2981 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2982 // Otherwise, this could be a loop like this: 2983 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2984 // In this case, j = {1,+,1} and BEValue is j. 2985 // Because the other in-value of i (0) fits the evolution of BEValue 2986 // i really is an addrec evolution. 2987 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2988 const SCEV *StartVal = getSCEV(StartValueV); 2989 2990 // If StartVal = j.start - j.stride, we can use StartVal as the 2991 // initial step of the addrec evolution. 2992 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2993 AddRec->getOperand(1))) { 2994 // FIXME: For constant StartVal, we should be able to infer 2995 // no-wrap flags. 2996 const SCEV *PHISCEV = 2997 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 2998 SCEV::FlagAnyWrap); 2999 3000 // Okay, for the entire analysis of this edge we assumed the PHI 3001 // to be symbolic. We now need to go back and purge all of the 3002 // entries for the scalars that use the symbolic expression. 3003 ForgetSymbolicName(PN, SymbolicName); 3004 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3005 return PHISCEV; 3006 } 3007 } 3008 } 3009 } 3010 } 3011 3012 // If the PHI has a single incoming value, follow that value, unless the 3013 // PHI's incoming blocks are in a different loop, in which case doing so 3014 // risks breaking LCSSA form. Instcombine would normally zap these, but 3015 // it doesn't have DominatorTree information, so it may miss cases. 3016 if (Value *V = SimplifyInstruction(PN, TD, DT)) 3017 if (LI->replacementPreservesLCSSAForm(PN, V)) 3018 return getSCEV(V); 3019 3020 // If it's not a loop phi, we can't handle it yet. 3021 return getUnknown(PN); 3022} 3023 3024/// createNodeForGEP - Expand GEP instructions into add and multiply 3025/// operations. This allows them to be analyzed by regular SCEV code. 3026/// 3027const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3028 3029 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3030 // Add expression, because the Instruction may be guarded by control flow 3031 // and the no-overflow bits may not be valid for the expression in any 3032 // context. 3033 bool isInBounds = GEP->isInBounds(); 3034 3035 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3036 Value *Base = GEP->getOperand(0); 3037 // Don't attempt to analyze GEPs over unsized objects. 3038 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 3039 return getUnknown(GEP); 3040 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3041 gep_type_iterator GTI = gep_type_begin(GEP); 3042 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 3043 E = GEP->op_end(); 3044 I != E; ++I) { 3045 Value *Index = *I; 3046 // Compute the (potentially symbolic) offset in bytes for this index. 3047 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3048 // For a struct, add the member offset. 3049 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3050 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 3051 3052 // Add the field offset to the running total offset. 3053 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3054 } else { 3055 // For an array, add the element offset, explicitly scaled. 3056 const SCEV *ElementSize = getSizeOfExpr(*GTI); 3057 const SCEV *IndexS = getSCEV(Index); 3058 // Getelementptr indices are signed. 3059 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3060 3061 // Multiply the index by the element size to compute the element offset. 3062 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 3063 isInBounds ? SCEV::FlagNSW : 3064 SCEV::FlagAnyWrap); 3065 3066 // Add the element offset to the running total offset. 3067 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3068 } 3069 } 3070 3071 // Get the SCEV for the GEP base. 3072 const SCEV *BaseS = getSCEV(Base); 3073 3074 // Add the total offset from all the GEP indices to the base. 3075 return getAddExpr(BaseS, TotalOffset, 3076 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3077} 3078 3079/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3080/// guaranteed to end in (at every loop iteration). It is, at the same time, 3081/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3082/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3083uint32_t 3084ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3085 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3086 return C->getValue()->getValue().countTrailingZeros(); 3087 3088 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3089 return std::min(GetMinTrailingZeros(T->getOperand()), 3090 (uint32_t)getTypeSizeInBits(T->getType())); 3091 3092 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3093 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3094 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3095 getTypeSizeInBits(E->getType()) : OpRes; 3096 } 3097 3098 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3099 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3100 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3101 getTypeSizeInBits(E->getType()) : OpRes; 3102 } 3103 3104 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3105 // The result is the min of all operands results. 3106 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3107 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3108 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3109 return MinOpRes; 3110 } 3111 3112 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3113 // The result is the sum of all operands results. 3114 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3115 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3116 for (unsigned i = 1, e = M->getNumOperands(); 3117 SumOpRes != BitWidth && i != e; ++i) 3118 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3119 BitWidth); 3120 return SumOpRes; 3121 } 3122 3123 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3124 // The result is the min of all operands results. 3125 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3126 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3127 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3128 return MinOpRes; 3129 } 3130 3131 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3132 // The result is the min of all operands results. 3133 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3134 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3135 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3136 return MinOpRes; 3137 } 3138 3139 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3140 // The result is the min of all operands results. 3141 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3142 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3143 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3144 return MinOpRes; 3145 } 3146 3147 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3148 // For a SCEVUnknown, ask ValueTracking. 3149 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3150 APInt Mask = APInt::getAllOnesValue(BitWidth); 3151 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3152 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3153 return Zeros.countTrailingOnes(); 3154 } 3155 3156 // SCEVUDivExpr 3157 return 0; 3158} 3159 3160/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3161/// 3162ConstantRange 3163ScalarEvolution::getUnsignedRange(const SCEV *S) { 3164 // See if we've computed this range already. 3165 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3166 if (I != UnsignedRanges.end()) 3167 return I->second; 3168 3169 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3170 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3171 3172 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3173 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3174 3175 // If the value has known zeros, the maximum unsigned value will have those 3176 // known zeros as well. 3177 uint32_t TZ = GetMinTrailingZeros(S); 3178 if (TZ != 0) 3179 ConservativeResult = 3180 ConstantRange(APInt::getMinValue(BitWidth), 3181 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3182 3183 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3184 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3185 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3186 X = X.add(getUnsignedRange(Add->getOperand(i))); 3187 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3188 } 3189 3190 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3191 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3192 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3193 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3194 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3195 } 3196 3197 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3198 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3199 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3200 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3201 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3202 } 3203 3204 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3205 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3206 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3207 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3208 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3209 } 3210 3211 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3212 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3213 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3214 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3215 } 3216 3217 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3218 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3219 return setUnsignedRange(ZExt, 3220 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3221 } 3222 3223 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3224 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3225 return setUnsignedRange(SExt, 3226 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3227 } 3228 3229 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3230 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3231 return setUnsignedRange(Trunc, 3232 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3233 } 3234 3235 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3236 // If there's no unsigned wrap, the value will never be less than its 3237 // initial value. 3238 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3239 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3240 if (!C->getValue()->isZero()) 3241 ConservativeResult = 3242 ConservativeResult.intersectWith( 3243 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3244 3245 // TODO: non-affine addrec 3246 if (AddRec->isAffine()) { 3247 Type *Ty = AddRec->getType(); 3248 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3249 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3250 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3251 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3252 3253 const SCEV *Start = AddRec->getStart(); 3254 const SCEV *Step = AddRec->getStepRecurrence(*this); 3255 3256 ConstantRange StartRange = getUnsignedRange(Start); 3257 ConstantRange StepRange = getSignedRange(Step); 3258 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3259 ConstantRange EndRange = 3260 StartRange.add(MaxBECountRange.multiply(StepRange)); 3261 3262 // Check for overflow. This must be done with ConstantRange arithmetic 3263 // because we could be called from within the ScalarEvolution overflow 3264 // checking code. 3265 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3266 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3267 ConstantRange ExtMaxBECountRange = 3268 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3269 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3270 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3271 ExtEndRange) 3272 return setUnsignedRange(AddRec, ConservativeResult); 3273 3274 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3275 EndRange.getUnsignedMin()); 3276 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3277 EndRange.getUnsignedMax()); 3278 if (Min.isMinValue() && Max.isMaxValue()) 3279 return setUnsignedRange(AddRec, ConservativeResult); 3280 return setUnsignedRange(AddRec, 3281 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3282 } 3283 } 3284 3285 return setUnsignedRange(AddRec, ConservativeResult); 3286 } 3287 3288 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3289 // For a SCEVUnknown, ask ValueTracking. 3290 APInt Mask = APInt::getAllOnesValue(BitWidth); 3291 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3292 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3293 if (Ones == ~Zeros + 1) 3294 return setUnsignedRange(U, ConservativeResult); 3295 return setUnsignedRange(U, 3296 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3297 } 3298 3299 return setUnsignedRange(S, ConservativeResult); 3300} 3301 3302/// getSignedRange - Determine the signed range for a particular SCEV. 3303/// 3304ConstantRange 3305ScalarEvolution::getSignedRange(const SCEV *S) { 3306 // See if we've computed this range already. 3307 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3308 if (I != SignedRanges.end()) 3309 return I->second; 3310 3311 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3312 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3313 3314 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3315 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3316 3317 // If the value has known zeros, the maximum signed value will have those 3318 // known zeros as well. 3319 uint32_t TZ = GetMinTrailingZeros(S); 3320 if (TZ != 0) 3321 ConservativeResult = 3322 ConstantRange(APInt::getSignedMinValue(BitWidth), 3323 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3324 3325 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3326 ConstantRange X = getSignedRange(Add->getOperand(0)); 3327 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3328 X = X.add(getSignedRange(Add->getOperand(i))); 3329 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3330 } 3331 3332 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3333 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3334 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3335 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3336 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3337 } 3338 3339 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3340 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3341 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3342 X = X.smax(getSignedRange(SMax->getOperand(i))); 3343 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3344 } 3345 3346 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3347 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3348 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3349 X = X.umax(getSignedRange(UMax->getOperand(i))); 3350 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3351 } 3352 3353 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3354 ConstantRange X = getSignedRange(UDiv->getLHS()); 3355 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3356 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3357 } 3358 3359 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3360 ConstantRange X = getSignedRange(ZExt->getOperand()); 3361 return setSignedRange(ZExt, 3362 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3363 } 3364 3365 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3366 ConstantRange X = getSignedRange(SExt->getOperand()); 3367 return setSignedRange(SExt, 3368 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3369 } 3370 3371 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3372 ConstantRange X = getSignedRange(Trunc->getOperand()); 3373 return setSignedRange(Trunc, 3374 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3375 } 3376 3377 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3378 // If there's no signed wrap, and all the operands have the same sign or 3379 // zero, the value won't ever change sign. 3380 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3381 bool AllNonNeg = true; 3382 bool AllNonPos = true; 3383 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3384 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3385 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3386 } 3387 if (AllNonNeg) 3388 ConservativeResult = ConservativeResult.intersectWith( 3389 ConstantRange(APInt(BitWidth, 0), 3390 APInt::getSignedMinValue(BitWidth))); 3391 else if (AllNonPos) 3392 ConservativeResult = ConservativeResult.intersectWith( 3393 ConstantRange(APInt::getSignedMinValue(BitWidth), 3394 APInt(BitWidth, 1))); 3395 } 3396 3397 // TODO: non-affine addrec 3398 if (AddRec->isAffine()) { 3399 Type *Ty = AddRec->getType(); 3400 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3401 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3402 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3403 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3404 3405 const SCEV *Start = AddRec->getStart(); 3406 const SCEV *Step = AddRec->getStepRecurrence(*this); 3407 3408 ConstantRange StartRange = getSignedRange(Start); 3409 ConstantRange StepRange = getSignedRange(Step); 3410 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3411 ConstantRange EndRange = 3412 StartRange.add(MaxBECountRange.multiply(StepRange)); 3413 3414 // Check for overflow. This must be done with ConstantRange arithmetic 3415 // because we could be called from within the ScalarEvolution overflow 3416 // checking code. 3417 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3418 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3419 ConstantRange ExtMaxBECountRange = 3420 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3421 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3422 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3423 ExtEndRange) 3424 return setSignedRange(AddRec, ConservativeResult); 3425 3426 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3427 EndRange.getSignedMin()); 3428 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3429 EndRange.getSignedMax()); 3430 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3431 return setSignedRange(AddRec, ConservativeResult); 3432 return setSignedRange(AddRec, 3433 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3434 } 3435 } 3436 3437 return setSignedRange(AddRec, ConservativeResult); 3438 } 3439 3440 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3441 // For a SCEVUnknown, ask ValueTracking. 3442 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3443 return setSignedRange(U, ConservativeResult); 3444 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3445 if (NS == 1) 3446 return setSignedRange(U, ConservativeResult); 3447 return setSignedRange(U, ConservativeResult.intersectWith( 3448 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3449 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3450 } 3451 3452 return setSignedRange(S, ConservativeResult); 3453} 3454 3455/// createSCEV - We know that there is no SCEV for the specified value. 3456/// Analyze the expression. 3457/// 3458const SCEV *ScalarEvolution::createSCEV(Value *V) { 3459 if (!isSCEVable(V->getType())) 3460 return getUnknown(V); 3461 3462 unsigned Opcode = Instruction::UserOp1; 3463 if (Instruction *I = dyn_cast<Instruction>(V)) { 3464 Opcode = I->getOpcode(); 3465 3466 // Don't attempt to analyze instructions in blocks that aren't 3467 // reachable. Such instructions don't matter, and they aren't required 3468 // to obey basic rules for definitions dominating uses which this 3469 // analysis depends on. 3470 if (!DT->isReachableFromEntry(I->getParent())) 3471 return getUnknown(V); 3472 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3473 Opcode = CE->getOpcode(); 3474 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3475 return getConstant(CI); 3476 else if (isa<ConstantPointerNull>(V)) 3477 return getConstant(V->getType(), 0); 3478 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3479 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3480 else 3481 return getUnknown(V); 3482 3483 Operator *U = cast<Operator>(V); 3484 switch (Opcode) { 3485 case Instruction::Add: { 3486 // The simple thing to do would be to just call getSCEV on both operands 3487 // and call getAddExpr with the result. However if we're looking at a 3488 // bunch of things all added together, this can be quite inefficient, 3489 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3490 // Instead, gather up all the operands and make a single getAddExpr call. 3491 // LLVM IR canonical form means we need only traverse the left operands. 3492 SmallVector<const SCEV *, 4> AddOps; 3493 AddOps.push_back(getSCEV(U->getOperand(1))); 3494 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3495 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3496 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3497 break; 3498 U = cast<Operator>(Op); 3499 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3500 if (Opcode == Instruction::Sub) 3501 AddOps.push_back(getNegativeSCEV(Op1)); 3502 else 3503 AddOps.push_back(Op1); 3504 } 3505 AddOps.push_back(getSCEV(U->getOperand(0))); 3506 return getAddExpr(AddOps); 3507 } 3508 case Instruction::Mul: { 3509 // See the Add code above. 3510 SmallVector<const SCEV *, 4> MulOps; 3511 MulOps.push_back(getSCEV(U->getOperand(1))); 3512 for (Value *Op = U->getOperand(0); 3513 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3514 Op = U->getOperand(0)) { 3515 U = cast<Operator>(Op); 3516 MulOps.push_back(getSCEV(U->getOperand(1))); 3517 } 3518 MulOps.push_back(getSCEV(U->getOperand(0))); 3519 return getMulExpr(MulOps); 3520 } 3521 case Instruction::UDiv: 3522 return getUDivExpr(getSCEV(U->getOperand(0)), 3523 getSCEV(U->getOperand(1))); 3524 case Instruction::Sub: 3525 return getMinusSCEV(getSCEV(U->getOperand(0)), 3526 getSCEV(U->getOperand(1))); 3527 case Instruction::And: 3528 // For an expression like x&255 that merely masks off the high bits, 3529 // use zext(trunc(x)) as the SCEV expression. 3530 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3531 if (CI->isNullValue()) 3532 return getSCEV(U->getOperand(1)); 3533 if (CI->isAllOnesValue()) 3534 return getSCEV(U->getOperand(0)); 3535 const APInt &A = CI->getValue(); 3536 3537 // Instcombine's ShrinkDemandedConstant may strip bits out of 3538 // constants, obscuring what would otherwise be a low-bits mask. 3539 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3540 // knew about to reconstruct a low-bits mask value. 3541 unsigned LZ = A.countLeadingZeros(); 3542 unsigned BitWidth = A.getBitWidth(); 3543 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3544 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3545 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3546 3547 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3548 3549 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3550 return 3551 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3552 IntegerType::get(getContext(), BitWidth - LZ)), 3553 U->getType()); 3554 } 3555 break; 3556 3557 case Instruction::Or: 3558 // If the RHS of the Or is a constant, we may have something like: 3559 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3560 // optimizations will transparently handle this case. 3561 // 3562 // In order for this transformation to be safe, the LHS must be of the 3563 // form X*(2^n) and the Or constant must be less than 2^n. 3564 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3565 const SCEV *LHS = getSCEV(U->getOperand(0)); 3566 const APInt &CIVal = CI->getValue(); 3567 if (GetMinTrailingZeros(LHS) >= 3568 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3569 // Build a plain add SCEV. 3570 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3571 // If the LHS of the add was an addrec and it has no-wrap flags, 3572 // transfer the no-wrap flags, since an or won't introduce a wrap. 3573 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3574 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3575 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3576 OldAR->getNoWrapFlags()); 3577 } 3578 return S; 3579 } 3580 } 3581 break; 3582 case Instruction::Xor: 3583 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3584 // If the RHS of the xor is a signbit, then this is just an add. 3585 // Instcombine turns add of signbit into xor as a strength reduction step. 3586 if (CI->getValue().isSignBit()) 3587 return getAddExpr(getSCEV(U->getOperand(0)), 3588 getSCEV(U->getOperand(1))); 3589 3590 // If the RHS of xor is -1, then this is a not operation. 3591 if (CI->isAllOnesValue()) 3592 return getNotSCEV(getSCEV(U->getOperand(0))); 3593 3594 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3595 // This is a variant of the check for xor with -1, and it handles 3596 // the case where instcombine has trimmed non-demanded bits out 3597 // of an xor with -1. 3598 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3599 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3600 if (BO->getOpcode() == Instruction::And && 3601 LCI->getValue() == CI->getValue()) 3602 if (const SCEVZeroExtendExpr *Z = 3603 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3604 Type *UTy = U->getType(); 3605 const SCEV *Z0 = Z->getOperand(); 3606 Type *Z0Ty = Z0->getType(); 3607 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3608 3609 // If C is a low-bits mask, the zero extend is serving to 3610 // mask off the high bits. Complement the operand and 3611 // re-apply the zext. 3612 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3613 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3614 3615 // If C is a single bit, it may be in the sign-bit position 3616 // before the zero-extend. In this case, represent the xor 3617 // using an add, which is equivalent, and re-apply the zext. 3618 APInt Trunc = CI->getValue().trunc(Z0TySize); 3619 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3620 Trunc.isSignBit()) 3621 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3622 UTy); 3623 } 3624 } 3625 break; 3626 3627 case Instruction::Shl: 3628 // Turn shift left of a constant amount into a multiply. 3629 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3630 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3631 3632 // If the shift count is not less than the bitwidth, the result of 3633 // the shift is undefined. Don't try to analyze it, because the 3634 // resolution chosen here may differ from the resolution chosen in 3635 // other parts of the compiler. 3636 if (SA->getValue().uge(BitWidth)) 3637 break; 3638 3639 Constant *X = ConstantInt::get(getContext(), 3640 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3641 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3642 } 3643 break; 3644 3645 case Instruction::LShr: 3646 // Turn logical shift right of a constant into a unsigned divide. 3647 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3648 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3649 3650 // If the shift count is not less than the bitwidth, the result of 3651 // the shift is undefined. Don't try to analyze it, because the 3652 // resolution chosen here may differ from the resolution chosen in 3653 // other parts of the compiler. 3654 if (SA->getValue().uge(BitWidth)) 3655 break; 3656 3657 Constant *X = ConstantInt::get(getContext(), 3658 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3659 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3660 } 3661 break; 3662 3663 case Instruction::AShr: 3664 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3665 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3666 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3667 if (L->getOpcode() == Instruction::Shl && 3668 L->getOperand(1) == U->getOperand(1)) { 3669 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3670 3671 // If the shift count is not less than the bitwidth, the result of 3672 // the shift is undefined. Don't try to analyze it, because the 3673 // resolution chosen here may differ from the resolution chosen in 3674 // other parts of the compiler. 3675 if (CI->getValue().uge(BitWidth)) 3676 break; 3677 3678 uint64_t Amt = BitWidth - CI->getZExtValue(); 3679 if (Amt == BitWidth) 3680 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3681 return 3682 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3683 IntegerType::get(getContext(), 3684 Amt)), 3685 U->getType()); 3686 } 3687 break; 3688 3689 case Instruction::Trunc: 3690 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3691 3692 case Instruction::ZExt: 3693 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3694 3695 case Instruction::SExt: 3696 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3697 3698 case Instruction::BitCast: 3699 // BitCasts are no-op casts so we just eliminate the cast. 3700 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3701 return getSCEV(U->getOperand(0)); 3702 break; 3703 3704 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3705 // lead to pointer expressions which cannot safely be expanded to GEPs, 3706 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3707 // simplifying integer expressions. 3708 3709 case Instruction::GetElementPtr: 3710 return createNodeForGEP(cast<GEPOperator>(U)); 3711 3712 case Instruction::PHI: 3713 return createNodeForPHI(cast<PHINode>(U)); 3714 3715 case Instruction::Select: 3716 // This could be a smax or umax that was lowered earlier. 3717 // Try to recover it. 3718 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3719 Value *LHS = ICI->getOperand(0); 3720 Value *RHS = ICI->getOperand(1); 3721 switch (ICI->getPredicate()) { 3722 case ICmpInst::ICMP_SLT: 3723 case ICmpInst::ICMP_SLE: 3724 std::swap(LHS, RHS); 3725 // fall through 3726 case ICmpInst::ICMP_SGT: 3727 case ICmpInst::ICMP_SGE: 3728 // a >s b ? a+x : b+x -> smax(a, b)+x 3729 // a >s b ? b+x : a+x -> smin(a, b)+x 3730 if (LHS->getType() == U->getType()) { 3731 const SCEV *LS = getSCEV(LHS); 3732 const SCEV *RS = getSCEV(RHS); 3733 const SCEV *LA = getSCEV(U->getOperand(1)); 3734 const SCEV *RA = getSCEV(U->getOperand(2)); 3735 const SCEV *LDiff = getMinusSCEV(LA, LS); 3736 const SCEV *RDiff = getMinusSCEV(RA, RS); 3737 if (LDiff == RDiff) 3738 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3739 LDiff = getMinusSCEV(LA, RS); 3740 RDiff = getMinusSCEV(RA, LS); 3741 if (LDiff == RDiff) 3742 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3743 } 3744 break; 3745 case ICmpInst::ICMP_ULT: 3746 case ICmpInst::ICMP_ULE: 3747 std::swap(LHS, RHS); 3748 // fall through 3749 case ICmpInst::ICMP_UGT: 3750 case ICmpInst::ICMP_UGE: 3751 // a >u b ? a+x : b+x -> umax(a, b)+x 3752 // a >u b ? b+x : a+x -> umin(a, b)+x 3753 if (LHS->getType() == U->getType()) { 3754 const SCEV *LS = getSCEV(LHS); 3755 const SCEV *RS = getSCEV(RHS); 3756 const SCEV *LA = getSCEV(U->getOperand(1)); 3757 const SCEV *RA = getSCEV(U->getOperand(2)); 3758 const SCEV *LDiff = getMinusSCEV(LA, LS); 3759 const SCEV *RDiff = getMinusSCEV(RA, RS); 3760 if (LDiff == RDiff) 3761 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3762 LDiff = getMinusSCEV(LA, RS); 3763 RDiff = getMinusSCEV(RA, LS); 3764 if (LDiff == RDiff) 3765 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3766 } 3767 break; 3768 case ICmpInst::ICMP_NE: 3769 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3770 if (LHS->getType() == U->getType() && 3771 isa<ConstantInt>(RHS) && 3772 cast<ConstantInt>(RHS)->isZero()) { 3773 const SCEV *One = getConstant(LHS->getType(), 1); 3774 const SCEV *LS = getSCEV(LHS); 3775 const SCEV *LA = getSCEV(U->getOperand(1)); 3776 const SCEV *RA = getSCEV(U->getOperand(2)); 3777 const SCEV *LDiff = getMinusSCEV(LA, LS); 3778 const SCEV *RDiff = getMinusSCEV(RA, One); 3779 if (LDiff == RDiff) 3780 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3781 } 3782 break; 3783 case ICmpInst::ICMP_EQ: 3784 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3785 if (LHS->getType() == U->getType() && 3786 isa<ConstantInt>(RHS) && 3787 cast<ConstantInt>(RHS)->isZero()) { 3788 const SCEV *One = getConstant(LHS->getType(), 1); 3789 const SCEV *LS = getSCEV(LHS); 3790 const SCEV *LA = getSCEV(U->getOperand(1)); 3791 const SCEV *RA = getSCEV(U->getOperand(2)); 3792 const SCEV *LDiff = getMinusSCEV(LA, One); 3793 const SCEV *RDiff = getMinusSCEV(RA, LS); 3794 if (LDiff == RDiff) 3795 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3796 } 3797 break; 3798 default: 3799 break; 3800 } 3801 } 3802 3803 default: // We cannot analyze this expression. 3804 break; 3805 } 3806 3807 return getUnknown(V); 3808} 3809 3810 3811 3812//===----------------------------------------------------------------------===// 3813// Iteration Count Computation Code 3814// 3815 3816// getExitCount - Get the expression for the number of loop iterations for which 3817// this loop is guaranteed not to exit via ExitintBlock. Otherwise return 3818// SCEVCouldNotCompute. 3819const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 3820 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 3821} 3822 3823/// getBackedgeTakenCount - If the specified loop has a predictable 3824/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3825/// object. The backedge-taken count is the number of times the loop header 3826/// will be branched to from within the loop. This is one less than the 3827/// trip count of the loop, since it doesn't count the first iteration, 3828/// when the header is branched to from outside the loop. 3829/// 3830/// Note that it is not valid to call this method on a loop without a 3831/// loop-invariant backedge-taken count (see 3832/// hasLoopInvariantBackedgeTakenCount). 3833/// 3834const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3835 return getBackedgeTakenInfo(L).getExact(this); 3836} 3837 3838/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3839/// return the least SCEV value that is known never to be less than the 3840/// actual backedge taken count. 3841const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3842 return getBackedgeTakenInfo(L).getMax(this); 3843} 3844 3845/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3846/// onto the given Worklist. 3847static void 3848PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3849 BasicBlock *Header = L->getHeader(); 3850 3851 // Push all Loop-header PHIs onto the Worklist stack. 3852 for (BasicBlock::iterator I = Header->begin(); 3853 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3854 Worklist.push_back(PN); 3855} 3856 3857const ScalarEvolution::BackedgeTakenInfo & 3858ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3859 // Initially insert an invalid entry for this loop. If the insertion 3860 // succeeds, proceed to actually compute a backedge-taken count and 3861 // update the value. The temporary CouldNotCompute value tells SCEV 3862 // code elsewhere that it shouldn't attempt to request a new 3863 // backedge-taken count, which could result in infinite recursion. 3864 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3865 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 3866 if (!Pair.second) 3867 return Pair.first->second; 3868 3869 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 3870 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 3871 // must be cleared in this scope. 3872 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 3873 3874 if (Result.getExact(this) != getCouldNotCompute()) { 3875 assert(isLoopInvariant(Result.getExact(this), L) && 3876 isLoopInvariant(Result.getMax(this), L) && 3877 "Computed backedge-taken count isn't loop invariant for loop!"); 3878 ++NumTripCountsComputed; 3879 } 3880 else if (Result.getMax(this) == getCouldNotCompute() && 3881 isa<PHINode>(L->getHeader()->begin())) { 3882 // Only count loops that have phi nodes as not being computable. 3883 ++NumTripCountsNotComputed; 3884 } 3885 3886 // Now that we know more about the trip count for this loop, forget any 3887 // existing SCEV values for PHI nodes in this loop since they are only 3888 // conservative estimates made without the benefit of trip count 3889 // information. This is similar to the code in forgetLoop, except that 3890 // it handles SCEVUnknown PHI nodes specially. 3891 if (Result.hasAnyInfo()) { 3892 SmallVector<Instruction *, 16> Worklist; 3893 PushLoopPHIs(L, Worklist); 3894 3895 SmallPtrSet<Instruction *, 8> Visited; 3896 while (!Worklist.empty()) { 3897 Instruction *I = Worklist.pop_back_val(); 3898 if (!Visited.insert(I)) continue; 3899 3900 ValueExprMapType::iterator It = 3901 ValueExprMap.find(static_cast<Value *>(I)); 3902 if (It != ValueExprMap.end()) { 3903 const SCEV *Old = It->second; 3904 3905 // SCEVUnknown for a PHI either means that it has an unrecognized 3906 // structure, or it's a PHI that's in the progress of being computed 3907 // by createNodeForPHI. In the former case, additional loop trip 3908 // count information isn't going to change anything. In the later 3909 // case, createNodeForPHI will perform the necessary updates on its 3910 // own when it gets to that point. 3911 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3912 forgetMemoizedResults(Old); 3913 ValueExprMap.erase(It); 3914 } 3915 if (PHINode *PN = dyn_cast<PHINode>(I)) 3916 ConstantEvolutionLoopExitValue.erase(PN); 3917 } 3918 3919 PushDefUseChildren(I, Worklist); 3920 } 3921 } 3922 3923 // Re-lookup the insert position, since the call to 3924 // ComputeBackedgeTakenCount above could result in a 3925 // recusive call to getBackedgeTakenInfo (on a different 3926 // loop), which would invalidate the iterator computed 3927 // earlier. 3928 return BackedgeTakenCounts.find(L)->second = Result; 3929} 3930 3931/// forgetLoop - This method should be called by the client when it has 3932/// changed a loop in a way that may effect ScalarEvolution's ability to 3933/// compute a trip count, or if the loop is deleted. 3934void ScalarEvolution::forgetLoop(const Loop *L) { 3935 // Drop any stored trip count value. 3936 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 3937 BackedgeTakenCounts.find(L); 3938 if (BTCPos != BackedgeTakenCounts.end()) { 3939 BTCPos->second.clear(); 3940 BackedgeTakenCounts.erase(BTCPos); 3941 } 3942 3943 // Drop information about expressions based on loop-header PHIs. 3944 SmallVector<Instruction *, 16> Worklist; 3945 PushLoopPHIs(L, Worklist); 3946 3947 SmallPtrSet<Instruction *, 8> Visited; 3948 while (!Worklist.empty()) { 3949 Instruction *I = Worklist.pop_back_val(); 3950 if (!Visited.insert(I)) continue; 3951 3952 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3953 if (It != ValueExprMap.end()) { 3954 forgetMemoizedResults(It->second); 3955 ValueExprMap.erase(It); 3956 if (PHINode *PN = dyn_cast<PHINode>(I)) 3957 ConstantEvolutionLoopExitValue.erase(PN); 3958 } 3959 3960 PushDefUseChildren(I, Worklist); 3961 } 3962 3963 // Forget all contained loops too, to avoid dangling entries in the 3964 // ValuesAtScopes map. 3965 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3966 forgetLoop(*I); 3967} 3968 3969/// forgetValue - This method should be called by the client when it has 3970/// changed a value in a way that may effect its value, or which may 3971/// disconnect it from a def-use chain linking it to a loop. 3972void ScalarEvolution::forgetValue(Value *V) { 3973 Instruction *I = dyn_cast<Instruction>(V); 3974 if (!I) return; 3975 3976 // Drop information about expressions based on loop-header PHIs. 3977 SmallVector<Instruction *, 16> Worklist; 3978 Worklist.push_back(I); 3979 3980 SmallPtrSet<Instruction *, 8> Visited; 3981 while (!Worklist.empty()) { 3982 I = Worklist.pop_back_val(); 3983 if (!Visited.insert(I)) continue; 3984 3985 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3986 if (It != ValueExprMap.end()) { 3987 forgetMemoizedResults(It->second); 3988 ValueExprMap.erase(It); 3989 if (PHINode *PN = dyn_cast<PHINode>(I)) 3990 ConstantEvolutionLoopExitValue.erase(PN); 3991 } 3992 3993 PushDefUseChildren(I, Worklist); 3994 } 3995} 3996 3997/// getExact - Get the exact loop backedge taken count considering all loop 3998/// exits. If all exits are computable, this is the minimum computed count. 3999const SCEV * 4000ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4001 // If any exits were not computable, the loop is not computable. 4002 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4003 4004 // We need at least one computable exit. 4005 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4006 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4007 4008 const SCEV *BECount = 0; 4009 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4010 ENT != 0; ENT = ENT->getNextExit()) { 4011 4012 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4013 4014 if (!BECount) 4015 BECount = ENT->ExactNotTaken; 4016 else 4017 BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken); 4018 } 4019 return BECount; 4020} 4021 4022/// getExact - Get the exact not taken count for this loop exit. 4023const SCEV * 4024ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4025 ScalarEvolution *SE) const { 4026 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4027 ENT != 0; ENT = ENT->getNextExit()) { 4028 4029 if (ENT->ExitingBlock == ExitingBlock) 4030 return ENT->ExactNotTaken; 4031 } 4032 return SE->getCouldNotCompute(); 4033} 4034 4035/// getMax - Get the max backedge taken count for the loop. 4036const SCEV * 4037ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4038 return Max ? Max : SE->getCouldNotCompute(); 4039} 4040 4041/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4042/// computable exit into a persistent ExitNotTakenInfo array. 4043ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4044 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4045 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4046 4047 if (!Complete) 4048 ExitNotTaken.setIncomplete(); 4049 4050 unsigned NumExits = ExitCounts.size(); 4051 if (NumExits == 0) return; 4052 4053 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4054 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4055 if (NumExits == 1) return; 4056 4057 // Handle the rare case of multiple computable exits. 4058 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4059 4060 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4061 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4062 PrevENT->setNextExit(ENT); 4063 ENT->ExitingBlock = ExitCounts[i].first; 4064 ENT->ExactNotTaken = ExitCounts[i].second; 4065 } 4066} 4067 4068/// clear - Invalidate this result and free the ExitNotTakenInfo array. 4069void ScalarEvolution::BackedgeTakenInfo::clear() { 4070 ExitNotTaken.ExitingBlock = 0; 4071 ExitNotTaken.ExactNotTaken = 0; 4072 delete[] ExitNotTaken.getNextExit(); 4073} 4074 4075/// ComputeBackedgeTakenCount - Compute the number of times the backedge 4076/// of the specified loop will execute. 4077ScalarEvolution::BackedgeTakenInfo 4078ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4079 SmallVector<BasicBlock *, 8> ExitingBlocks; 4080 L->getExitingBlocks(ExitingBlocks); 4081 4082 // Examine all exits and pick the most conservative values. 4083 const SCEV *MaxBECount = getCouldNotCompute(); 4084 bool CouldComputeBECount = true; 4085 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4086 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4087 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]); 4088 if (EL.Exact == getCouldNotCompute()) 4089 // We couldn't compute an exact value for this exit, so 4090 // we won't be able to compute an exact value for the loop. 4091 CouldComputeBECount = false; 4092 else 4093 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact)); 4094 4095 if (MaxBECount == getCouldNotCompute()) 4096 MaxBECount = EL.Max; 4097 else if (EL.Max != getCouldNotCompute()) 4098 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max); 4099 } 4100 4101 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4102} 4103 4104/// ComputeExitLimit - Compute the number of times the backedge of the specified 4105/// loop will execute if it exits via the specified block. 4106ScalarEvolution::ExitLimit 4107ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4108 4109 // Okay, we've chosen an exiting block. See what condition causes us to 4110 // exit at this block. 4111 // 4112 // FIXME: we should be able to handle switch instructions (with a single exit) 4113 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 4114 if (ExitBr == 0) return getCouldNotCompute(); 4115 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 4116 4117 // At this point, we know we have a conditional branch that determines whether 4118 // the loop is exited. However, we don't know if the branch is executed each 4119 // time through the loop. If not, then the execution count of the branch will 4120 // not be equal to the trip count of the loop. 4121 // 4122 // Currently we check for this by checking to see if the Exit branch goes to 4123 // the loop header. If so, we know it will always execute the same number of 4124 // times as the loop. We also handle the case where the exit block *is* the 4125 // loop header. This is common for un-rotated loops. 4126 // 4127 // If both of those tests fail, walk up the unique predecessor chain to the 4128 // header, stopping if there is an edge that doesn't exit the loop. If the 4129 // header is reached, the execution count of the branch will be equal to the 4130 // trip count of the loop. 4131 // 4132 // More extensive analysis could be done to handle more cases here. 4133 // 4134 if (ExitBr->getSuccessor(0) != L->getHeader() && 4135 ExitBr->getSuccessor(1) != L->getHeader() && 4136 ExitBr->getParent() != L->getHeader()) { 4137 // The simple checks failed, try climbing the unique predecessor chain 4138 // up to the header. 4139 bool Ok = false; 4140 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 4141 BasicBlock *Pred = BB->getUniquePredecessor(); 4142 if (!Pred) 4143 return getCouldNotCompute(); 4144 TerminatorInst *PredTerm = Pred->getTerminator(); 4145 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4146 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4147 if (PredSucc == BB) 4148 continue; 4149 // If the predecessor has a successor that isn't BB and isn't 4150 // outside the loop, assume the worst. 4151 if (L->contains(PredSucc)) 4152 return getCouldNotCompute(); 4153 } 4154 if (Pred == L->getHeader()) { 4155 Ok = true; 4156 break; 4157 } 4158 BB = Pred; 4159 } 4160 if (!Ok) 4161 return getCouldNotCompute(); 4162 } 4163 4164 // Proceed to the next level to examine the exit condition expression. 4165 return ComputeExitLimitFromCond(L, ExitBr->getCondition(), 4166 ExitBr->getSuccessor(0), 4167 ExitBr->getSuccessor(1)); 4168} 4169 4170/// ComputeExitLimitFromCond - Compute the number of times the 4171/// backedge of the specified loop will execute if its exit condition 4172/// were a conditional branch of ExitCond, TBB, and FBB. 4173ScalarEvolution::ExitLimit 4174ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4175 Value *ExitCond, 4176 BasicBlock *TBB, 4177 BasicBlock *FBB) { 4178 // Check if the controlling expression for this loop is an And or Or. 4179 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4180 if (BO->getOpcode() == Instruction::And) { 4181 // Recurse on the operands of the and. 4182 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4183 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4184 const SCEV *BECount = getCouldNotCompute(); 4185 const SCEV *MaxBECount = getCouldNotCompute(); 4186 if (L->contains(TBB)) { 4187 // Both conditions must be true for the loop to continue executing. 4188 // Choose the less conservative count. 4189 if (EL0.Exact == getCouldNotCompute() || 4190 EL1.Exact == getCouldNotCompute()) 4191 BECount = getCouldNotCompute(); 4192 else 4193 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4194 if (EL0.Max == getCouldNotCompute()) 4195 MaxBECount = EL1.Max; 4196 else if (EL1.Max == getCouldNotCompute()) 4197 MaxBECount = EL0.Max; 4198 else 4199 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4200 } else { 4201 // Both conditions must be true at the same time for the loop to exit. 4202 // For now, be conservative. 4203 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4204 if (EL0.Max == EL1.Max) 4205 MaxBECount = EL0.Max; 4206 if (EL0.Exact == EL1.Exact) 4207 BECount = EL0.Exact; 4208 } 4209 4210 return ExitLimit(BECount, MaxBECount); 4211 } 4212 if (BO->getOpcode() == Instruction::Or) { 4213 // Recurse on the operands of the or. 4214 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4215 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4216 const SCEV *BECount = getCouldNotCompute(); 4217 const SCEV *MaxBECount = getCouldNotCompute(); 4218 if (L->contains(FBB)) { 4219 // Both conditions must be false for the loop to continue executing. 4220 // Choose the less conservative count. 4221 if (EL0.Exact == getCouldNotCompute() || 4222 EL1.Exact == getCouldNotCompute()) 4223 BECount = getCouldNotCompute(); 4224 else 4225 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4226 if (EL0.Max == getCouldNotCompute()) 4227 MaxBECount = EL1.Max; 4228 else if (EL1.Max == getCouldNotCompute()) 4229 MaxBECount = EL0.Max; 4230 else 4231 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4232 } else { 4233 // Both conditions must be false at the same time for the loop to exit. 4234 // For now, be conservative. 4235 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4236 if (EL0.Max == EL1.Max) 4237 MaxBECount = EL0.Max; 4238 if (EL0.Exact == EL1.Exact) 4239 BECount = EL0.Exact; 4240 } 4241 4242 return ExitLimit(BECount, MaxBECount); 4243 } 4244 } 4245 4246 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4247 // Proceed to the next level to examine the icmp. 4248 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4249 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB); 4250 4251 // Check for a constant condition. These are normally stripped out by 4252 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4253 // preserve the CFG and is temporarily leaving constant conditions 4254 // in place. 4255 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4256 if (L->contains(FBB) == !CI->getZExtValue()) 4257 // The backedge is always taken. 4258 return getCouldNotCompute(); 4259 else 4260 // The backedge is never taken. 4261 return getConstant(CI->getType(), 0); 4262 } 4263 4264 // If it's not an integer or pointer comparison then compute it the hard way. 4265 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4266} 4267 4268/// ComputeExitLimitFromICmp - Compute the number of times the 4269/// backedge of the specified loop will execute if its exit condition 4270/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4271ScalarEvolution::ExitLimit 4272ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 4273 ICmpInst *ExitCond, 4274 BasicBlock *TBB, 4275 BasicBlock *FBB) { 4276 4277 // If the condition was exit on true, convert the condition to exit on false 4278 ICmpInst::Predicate Cond; 4279 if (!L->contains(FBB)) 4280 Cond = ExitCond->getPredicate(); 4281 else 4282 Cond = ExitCond->getInversePredicate(); 4283 4284 // Handle common loops like: for (X = "string"; *X; ++X) 4285 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4286 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4287 ExitLimit ItCnt = 4288 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 4289 if (ItCnt.hasAnyInfo()) 4290 return ItCnt; 4291 } 4292 4293 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4294 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4295 4296 // Try to evaluate any dependencies out of the loop. 4297 LHS = getSCEVAtScope(LHS, L); 4298 RHS = getSCEVAtScope(RHS, L); 4299 4300 // At this point, we would like to compute how many iterations of the 4301 // loop the predicate will return true for these inputs. 4302 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4303 // If there is a loop-invariant, force it into the RHS. 4304 std::swap(LHS, RHS); 4305 Cond = ICmpInst::getSwappedPredicate(Cond); 4306 } 4307 4308 // Simplify the operands before analyzing them. 4309 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4310 4311 // If we have a comparison of a chrec against a constant, try to use value 4312 // ranges to answer this query. 4313 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4314 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4315 if (AddRec->getLoop() == L) { 4316 // Form the constant range. 4317 ConstantRange CompRange( 4318 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4319 4320 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4321 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4322 } 4323 4324 switch (Cond) { 4325 case ICmpInst::ICMP_NE: { // while (X != Y) 4326 // Convert to: while (X-Y != 0) 4327 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4328 if (EL.hasAnyInfo()) return EL; 4329 break; 4330 } 4331 case ICmpInst::ICMP_EQ: { // while (X == Y) 4332 // Convert to: while (X-Y == 0) 4333 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4334 if (EL.hasAnyInfo()) return EL; 4335 break; 4336 } 4337 case ICmpInst::ICMP_SLT: { 4338 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true); 4339 if (EL.hasAnyInfo()) return EL; 4340 break; 4341 } 4342 case ICmpInst::ICMP_SGT: { 4343 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4344 getNotSCEV(RHS), L, true); 4345 if (EL.hasAnyInfo()) return EL; 4346 break; 4347 } 4348 case ICmpInst::ICMP_ULT: { 4349 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false); 4350 if (EL.hasAnyInfo()) return EL; 4351 break; 4352 } 4353 case ICmpInst::ICMP_UGT: { 4354 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4355 getNotSCEV(RHS), L, false); 4356 if (EL.hasAnyInfo()) return EL; 4357 break; 4358 } 4359 default: 4360#if 0 4361 dbgs() << "ComputeBackedgeTakenCount "; 4362 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4363 dbgs() << "[unsigned] "; 4364 dbgs() << *LHS << " " 4365 << Instruction::getOpcodeName(Instruction::ICmp) 4366 << " " << *RHS << "\n"; 4367#endif 4368 break; 4369 } 4370 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4371} 4372 4373static ConstantInt * 4374EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4375 ScalarEvolution &SE) { 4376 const SCEV *InVal = SE.getConstant(C); 4377 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4378 assert(isa<SCEVConstant>(Val) && 4379 "Evaluation of SCEV at constant didn't fold correctly?"); 4380 return cast<SCEVConstant>(Val)->getValue(); 4381} 4382 4383/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4384/// and a GEP expression (missing the pointer index) indexing into it, return 4385/// the addressed element of the initializer or null if the index expression is 4386/// invalid. 4387static Constant * 4388GetAddressedElementFromGlobal(GlobalVariable *GV, 4389 const std::vector<ConstantInt*> &Indices) { 4390 Constant *Init = GV->getInitializer(); 4391 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4392 uint64_t Idx = Indices[i]->getZExtValue(); 4393 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4394 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4395 Init = cast<Constant>(CS->getOperand(Idx)); 4396 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4397 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4398 Init = cast<Constant>(CA->getOperand(Idx)); 4399 } else if (isa<ConstantAggregateZero>(Init)) { 4400 if (StructType *STy = dyn_cast<StructType>(Init->getType())) { 4401 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4402 Init = Constant::getNullValue(STy->getElementType(Idx)); 4403 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4404 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4405 Init = Constant::getNullValue(ATy->getElementType()); 4406 } else { 4407 llvm_unreachable("Unknown constant aggregate type!"); 4408 } 4409 return 0; 4410 } else { 4411 return 0; // Unknown initializer type 4412 } 4413 } 4414 return Init; 4415} 4416 4417/// ComputeLoadConstantCompareExitLimit - Given an exit condition of 4418/// 'icmp op load X, cst', try to see if we can compute the backedge 4419/// execution count. 4420ScalarEvolution::ExitLimit 4421ScalarEvolution::ComputeLoadConstantCompareExitLimit( 4422 LoadInst *LI, 4423 Constant *RHS, 4424 const Loop *L, 4425 ICmpInst::Predicate predicate) { 4426 4427 if (LI->isVolatile()) return getCouldNotCompute(); 4428 4429 // Check to see if the loaded pointer is a getelementptr of a global. 4430 // TODO: Use SCEV instead of manually grubbing with GEPs. 4431 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4432 if (!GEP) return getCouldNotCompute(); 4433 4434 // Make sure that it is really a constant global we are gepping, with an 4435 // initializer, and make sure the first IDX is really 0. 4436 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4437 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4438 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4439 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4440 return getCouldNotCompute(); 4441 4442 // Okay, we allow one non-constant index into the GEP instruction. 4443 Value *VarIdx = 0; 4444 std::vector<ConstantInt*> Indexes; 4445 unsigned VarIdxNum = 0; 4446 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4447 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4448 Indexes.push_back(CI); 4449 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4450 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4451 VarIdx = GEP->getOperand(i); 4452 VarIdxNum = i-2; 4453 Indexes.push_back(0); 4454 } 4455 4456 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4457 // Check to see if X is a loop variant variable value now. 4458 const SCEV *Idx = getSCEV(VarIdx); 4459 Idx = getSCEVAtScope(Idx, L); 4460 4461 // We can only recognize very limited forms of loop index expressions, in 4462 // particular, only affine AddRec's like {C1,+,C2}. 4463 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4464 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4465 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4466 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4467 return getCouldNotCompute(); 4468 4469 unsigned MaxSteps = MaxBruteForceIterations; 4470 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4471 ConstantInt *ItCst = ConstantInt::get( 4472 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4473 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4474 4475 // Form the GEP offset. 4476 Indexes[VarIdxNum] = Val; 4477 4478 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4479 if (Result == 0) break; // Cannot compute! 4480 4481 // Evaluate the condition for this iteration. 4482 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4483 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4484 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4485#if 0 4486 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4487 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4488 << "***\n"; 4489#endif 4490 ++NumArrayLenItCounts; 4491 return getConstant(ItCst); // Found terminating iteration! 4492 } 4493 } 4494 return getCouldNotCompute(); 4495} 4496 4497 4498/// CanConstantFold - Return true if we can constant fold an instruction of the 4499/// specified type, assuming that all operands were constants. 4500static bool CanConstantFold(const Instruction *I) { 4501 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4502 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4503 return true; 4504 4505 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4506 if (const Function *F = CI->getCalledFunction()) 4507 return canConstantFoldCallTo(F); 4508 return false; 4509} 4510 4511/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4512/// in the loop that V is derived from. We allow arbitrary operations along the 4513/// way, but the operands of an operation must either be constants or a value 4514/// derived from a constant PHI. If this expression does not fit with these 4515/// constraints, return null. 4516static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4517 // If this is not an instruction, or if this is an instruction outside of the 4518 // loop, it can't be derived from a loop PHI. 4519 Instruction *I = dyn_cast<Instruction>(V); 4520 if (I == 0 || !L->contains(I)) return 0; 4521 4522 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4523 if (L->getHeader() == I->getParent()) 4524 return PN; 4525 else 4526 // We don't currently keep track of the control flow needed to evaluate 4527 // PHIs, so we cannot handle PHIs inside of loops. 4528 return 0; 4529 } 4530 4531 // If we won't be able to constant fold this expression even if the operands 4532 // are constants, return early. 4533 if (!CanConstantFold(I)) return 0; 4534 4535 // Otherwise, we can evaluate this instruction if all of its operands are 4536 // constant or derived from a PHI node themselves. 4537 PHINode *PHI = 0; 4538 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4539 if (!isa<Constant>(I->getOperand(Op))) { 4540 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4541 if (P == 0) return 0; // Not evolving from PHI 4542 if (PHI == 0) 4543 PHI = P; 4544 else if (PHI != P) 4545 return 0; // Evolving from multiple different PHIs. 4546 } 4547 4548 // This is a expression evolving from a constant PHI! 4549 return PHI; 4550} 4551 4552/// EvaluateExpression - Given an expression that passes the 4553/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4554/// in the loop has the value PHIVal. If we can't fold this expression for some 4555/// reason, return null. 4556static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4557 const TargetData *TD) { 4558 if (isa<PHINode>(V)) return PHIVal; 4559 if (Constant *C = dyn_cast<Constant>(V)) return C; 4560 Instruction *I = cast<Instruction>(V); 4561 4562 std::vector<Constant*> Operands(I->getNumOperands()); 4563 4564 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4565 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4566 if (Operands[i] == 0) return 0; 4567 } 4568 4569 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4570 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4571 Operands[1], TD); 4572 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD); 4573} 4574 4575/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4576/// in the header of its containing loop, we know the loop executes a 4577/// constant number of times, and the PHI node is just a recurrence 4578/// involving constants, fold it. 4579Constant * 4580ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4581 const APInt &BEs, 4582 const Loop *L) { 4583 DenseMap<PHINode*, Constant*>::const_iterator I = 4584 ConstantEvolutionLoopExitValue.find(PN); 4585 if (I != ConstantEvolutionLoopExitValue.end()) 4586 return I->second; 4587 4588 if (BEs.ugt(MaxBruteForceIterations)) 4589 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4590 4591 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4592 4593 // Since the loop is canonicalized, the PHI node must have two entries. One 4594 // entry must be a constant (coming in from outside of the loop), and the 4595 // second must be derived from the same PHI. 4596 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4597 Constant *StartCST = 4598 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4599 if (StartCST == 0) 4600 return RetVal = 0; // Must be a constant. 4601 4602 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4603 if (getConstantEvolvingPHI(BEValue, L) != PN && 4604 !isa<Constant>(BEValue)) 4605 return RetVal = 0; // Not derived from same PHI. 4606 4607 // Execute the loop symbolically to determine the exit value. 4608 if (BEs.getActiveBits() >= 32) 4609 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4610 4611 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4612 unsigned IterationNum = 0; 4613 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4614 if (IterationNum == NumIterations) 4615 return RetVal = PHIVal; // Got exit value! 4616 4617 // Compute the value of the PHI node for the next iteration. 4618 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4619 if (NextPHI == PHIVal) 4620 return RetVal = NextPHI; // Stopped evolving! 4621 if (NextPHI == 0) 4622 return 0; // Couldn't evaluate! 4623 PHIVal = NextPHI; 4624 } 4625} 4626 4627/// ComputeExitCountExhaustively - If the loop is known to execute a 4628/// constant number of times (the condition evolves only from constants), 4629/// try to evaluate a few iterations of the loop until we get the exit 4630/// condition gets a value of ExitWhen (true or false). If we cannot 4631/// evaluate the trip count of the loop, return getCouldNotCompute(). 4632const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 4633 Value *Cond, 4634 bool ExitWhen) { 4635 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4636 if (PN == 0) return getCouldNotCompute(); 4637 4638 // If the loop is canonicalized, the PHI will have exactly two entries. 4639 // That's the only form we support here. 4640 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4641 4642 // One entry must be a constant (coming in from outside of the loop), and the 4643 // second must be derived from the same PHI. 4644 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4645 Constant *StartCST = 4646 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4647 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4648 4649 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4650 if (getConstantEvolvingPHI(BEValue, L) != PN && 4651 !isa<Constant>(BEValue)) 4652 return getCouldNotCompute(); // Not derived from same PHI. 4653 4654 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4655 // the loop symbolically to determine when the condition gets a value of 4656 // "ExitWhen". 4657 unsigned IterationNum = 0; 4658 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4659 for (Constant *PHIVal = StartCST; 4660 IterationNum != MaxIterations; ++IterationNum) { 4661 ConstantInt *CondVal = 4662 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4663 4664 // Couldn't symbolically evaluate. 4665 if (!CondVal) return getCouldNotCompute(); 4666 4667 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4668 ++NumBruteForceTripCountsComputed; 4669 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4670 } 4671 4672 // Compute the value of the PHI node for the next iteration. 4673 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4674 if (NextPHI == 0 || NextPHI == PHIVal) 4675 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4676 PHIVal = NextPHI; 4677 } 4678 4679 // Too many iterations were needed to evaluate. 4680 return getCouldNotCompute(); 4681} 4682 4683/// getSCEVAtScope - Return a SCEV expression for the specified value 4684/// at the specified scope in the program. The L value specifies a loop 4685/// nest to evaluate the expression at, where null is the top-level or a 4686/// specified loop is immediately inside of the loop. 4687/// 4688/// This method can be used to compute the exit value for a variable defined 4689/// in a loop by querying what the value will hold in the parent loop. 4690/// 4691/// In the case that a relevant loop exit value cannot be computed, the 4692/// original value V is returned. 4693const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4694 // Check to see if we've folded this expression at this loop before. 4695 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4696 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4697 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4698 if (!Pair.second) 4699 return Pair.first->second ? Pair.first->second : V; 4700 4701 // Otherwise compute it. 4702 const SCEV *C = computeSCEVAtScope(V, L); 4703 ValuesAtScopes[V][L] = C; 4704 return C; 4705} 4706 4707const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4708 if (isa<SCEVConstant>(V)) return V; 4709 4710 // If this instruction is evolved from a constant-evolving PHI, compute the 4711 // exit value from the loop without using SCEVs. 4712 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4713 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4714 const Loop *LI = (*this->LI)[I->getParent()]; 4715 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4716 if (PHINode *PN = dyn_cast<PHINode>(I)) 4717 if (PN->getParent() == LI->getHeader()) { 4718 // Okay, there is no closed form solution for the PHI node. Check 4719 // to see if the loop that contains it has a known backedge-taken 4720 // count. If so, we may be able to force computation of the exit 4721 // value. 4722 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4723 if (const SCEVConstant *BTCC = 4724 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4725 // Okay, we know how many times the containing loop executes. If 4726 // this is a constant evolving PHI node, get the final value at 4727 // the specified iteration number. 4728 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4729 BTCC->getValue()->getValue(), 4730 LI); 4731 if (RV) return getSCEV(RV); 4732 } 4733 } 4734 4735 // Okay, this is an expression that we cannot symbolically evaluate 4736 // into a SCEV. Check to see if it's possible to symbolically evaluate 4737 // the arguments into constants, and if so, try to constant propagate the 4738 // result. This is particularly useful for computing loop exit values. 4739 if (CanConstantFold(I)) { 4740 SmallVector<Constant *, 4> Operands; 4741 bool MadeImprovement = false; 4742 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4743 Value *Op = I->getOperand(i); 4744 if (Constant *C = dyn_cast<Constant>(Op)) { 4745 Operands.push_back(C); 4746 continue; 4747 } 4748 4749 // If any of the operands is non-constant and if they are 4750 // non-integer and non-pointer, don't even try to analyze them 4751 // with scev techniques. 4752 if (!isSCEVable(Op->getType())) 4753 return V; 4754 4755 const SCEV *OrigV = getSCEV(Op); 4756 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4757 MadeImprovement |= OrigV != OpV; 4758 4759 Constant *C = 0; 4760 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4761 C = SC->getValue(); 4762 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4763 C = dyn_cast<Constant>(SU->getValue()); 4764 if (!C) return V; 4765 if (C->getType() != Op->getType()) 4766 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4767 Op->getType(), 4768 false), 4769 C, Op->getType()); 4770 Operands.push_back(C); 4771 } 4772 4773 // Check to see if getSCEVAtScope actually made an improvement. 4774 if (MadeImprovement) { 4775 Constant *C = 0; 4776 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4777 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4778 Operands[0], Operands[1], TD); 4779 else 4780 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4781 Operands, TD); 4782 if (!C) return V; 4783 return getSCEV(C); 4784 } 4785 } 4786 } 4787 4788 // This is some other type of SCEVUnknown, just return it. 4789 return V; 4790 } 4791 4792 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4793 // Avoid performing the look-up in the common case where the specified 4794 // expression has no loop-variant portions. 4795 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4796 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4797 if (OpAtScope != Comm->getOperand(i)) { 4798 // Okay, at least one of these operands is loop variant but might be 4799 // foldable. Build a new instance of the folded commutative expression. 4800 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4801 Comm->op_begin()+i); 4802 NewOps.push_back(OpAtScope); 4803 4804 for (++i; i != e; ++i) { 4805 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4806 NewOps.push_back(OpAtScope); 4807 } 4808 if (isa<SCEVAddExpr>(Comm)) 4809 return getAddExpr(NewOps); 4810 if (isa<SCEVMulExpr>(Comm)) 4811 return getMulExpr(NewOps); 4812 if (isa<SCEVSMaxExpr>(Comm)) 4813 return getSMaxExpr(NewOps); 4814 if (isa<SCEVUMaxExpr>(Comm)) 4815 return getUMaxExpr(NewOps); 4816 llvm_unreachable("Unknown commutative SCEV type!"); 4817 } 4818 } 4819 // If we got here, all operands are loop invariant. 4820 return Comm; 4821 } 4822 4823 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4824 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4825 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4826 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4827 return Div; // must be loop invariant 4828 return getUDivExpr(LHS, RHS); 4829 } 4830 4831 // If this is a loop recurrence for a loop that does not contain L, then we 4832 // are dealing with the final value computed by the loop. 4833 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4834 // First, attempt to evaluate each operand. 4835 // Avoid performing the look-up in the common case where the specified 4836 // expression has no loop-variant portions. 4837 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4838 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4839 if (OpAtScope == AddRec->getOperand(i)) 4840 continue; 4841 4842 // Okay, at least one of these operands is loop variant but might be 4843 // foldable. Build a new instance of the folded commutative expression. 4844 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4845 AddRec->op_begin()+i); 4846 NewOps.push_back(OpAtScope); 4847 for (++i; i != e; ++i) 4848 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4849 4850 const SCEV *FoldedRec = 4851 getAddRecExpr(NewOps, AddRec->getLoop(), 4852 AddRec->getNoWrapFlags(SCEV::FlagNW)); 4853 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 4854 // The addrec may be folded to a nonrecurrence, for example, if the 4855 // induction variable is multiplied by zero after constant folding. Go 4856 // ahead and return the folded value. 4857 if (!AddRec) 4858 return FoldedRec; 4859 break; 4860 } 4861 4862 // If the scope is outside the addrec's loop, evaluate it by using the 4863 // loop exit value of the addrec. 4864 if (!AddRec->getLoop()->contains(L)) { 4865 // To evaluate this recurrence, we need to know how many times the AddRec 4866 // loop iterates. Compute this now. 4867 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4868 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4869 4870 // Then, evaluate the AddRec. 4871 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4872 } 4873 4874 return AddRec; 4875 } 4876 4877 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4878 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4879 if (Op == Cast->getOperand()) 4880 return Cast; // must be loop invariant 4881 return getZeroExtendExpr(Op, Cast->getType()); 4882 } 4883 4884 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4885 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4886 if (Op == Cast->getOperand()) 4887 return Cast; // must be loop invariant 4888 return getSignExtendExpr(Op, Cast->getType()); 4889 } 4890 4891 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4892 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4893 if (Op == Cast->getOperand()) 4894 return Cast; // must be loop invariant 4895 return getTruncateExpr(Op, Cast->getType()); 4896 } 4897 4898 llvm_unreachable("Unknown SCEV type!"); 4899 return 0; 4900} 4901 4902/// getSCEVAtScope - This is a convenience function which does 4903/// getSCEVAtScope(getSCEV(V), L). 4904const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4905 return getSCEVAtScope(getSCEV(V), L); 4906} 4907 4908/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4909/// following equation: 4910/// 4911/// A * X = B (mod N) 4912/// 4913/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4914/// A and B isn't important. 4915/// 4916/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4917static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4918 ScalarEvolution &SE) { 4919 uint32_t BW = A.getBitWidth(); 4920 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4921 assert(A != 0 && "A must be non-zero."); 4922 4923 // 1. D = gcd(A, N) 4924 // 4925 // The gcd of A and N may have only one prime factor: 2. The number of 4926 // trailing zeros in A is its multiplicity 4927 uint32_t Mult2 = A.countTrailingZeros(); 4928 // D = 2^Mult2 4929 4930 // 2. Check if B is divisible by D. 4931 // 4932 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4933 // is not less than multiplicity of this prime factor for D. 4934 if (B.countTrailingZeros() < Mult2) 4935 return SE.getCouldNotCompute(); 4936 4937 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4938 // modulo (N / D). 4939 // 4940 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4941 // bit width during computations. 4942 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4943 APInt Mod(BW + 1, 0); 4944 Mod.setBit(BW - Mult2); // Mod = N / D 4945 APInt I = AD.multiplicativeInverse(Mod); 4946 4947 // 4. Compute the minimum unsigned root of the equation: 4948 // I * (B / D) mod (N / D) 4949 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4950 4951 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4952 // bits. 4953 return SE.getConstant(Result.trunc(BW)); 4954} 4955 4956/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4957/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4958/// might be the same) or two SCEVCouldNotCompute objects. 4959/// 4960static std::pair<const SCEV *,const SCEV *> 4961SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4962 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4963 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4964 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4965 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4966 4967 // We currently can only solve this if the coefficients are constants. 4968 if (!LC || !MC || !NC) { 4969 const SCEV *CNC = SE.getCouldNotCompute(); 4970 return std::make_pair(CNC, CNC); 4971 } 4972 4973 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4974 const APInt &L = LC->getValue()->getValue(); 4975 const APInt &M = MC->getValue()->getValue(); 4976 const APInt &N = NC->getValue()->getValue(); 4977 APInt Two(BitWidth, 2); 4978 APInt Four(BitWidth, 4); 4979 4980 { 4981 using namespace APIntOps; 4982 const APInt& C = L; 4983 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4984 // The B coefficient is M-N/2 4985 APInt B(M); 4986 B -= sdiv(N,Two); 4987 4988 // The A coefficient is N/2 4989 APInt A(N.sdiv(Two)); 4990 4991 // Compute the B^2-4ac term. 4992 APInt SqrtTerm(B); 4993 SqrtTerm *= B; 4994 SqrtTerm -= Four * (A * C); 4995 4996 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4997 // integer value or else APInt::sqrt() will assert. 4998 APInt SqrtVal(SqrtTerm.sqrt()); 4999 5000 // Compute the two solutions for the quadratic formula. 5001 // The divisions must be performed as signed divisions. 5002 APInt NegB(-B); 5003 APInt TwoA( A << 1 ); 5004 if (TwoA.isMinValue()) { 5005 const SCEV *CNC = SE.getCouldNotCompute(); 5006 return std::make_pair(CNC, CNC); 5007 } 5008 5009 LLVMContext &Context = SE.getContext(); 5010 5011 ConstantInt *Solution1 = 5012 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 5013 ConstantInt *Solution2 = 5014 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 5015 5016 return std::make_pair(SE.getConstant(Solution1), 5017 SE.getConstant(Solution2)); 5018 } // end APIntOps namespace 5019} 5020 5021/// HowFarToZero - Return the number of times a backedge comparing the specified 5022/// value to zero will execute. If not computable, return CouldNotCompute. 5023/// 5024/// This is only used for loops with a "x != y" exit test. The exit condition is 5025/// now expressed as a single expression, V = x-y. So the exit test is 5026/// effectively V != 0. We know and take advantage of the fact that this 5027/// expression only being used in a comparison by zero context. 5028ScalarEvolution::ExitLimit 5029ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 5030 // If the value is a constant 5031 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5032 // If the value is already zero, the branch will execute zero times. 5033 if (C->getValue()->isZero()) return C; 5034 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5035 } 5036 5037 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 5038 if (!AddRec || AddRec->getLoop() != L) 5039 return getCouldNotCompute(); 5040 5041 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 5042 // the quadratic equation to solve it. 5043 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 5044 std::pair<const SCEV *,const SCEV *> Roots = 5045 SolveQuadraticEquation(AddRec, *this); 5046 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5047 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5048 if (R1 && R2) { 5049#if 0 5050 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 5051 << " sol#2: " << *R2 << "\n"; 5052#endif 5053 // Pick the smallest positive root value. 5054 if (ConstantInt *CB = 5055 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 5056 R1->getValue(), 5057 R2->getValue()))) { 5058 if (CB->getZExtValue() == false) 5059 std::swap(R1, R2); // R1 is the minimum root now. 5060 5061 // We can only use this value if the chrec ends up with an exact zero 5062 // value at this index. When solving for "X*X != 5", for example, we 5063 // should not accept a root of 2. 5064 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 5065 if (Val->isZero()) 5066 return R1; // We found a quadratic root! 5067 } 5068 } 5069 return getCouldNotCompute(); 5070 } 5071 5072 // Otherwise we can only handle this if it is affine. 5073 if (!AddRec->isAffine()) 5074 return getCouldNotCompute(); 5075 5076 // If this is an affine expression, the execution count of this branch is 5077 // the minimum unsigned root of the following equation: 5078 // 5079 // Start + Step*N = 0 (mod 2^BW) 5080 // 5081 // equivalent to: 5082 // 5083 // Step*N = -Start (mod 2^BW) 5084 // 5085 // where BW is the common bit width of Start and Step. 5086 5087 // Get the initial value for the loop. 5088 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 5089 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 5090 5091 // For now we handle only constant steps. 5092 // 5093 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 5094 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 5095 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 5096 // We have not yet seen any such cases. 5097 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 5098 if (StepC == 0) 5099 return getCouldNotCompute(); 5100 5101 // For positive steps (counting up until unsigned overflow): 5102 // N = -Start/Step (as unsigned) 5103 // For negative steps (counting down to zero): 5104 // N = Start/-Step 5105 // First compute the unsigned distance from zero in the direction of Step. 5106 bool CountDown = StepC->getValue()->getValue().isNegative(); 5107 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 5108 5109 // Handle unitary steps, which cannot wraparound. 5110 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 5111 // N = Distance (as unsigned) 5112 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) 5113 return Distance; 5114 5115 // If the recurrence is known not to wraparound, unsigned divide computes the 5116 // back edge count. We know that the value will either become zero (and thus 5117 // the loop terminates), that the loop will terminate through some other exit 5118 // condition first, or that the loop has undefined behavior. This means 5119 // we can't "miss" the exit value, even with nonunit stride. 5120 // 5121 // FIXME: Prove that loops always exhibits *acceptable* undefined 5122 // behavior. Loops must exhibit defined behavior until a wrapped value is 5123 // actually used. So the trip count computed by udiv could be smaller than the 5124 // number of well-defined iterations. 5125 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) 5126 // FIXME: We really want an "isexact" bit for udiv. 5127 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 5128 5129 // Then, try to solve the above equation provided that Start is constant. 5130 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 5131 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 5132 -StartC->getValue()->getValue(), 5133 *this); 5134 return getCouldNotCompute(); 5135} 5136 5137/// HowFarToNonZero - Return the number of times a backedge checking the 5138/// specified value for nonzero will execute. If not computable, return 5139/// CouldNotCompute 5140ScalarEvolution::ExitLimit 5141ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 5142 // Loops that look like: while (X == 0) are very strange indeed. We don't 5143 // handle them yet except for the trivial case. This could be expanded in the 5144 // future as needed. 5145 5146 // If the value is a constant, check to see if it is known to be non-zero 5147 // already. If so, the backedge will execute zero times. 5148 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5149 if (!C->getValue()->isNullValue()) 5150 return getConstant(C->getType(), 0); 5151 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5152 } 5153 5154 // We could implement others, but I really doubt anyone writes loops like 5155 // this, and if they did, they would already be constant folded. 5156 return getCouldNotCompute(); 5157} 5158 5159/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5160/// (which may not be an immediate predecessor) which has exactly one 5161/// successor from which BB is reachable, or null if no such block is 5162/// found. 5163/// 5164std::pair<BasicBlock *, BasicBlock *> 5165ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5166 // If the block has a unique predecessor, then there is no path from the 5167 // predecessor to the block that does not go through the direct edge 5168 // from the predecessor to the block. 5169 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5170 return std::make_pair(Pred, BB); 5171 5172 // A loop's header is defined to be a block that dominates the loop. 5173 // If the header has a unique predecessor outside the loop, it must be 5174 // a block that has exactly one successor that can reach the loop. 5175 if (Loop *L = LI->getLoopFor(BB)) 5176 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5177 5178 return std::pair<BasicBlock *, BasicBlock *>(); 5179} 5180 5181/// HasSameValue - SCEV structural equivalence is usually sufficient for 5182/// testing whether two expressions are equal, however for the purposes of 5183/// looking for a condition guarding a loop, it can be useful to be a little 5184/// more general, since a front-end may have replicated the controlling 5185/// expression. 5186/// 5187static bool HasSameValue(const SCEV *A, const SCEV *B) { 5188 // Quick check to see if they are the same SCEV. 5189 if (A == B) return true; 5190 5191 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5192 // two different instructions with the same value. Check for this case. 5193 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5194 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5195 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5196 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5197 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5198 return true; 5199 5200 // Otherwise assume they may have a different value. 5201 return false; 5202} 5203 5204/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5205/// predicate Pred. Return true iff any changes were made. 5206/// 5207bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5208 const SCEV *&LHS, const SCEV *&RHS) { 5209 bool Changed = false; 5210 5211 // Canonicalize a constant to the right side. 5212 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5213 // Check for both operands constant. 5214 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5215 if (ConstantExpr::getICmp(Pred, 5216 LHSC->getValue(), 5217 RHSC->getValue())->isNullValue()) 5218 goto trivially_false; 5219 else 5220 goto trivially_true; 5221 } 5222 // Otherwise swap the operands to put the constant on the right. 5223 std::swap(LHS, RHS); 5224 Pred = ICmpInst::getSwappedPredicate(Pred); 5225 Changed = true; 5226 } 5227 5228 // If we're comparing an addrec with a value which is loop-invariant in the 5229 // addrec's loop, put the addrec on the left. Also make a dominance check, 5230 // as both operands could be addrecs loop-invariant in each other's loop. 5231 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5232 const Loop *L = AR->getLoop(); 5233 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5234 std::swap(LHS, RHS); 5235 Pred = ICmpInst::getSwappedPredicate(Pred); 5236 Changed = true; 5237 } 5238 } 5239 5240 // If there's a constant operand, canonicalize comparisons with boundary 5241 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5242 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5243 const APInt &RA = RC->getValue()->getValue(); 5244 switch (Pred) { 5245 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5246 case ICmpInst::ICMP_EQ: 5247 case ICmpInst::ICMP_NE: 5248 break; 5249 case ICmpInst::ICMP_UGE: 5250 if ((RA - 1).isMinValue()) { 5251 Pred = ICmpInst::ICMP_NE; 5252 RHS = getConstant(RA - 1); 5253 Changed = true; 5254 break; 5255 } 5256 if (RA.isMaxValue()) { 5257 Pred = ICmpInst::ICMP_EQ; 5258 Changed = true; 5259 break; 5260 } 5261 if (RA.isMinValue()) goto trivially_true; 5262 5263 Pred = ICmpInst::ICMP_UGT; 5264 RHS = getConstant(RA - 1); 5265 Changed = true; 5266 break; 5267 case ICmpInst::ICMP_ULE: 5268 if ((RA + 1).isMaxValue()) { 5269 Pred = ICmpInst::ICMP_NE; 5270 RHS = getConstant(RA + 1); 5271 Changed = true; 5272 break; 5273 } 5274 if (RA.isMinValue()) { 5275 Pred = ICmpInst::ICMP_EQ; 5276 Changed = true; 5277 break; 5278 } 5279 if (RA.isMaxValue()) goto trivially_true; 5280 5281 Pred = ICmpInst::ICMP_ULT; 5282 RHS = getConstant(RA + 1); 5283 Changed = true; 5284 break; 5285 case ICmpInst::ICMP_SGE: 5286 if ((RA - 1).isMinSignedValue()) { 5287 Pred = ICmpInst::ICMP_NE; 5288 RHS = getConstant(RA - 1); 5289 Changed = true; 5290 break; 5291 } 5292 if (RA.isMaxSignedValue()) { 5293 Pred = ICmpInst::ICMP_EQ; 5294 Changed = true; 5295 break; 5296 } 5297 if (RA.isMinSignedValue()) goto trivially_true; 5298 5299 Pred = ICmpInst::ICMP_SGT; 5300 RHS = getConstant(RA - 1); 5301 Changed = true; 5302 break; 5303 case ICmpInst::ICMP_SLE: 5304 if ((RA + 1).isMaxSignedValue()) { 5305 Pred = ICmpInst::ICMP_NE; 5306 RHS = getConstant(RA + 1); 5307 Changed = true; 5308 break; 5309 } 5310 if (RA.isMinSignedValue()) { 5311 Pred = ICmpInst::ICMP_EQ; 5312 Changed = true; 5313 break; 5314 } 5315 if (RA.isMaxSignedValue()) goto trivially_true; 5316 5317 Pred = ICmpInst::ICMP_SLT; 5318 RHS = getConstant(RA + 1); 5319 Changed = true; 5320 break; 5321 case ICmpInst::ICMP_UGT: 5322 if (RA.isMinValue()) { 5323 Pred = ICmpInst::ICMP_NE; 5324 Changed = true; 5325 break; 5326 } 5327 if ((RA + 1).isMaxValue()) { 5328 Pred = ICmpInst::ICMP_EQ; 5329 RHS = getConstant(RA + 1); 5330 Changed = true; 5331 break; 5332 } 5333 if (RA.isMaxValue()) goto trivially_false; 5334 break; 5335 case ICmpInst::ICMP_ULT: 5336 if (RA.isMaxValue()) { 5337 Pred = ICmpInst::ICMP_NE; 5338 Changed = true; 5339 break; 5340 } 5341 if ((RA - 1).isMinValue()) { 5342 Pred = ICmpInst::ICMP_EQ; 5343 RHS = getConstant(RA - 1); 5344 Changed = true; 5345 break; 5346 } 5347 if (RA.isMinValue()) goto trivially_false; 5348 break; 5349 case ICmpInst::ICMP_SGT: 5350 if (RA.isMinSignedValue()) { 5351 Pred = ICmpInst::ICMP_NE; 5352 Changed = true; 5353 break; 5354 } 5355 if ((RA + 1).isMaxSignedValue()) { 5356 Pred = ICmpInst::ICMP_EQ; 5357 RHS = getConstant(RA + 1); 5358 Changed = true; 5359 break; 5360 } 5361 if (RA.isMaxSignedValue()) goto trivially_false; 5362 break; 5363 case ICmpInst::ICMP_SLT: 5364 if (RA.isMaxSignedValue()) { 5365 Pred = ICmpInst::ICMP_NE; 5366 Changed = true; 5367 break; 5368 } 5369 if ((RA - 1).isMinSignedValue()) { 5370 Pred = ICmpInst::ICMP_EQ; 5371 RHS = getConstant(RA - 1); 5372 Changed = true; 5373 break; 5374 } 5375 if (RA.isMinSignedValue()) goto trivially_false; 5376 break; 5377 } 5378 } 5379 5380 // Check for obvious equality. 5381 if (HasSameValue(LHS, RHS)) { 5382 if (ICmpInst::isTrueWhenEqual(Pred)) 5383 goto trivially_true; 5384 if (ICmpInst::isFalseWhenEqual(Pred)) 5385 goto trivially_false; 5386 } 5387 5388 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5389 // adding or subtracting 1 from one of the operands. 5390 switch (Pred) { 5391 case ICmpInst::ICMP_SLE: 5392 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5393 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5394 SCEV::FlagNSW); 5395 Pred = ICmpInst::ICMP_SLT; 5396 Changed = true; 5397 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5398 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5399 SCEV::FlagNSW); 5400 Pred = ICmpInst::ICMP_SLT; 5401 Changed = true; 5402 } 5403 break; 5404 case ICmpInst::ICMP_SGE: 5405 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5406 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5407 SCEV::FlagNSW); 5408 Pred = ICmpInst::ICMP_SGT; 5409 Changed = true; 5410 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5411 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5412 SCEV::FlagNSW); 5413 Pred = ICmpInst::ICMP_SGT; 5414 Changed = true; 5415 } 5416 break; 5417 case ICmpInst::ICMP_ULE: 5418 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5419 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5420 SCEV::FlagNUW); 5421 Pred = ICmpInst::ICMP_ULT; 5422 Changed = true; 5423 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5424 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5425 SCEV::FlagNUW); 5426 Pred = ICmpInst::ICMP_ULT; 5427 Changed = true; 5428 } 5429 break; 5430 case ICmpInst::ICMP_UGE: 5431 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5432 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5433 SCEV::FlagNUW); 5434 Pred = ICmpInst::ICMP_UGT; 5435 Changed = true; 5436 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5437 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5438 SCEV::FlagNUW); 5439 Pred = ICmpInst::ICMP_UGT; 5440 Changed = true; 5441 } 5442 break; 5443 default: 5444 break; 5445 } 5446 5447 // TODO: More simplifications are possible here. 5448 5449 return Changed; 5450 5451trivially_true: 5452 // Return 0 == 0. 5453 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5454 Pred = ICmpInst::ICMP_EQ; 5455 return true; 5456 5457trivially_false: 5458 // Return 0 != 0. 5459 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5460 Pred = ICmpInst::ICMP_NE; 5461 return true; 5462} 5463 5464bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5465 return getSignedRange(S).getSignedMax().isNegative(); 5466} 5467 5468bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5469 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5470} 5471 5472bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5473 return !getSignedRange(S).getSignedMin().isNegative(); 5474} 5475 5476bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5477 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5478} 5479 5480bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5481 return isKnownNegative(S) || isKnownPositive(S); 5482} 5483 5484bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5485 const SCEV *LHS, const SCEV *RHS) { 5486 // Canonicalize the inputs first. 5487 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5488 5489 // If LHS or RHS is an addrec, check to see if the condition is true in 5490 // every iteration of the loop. 5491 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5492 if (isLoopEntryGuardedByCond( 5493 AR->getLoop(), Pred, AR->getStart(), RHS) && 5494 isLoopBackedgeGuardedByCond( 5495 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5496 return true; 5497 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5498 if (isLoopEntryGuardedByCond( 5499 AR->getLoop(), Pred, LHS, AR->getStart()) && 5500 isLoopBackedgeGuardedByCond( 5501 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5502 return true; 5503 5504 // Otherwise see what can be done with known constant ranges. 5505 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5506} 5507 5508bool 5509ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5510 const SCEV *LHS, const SCEV *RHS) { 5511 if (HasSameValue(LHS, RHS)) 5512 return ICmpInst::isTrueWhenEqual(Pred); 5513 5514 // This code is split out from isKnownPredicate because it is called from 5515 // within isLoopEntryGuardedByCond. 5516 switch (Pred) { 5517 default: 5518 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5519 break; 5520 case ICmpInst::ICMP_SGT: 5521 Pred = ICmpInst::ICMP_SLT; 5522 std::swap(LHS, RHS); 5523 case ICmpInst::ICMP_SLT: { 5524 ConstantRange LHSRange = getSignedRange(LHS); 5525 ConstantRange RHSRange = getSignedRange(RHS); 5526 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5527 return true; 5528 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5529 return false; 5530 break; 5531 } 5532 case ICmpInst::ICMP_SGE: 5533 Pred = ICmpInst::ICMP_SLE; 5534 std::swap(LHS, RHS); 5535 case ICmpInst::ICMP_SLE: { 5536 ConstantRange LHSRange = getSignedRange(LHS); 5537 ConstantRange RHSRange = getSignedRange(RHS); 5538 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5539 return true; 5540 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5541 return false; 5542 break; 5543 } 5544 case ICmpInst::ICMP_UGT: 5545 Pred = ICmpInst::ICMP_ULT; 5546 std::swap(LHS, RHS); 5547 case ICmpInst::ICMP_ULT: { 5548 ConstantRange LHSRange = getUnsignedRange(LHS); 5549 ConstantRange RHSRange = getUnsignedRange(RHS); 5550 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5551 return true; 5552 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5553 return false; 5554 break; 5555 } 5556 case ICmpInst::ICMP_UGE: 5557 Pred = ICmpInst::ICMP_ULE; 5558 std::swap(LHS, RHS); 5559 case ICmpInst::ICMP_ULE: { 5560 ConstantRange LHSRange = getUnsignedRange(LHS); 5561 ConstantRange RHSRange = getUnsignedRange(RHS); 5562 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5563 return true; 5564 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5565 return false; 5566 break; 5567 } 5568 case ICmpInst::ICMP_NE: { 5569 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5570 return true; 5571 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5572 return true; 5573 5574 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5575 if (isKnownNonZero(Diff)) 5576 return true; 5577 break; 5578 } 5579 case ICmpInst::ICMP_EQ: 5580 // The check at the top of the function catches the case where 5581 // the values are known to be equal. 5582 break; 5583 } 5584 return false; 5585} 5586 5587/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5588/// protected by a conditional between LHS and RHS. This is used to 5589/// to eliminate casts. 5590bool 5591ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5592 ICmpInst::Predicate Pred, 5593 const SCEV *LHS, const SCEV *RHS) { 5594 // Interpret a null as meaning no loop, where there is obviously no guard 5595 // (interprocedural conditions notwithstanding). 5596 if (!L) return true; 5597 5598 BasicBlock *Latch = L->getLoopLatch(); 5599 if (!Latch) 5600 return false; 5601 5602 BranchInst *LoopContinuePredicate = 5603 dyn_cast<BranchInst>(Latch->getTerminator()); 5604 if (!LoopContinuePredicate || 5605 LoopContinuePredicate->isUnconditional()) 5606 return false; 5607 5608 return isImpliedCond(Pred, LHS, RHS, 5609 LoopContinuePredicate->getCondition(), 5610 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5611} 5612 5613/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5614/// by a conditional between LHS and RHS. This is used to help avoid max 5615/// expressions in loop trip counts, and to eliminate casts. 5616bool 5617ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5618 ICmpInst::Predicate Pred, 5619 const SCEV *LHS, const SCEV *RHS) { 5620 // Interpret a null as meaning no loop, where there is obviously no guard 5621 // (interprocedural conditions notwithstanding). 5622 if (!L) return false; 5623 5624 // Starting at the loop predecessor, climb up the predecessor chain, as long 5625 // as there are predecessors that can be found that have unique successors 5626 // leading to the original header. 5627 for (std::pair<BasicBlock *, BasicBlock *> 5628 Pair(L->getLoopPredecessor(), L->getHeader()); 5629 Pair.first; 5630 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5631 5632 BranchInst *LoopEntryPredicate = 5633 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5634 if (!LoopEntryPredicate || 5635 LoopEntryPredicate->isUnconditional()) 5636 continue; 5637 5638 if (isImpliedCond(Pred, LHS, RHS, 5639 LoopEntryPredicate->getCondition(), 5640 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5641 return true; 5642 } 5643 5644 return false; 5645} 5646 5647/// isImpliedCond - Test whether the condition described by Pred, LHS, 5648/// and RHS is true whenever the given Cond value evaluates to true. 5649bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5650 const SCEV *LHS, const SCEV *RHS, 5651 Value *FoundCondValue, 5652 bool Inverse) { 5653 // Recursively handle And and Or conditions. 5654 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5655 if (BO->getOpcode() == Instruction::And) { 5656 if (!Inverse) 5657 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5658 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5659 } else if (BO->getOpcode() == Instruction::Or) { 5660 if (Inverse) 5661 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5662 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5663 } 5664 } 5665 5666 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5667 if (!ICI) return false; 5668 5669 // Bail if the ICmp's operands' types are wider than the needed type 5670 // before attempting to call getSCEV on them. This avoids infinite 5671 // recursion, since the analysis of widening casts can require loop 5672 // exit condition information for overflow checking, which would 5673 // lead back here. 5674 if (getTypeSizeInBits(LHS->getType()) < 5675 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5676 return false; 5677 5678 // Now that we found a conditional branch that dominates the loop, check to 5679 // see if it is the comparison we are looking for. 5680 ICmpInst::Predicate FoundPred; 5681 if (Inverse) 5682 FoundPred = ICI->getInversePredicate(); 5683 else 5684 FoundPred = ICI->getPredicate(); 5685 5686 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5687 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5688 5689 // Balance the types. The case where FoundLHS' type is wider than 5690 // LHS' type is checked for above. 5691 if (getTypeSizeInBits(LHS->getType()) > 5692 getTypeSizeInBits(FoundLHS->getType())) { 5693 if (CmpInst::isSigned(Pred)) { 5694 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5695 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5696 } else { 5697 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5698 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5699 } 5700 } 5701 5702 // Canonicalize the query to match the way instcombine will have 5703 // canonicalized the comparison. 5704 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5705 if (LHS == RHS) 5706 return CmpInst::isTrueWhenEqual(Pred); 5707 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5708 if (FoundLHS == FoundRHS) 5709 return CmpInst::isFalseWhenEqual(Pred); 5710 5711 // Check to see if we can make the LHS or RHS match. 5712 if (LHS == FoundRHS || RHS == FoundLHS) { 5713 if (isa<SCEVConstant>(RHS)) { 5714 std::swap(FoundLHS, FoundRHS); 5715 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5716 } else { 5717 std::swap(LHS, RHS); 5718 Pred = ICmpInst::getSwappedPredicate(Pred); 5719 } 5720 } 5721 5722 // Check whether the found predicate is the same as the desired predicate. 5723 if (FoundPred == Pred) 5724 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5725 5726 // Check whether swapping the found predicate makes it the same as the 5727 // desired predicate. 5728 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5729 if (isa<SCEVConstant>(RHS)) 5730 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5731 else 5732 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5733 RHS, LHS, FoundLHS, FoundRHS); 5734 } 5735 5736 // Check whether the actual condition is beyond sufficient. 5737 if (FoundPred == ICmpInst::ICMP_EQ) 5738 if (ICmpInst::isTrueWhenEqual(Pred)) 5739 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5740 return true; 5741 if (Pred == ICmpInst::ICMP_NE) 5742 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5743 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5744 return true; 5745 5746 // Otherwise assume the worst. 5747 return false; 5748} 5749 5750/// isImpliedCondOperands - Test whether the condition described by Pred, 5751/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5752/// and FoundRHS is true. 5753bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5754 const SCEV *LHS, const SCEV *RHS, 5755 const SCEV *FoundLHS, 5756 const SCEV *FoundRHS) { 5757 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5758 FoundLHS, FoundRHS) || 5759 // ~x < ~y --> x > y 5760 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5761 getNotSCEV(FoundRHS), 5762 getNotSCEV(FoundLHS)); 5763} 5764 5765/// isImpliedCondOperandsHelper - Test whether the condition described by 5766/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5767/// FoundLHS, and FoundRHS is true. 5768bool 5769ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5770 const SCEV *LHS, const SCEV *RHS, 5771 const SCEV *FoundLHS, 5772 const SCEV *FoundRHS) { 5773 switch (Pred) { 5774 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5775 case ICmpInst::ICMP_EQ: 5776 case ICmpInst::ICMP_NE: 5777 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5778 return true; 5779 break; 5780 case ICmpInst::ICMP_SLT: 5781 case ICmpInst::ICMP_SLE: 5782 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5783 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5784 return true; 5785 break; 5786 case ICmpInst::ICMP_SGT: 5787 case ICmpInst::ICMP_SGE: 5788 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5789 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5790 return true; 5791 break; 5792 case ICmpInst::ICMP_ULT: 5793 case ICmpInst::ICMP_ULE: 5794 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5795 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5796 return true; 5797 break; 5798 case ICmpInst::ICMP_UGT: 5799 case ICmpInst::ICMP_UGE: 5800 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5801 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5802 return true; 5803 break; 5804 } 5805 5806 return false; 5807} 5808 5809/// getBECount - Subtract the end and start values and divide by the step, 5810/// rounding up, to get the number of times the backedge is executed. Return 5811/// CouldNotCompute if an intermediate computation overflows. 5812const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5813 const SCEV *End, 5814 const SCEV *Step, 5815 bool NoWrap) { 5816 assert(!isKnownNegative(Step) && 5817 "This code doesn't handle negative strides yet!"); 5818 5819 Type *Ty = Start->getType(); 5820 5821 // When Start == End, we have an exact BECount == 0. Short-circuit this case 5822 // here because SCEV may not be able to determine that the unsigned division 5823 // after rounding is zero. 5824 if (Start == End) 5825 return getConstant(Ty, 0); 5826 5827 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5828 const SCEV *Diff = getMinusSCEV(End, Start); 5829 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5830 5831 // Add an adjustment to the difference between End and Start so that 5832 // the division will effectively round up. 5833 const SCEV *Add = getAddExpr(Diff, RoundUp); 5834 5835 if (!NoWrap) { 5836 // Check Add for unsigned overflow. 5837 // TODO: More sophisticated things could be done here. 5838 Type *WideTy = IntegerType::get(getContext(), 5839 getTypeSizeInBits(Ty) + 1); 5840 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5841 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5842 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5843 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5844 return getCouldNotCompute(); 5845 } 5846 5847 return getUDivExpr(Add, Step); 5848} 5849 5850/// HowManyLessThans - Return the number of times a backedge containing the 5851/// specified less-than comparison will execute. If not computable, return 5852/// CouldNotCompute. 5853ScalarEvolution::ExitLimit 5854ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5855 const Loop *L, bool isSigned) { 5856 // Only handle: "ADDREC < LoopInvariant". 5857 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5858 5859 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5860 if (!AddRec || AddRec->getLoop() != L) 5861 return getCouldNotCompute(); 5862 5863 // Check to see if we have a flag which makes analysis easy. 5864 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) : 5865 AddRec->getNoWrapFlags(SCEV::FlagNUW); 5866 5867 if (AddRec->isAffine()) { 5868 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5869 const SCEV *Step = AddRec->getStepRecurrence(*this); 5870 5871 if (Step->isZero()) 5872 return getCouldNotCompute(); 5873 if (Step->isOne()) { 5874 // With unit stride, the iteration never steps past the limit value. 5875 } else if (isKnownPositive(Step)) { 5876 // Test whether a positive iteration can step past the limit 5877 // value and past the maximum value for its type in a single step. 5878 // Note that it's not sufficient to check NoWrap here, because even 5879 // though the value after a wrap is undefined, it's not undefined 5880 // behavior, so if wrap does occur, the loop could either terminate or 5881 // loop infinitely, but in either case, the loop is guaranteed to 5882 // iterate at least until the iteration where the wrapping occurs. 5883 const SCEV *One = getConstant(Step->getType(), 1); 5884 if (isSigned) { 5885 APInt Max = APInt::getSignedMaxValue(BitWidth); 5886 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5887 .slt(getSignedRange(RHS).getSignedMax())) 5888 return getCouldNotCompute(); 5889 } else { 5890 APInt Max = APInt::getMaxValue(BitWidth); 5891 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5892 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5893 return getCouldNotCompute(); 5894 } 5895 } else 5896 // TODO: Handle negative strides here and below. 5897 return getCouldNotCompute(); 5898 5899 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5900 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5901 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5902 // treat m-n as signed nor unsigned due to overflow possibility. 5903 5904 // First, we get the value of the LHS in the first iteration: n 5905 const SCEV *Start = AddRec->getOperand(0); 5906 5907 // Determine the minimum constant start value. 5908 const SCEV *MinStart = getConstant(isSigned ? 5909 getSignedRange(Start).getSignedMin() : 5910 getUnsignedRange(Start).getUnsignedMin()); 5911 5912 // If we know that the condition is true in order to enter the loop, 5913 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5914 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5915 // the division must round up. 5916 const SCEV *End = RHS; 5917 if (!isLoopEntryGuardedByCond(L, 5918 isSigned ? ICmpInst::ICMP_SLT : 5919 ICmpInst::ICMP_ULT, 5920 getMinusSCEV(Start, Step), RHS)) 5921 End = isSigned ? getSMaxExpr(RHS, Start) 5922 : getUMaxExpr(RHS, Start); 5923 5924 // Determine the maximum constant end value. 5925 const SCEV *MaxEnd = getConstant(isSigned ? 5926 getSignedRange(End).getSignedMax() : 5927 getUnsignedRange(End).getUnsignedMax()); 5928 5929 // If MaxEnd is within a step of the maximum integer value in its type, 5930 // adjust it down to the minimum value which would produce the same effect. 5931 // This allows the subsequent ceiling division of (N+(step-1))/step to 5932 // compute the correct value. 5933 const SCEV *StepMinusOne = getMinusSCEV(Step, 5934 getConstant(Step->getType(), 1)); 5935 MaxEnd = isSigned ? 5936 getSMinExpr(MaxEnd, 5937 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5938 StepMinusOne)) : 5939 getUMinExpr(MaxEnd, 5940 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5941 StepMinusOne)); 5942 5943 // Finally, we subtract these two values and divide, rounding up, to get 5944 // the number of times the backedge is executed. 5945 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5946 5947 // The maximum backedge count is similar, except using the minimum start 5948 // value and the maximum end value. 5949 // If we already have an exact constant BECount, use it instead. 5950 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 5951 : getBECount(MinStart, MaxEnd, Step, NoWrap); 5952 5953 // If the stride is nonconstant, and NoWrap == true, then 5954 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 5955 // exact BECount and invalid MaxBECount, which should be avoided to catch 5956 // more optimization opportunities. 5957 if (isa<SCEVCouldNotCompute>(MaxBECount)) 5958 MaxBECount = BECount; 5959 5960 return ExitLimit(BECount, MaxBECount); 5961 } 5962 5963 return getCouldNotCompute(); 5964} 5965 5966/// getNumIterationsInRange - Return the number of iterations of this loop that 5967/// produce values in the specified constant range. Another way of looking at 5968/// this is that it returns the first iteration number where the value is not in 5969/// the condition, thus computing the exit count. If the iteration count can't 5970/// be computed, an instance of SCEVCouldNotCompute is returned. 5971const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5972 ScalarEvolution &SE) const { 5973 if (Range.isFullSet()) // Infinite loop. 5974 return SE.getCouldNotCompute(); 5975 5976 // If the start is a non-zero constant, shift the range to simplify things. 5977 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5978 if (!SC->getValue()->isZero()) { 5979 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5980 Operands[0] = SE.getConstant(SC->getType(), 0); 5981 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 5982 getNoWrapFlags(FlagNW)); 5983 if (const SCEVAddRecExpr *ShiftedAddRec = 5984 dyn_cast<SCEVAddRecExpr>(Shifted)) 5985 return ShiftedAddRec->getNumIterationsInRange( 5986 Range.subtract(SC->getValue()->getValue()), SE); 5987 // This is strange and shouldn't happen. 5988 return SE.getCouldNotCompute(); 5989 } 5990 5991 // The only time we can solve this is when we have all constant indices. 5992 // Otherwise, we cannot determine the overflow conditions. 5993 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5994 if (!isa<SCEVConstant>(getOperand(i))) 5995 return SE.getCouldNotCompute(); 5996 5997 5998 // Okay at this point we know that all elements of the chrec are constants and 5999 // that the start element is zero. 6000 6001 // First check to see if the range contains zero. If not, the first 6002 // iteration exits. 6003 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 6004 if (!Range.contains(APInt(BitWidth, 0))) 6005 return SE.getConstant(getType(), 0); 6006 6007 if (isAffine()) { 6008 // If this is an affine expression then we have this situation: 6009 // Solve {0,+,A} in Range === Ax in Range 6010 6011 // We know that zero is in the range. If A is positive then we know that 6012 // the upper value of the range must be the first possible exit value. 6013 // If A is negative then the lower of the range is the last possible loop 6014 // value. Also note that we already checked for a full range. 6015 APInt One(BitWidth,1); 6016 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 6017 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 6018 6019 // The exit value should be (End+A)/A. 6020 APInt ExitVal = (End + A).udiv(A); 6021 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 6022 6023 // Evaluate at the exit value. If we really did fall out of the valid 6024 // range, then we computed our trip count, otherwise wrap around or other 6025 // things must have happened. 6026 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 6027 if (Range.contains(Val->getValue())) 6028 return SE.getCouldNotCompute(); // Something strange happened 6029 6030 // Ensure that the previous value is in the range. This is a sanity check. 6031 assert(Range.contains( 6032 EvaluateConstantChrecAtConstant(this, 6033 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 6034 "Linear scev computation is off in a bad way!"); 6035 return SE.getConstant(ExitValue); 6036 } else if (isQuadratic()) { 6037 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 6038 // quadratic equation to solve it. To do this, we must frame our problem in 6039 // terms of figuring out when zero is crossed, instead of when 6040 // Range.getUpper() is crossed. 6041 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 6042 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 6043 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 6044 // getNoWrapFlags(FlagNW) 6045 FlagAnyWrap); 6046 6047 // Next, solve the constructed addrec 6048 std::pair<const SCEV *,const SCEV *> Roots = 6049 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 6050 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6051 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6052 if (R1) { 6053 // Pick the smallest positive root value. 6054 if (ConstantInt *CB = 6055 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 6056 R1->getValue(), R2->getValue()))) { 6057 if (CB->getZExtValue() == false) 6058 std::swap(R1, R2); // R1 is the minimum root now. 6059 6060 // Make sure the root is not off by one. The returned iteration should 6061 // not be in the range, but the previous one should be. When solving 6062 // for "X*X < 5", for example, we should not return a root of 2. 6063 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 6064 R1->getValue(), 6065 SE); 6066 if (Range.contains(R1Val->getValue())) { 6067 // The next iteration must be out of the range... 6068 ConstantInt *NextVal = 6069 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 6070 6071 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6072 if (!Range.contains(R1Val->getValue())) 6073 return SE.getConstant(NextVal); 6074 return SE.getCouldNotCompute(); // Something strange happened 6075 } 6076 6077 // If R1 was not in the range, then it is a good return value. Make 6078 // sure that R1-1 WAS in the range though, just in case. 6079 ConstantInt *NextVal = 6080 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 6081 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6082 if (Range.contains(R1Val->getValue())) 6083 return R1; 6084 return SE.getCouldNotCompute(); // Something strange happened 6085 } 6086 } 6087 } 6088 6089 return SE.getCouldNotCompute(); 6090} 6091 6092 6093 6094//===----------------------------------------------------------------------===// 6095// SCEVCallbackVH Class Implementation 6096//===----------------------------------------------------------------------===// 6097 6098void ScalarEvolution::SCEVCallbackVH::deleted() { 6099 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6100 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 6101 SE->ConstantEvolutionLoopExitValue.erase(PN); 6102 SE->ValueExprMap.erase(getValPtr()); 6103 // this now dangles! 6104} 6105 6106void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 6107 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6108 6109 // Forget all the expressions associated with users of the old value, 6110 // so that future queries will recompute the expressions using the new 6111 // value. 6112 Value *Old = getValPtr(); 6113 SmallVector<User *, 16> Worklist; 6114 SmallPtrSet<User *, 8> Visited; 6115 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 6116 UI != UE; ++UI) 6117 Worklist.push_back(*UI); 6118 while (!Worklist.empty()) { 6119 User *U = Worklist.pop_back_val(); 6120 // Deleting the Old value will cause this to dangle. Postpone 6121 // that until everything else is done. 6122 if (U == Old) 6123 continue; 6124 if (!Visited.insert(U)) 6125 continue; 6126 if (PHINode *PN = dyn_cast<PHINode>(U)) 6127 SE->ConstantEvolutionLoopExitValue.erase(PN); 6128 SE->ValueExprMap.erase(U); 6129 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 6130 UI != UE; ++UI) 6131 Worklist.push_back(*UI); 6132 } 6133 // Delete the Old value. 6134 if (PHINode *PN = dyn_cast<PHINode>(Old)) 6135 SE->ConstantEvolutionLoopExitValue.erase(PN); 6136 SE->ValueExprMap.erase(Old); 6137 // this now dangles! 6138} 6139 6140ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 6141 : CallbackVH(V), SE(se) {} 6142 6143//===----------------------------------------------------------------------===// 6144// ScalarEvolution Class Implementation 6145//===----------------------------------------------------------------------===// 6146 6147ScalarEvolution::ScalarEvolution() 6148 : FunctionPass(ID), FirstUnknown(0) { 6149 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 6150} 6151 6152bool ScalarEvolution::runOnFunction(Function &F) { 6153 this->F = &F; 6154 LI = &getAnalysis<LoopInfo>(); 6155 TD = getAnalysisIfAvailable<TargetData>(); 6156 DT = &getAnalysis<DominatorTree>(); 6157 return false; 6158} 6159 6160void ScalarEvolution::releaseMemory() { 6161 // Iterate through all the SCEVUnknown instances and call their 6162 // destructors, so that they release their references to their values. 6163 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6164 U->~SCEVUnknown(); 6165 FirstUnknown = 0; 6166 6167 ValueExprMap.clear(); 6168 6169 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 6170 // that a loop had multiple computable exits. 6171 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 6172 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 6173 I != E; ++I) { 6174 I->second.clear(); 6175 } 6176 6177 BackedgeTakenCounts.clear(); 6178 ConstantEvolutionLoopExitValue.clear(); 6179 ValuesAtScopes.clear(); 6180 LoopDispositions.clear(); 6181 BlockDispositions.clear(); 6182 UnsignedRanges.clear(); 6183 SignedRanges.clear(); 6184 UniqueSCEVs.clear(); 6185 SCEVAllocator.Reset(); 6186} 6187 6188void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6189 AU.setPreservesAll(); 6190 AU.addRequiredTransitive<LoopInfo>(); 6191 AU.addRequiredTransitive<DominatorTree>(); 6192} 6193 6194bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6195 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6196} 6197 6198static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6199 const Loop *L) { 6200 // Print all inner loops first 6201 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6202 PrintLoopInfo(OS, SE, *I); 6203 6204 OS << "Loop "; 6205 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6206 OS << ": "; 6207 6208 SmallVector<BasicBlock *, 8> ExitBlocks; 6209 L->getExitBlocks(ExitBlocks); 6210 if (ExitBlocks.size() != 1) 6211 OS << "<multiple exits> "; 6212 6213 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6214 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6215 } else { 6216 OS << "Unpredictable backedge-taken count. "; 6217 } 6218 6219 OS << "\n" 6220 "Loop "; 6221 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6222 OS << ": "; 6223 6224 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6225 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6226 } else { 6227 OS << "Unpredictable max backedge-taken count. "; 6228 } 6229 6230 OS << "\n"; 6231} 6232 6233void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6234 // ScalarEvolution's implementation of the print method is to print 6235 // out SCEV values of all instructions that are interesting. Doing 6236 // this potentially causes it to create new SCEV objects though, 6237 // which technically conflicts with the const qualifier. This isn't 6238 // observable from outside the class though, so casting away the 6239 // const isn't dangerous. 6240 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6241 6242 OS << "Classifying expressions for: "; 6243 WriteAsOperand(OS, F, /*PrintType=*/false); 6244 OS << "\n"; 6245 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6246 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6247 OS << *I << '\n'; 6248 OS << " --> "; 6249 const SCEV *SV = SE.getSCEV(&*I); 6250 SV->print(OS); 6251 6252 const Loop *L = LI->getLoopFor((*I).getParent()); 6253 6254 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6255 if (AtUse != SV) { 6256 OS << " --> "; 6257 AtUse->print(OS); 6258 } 6259 6260 if (L) { 6261 OS << "\t\t" "Exits: "; 6262 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6263 if (!SE.isLoopInvariant(ExitValue, L)) { 6264 OS << "<<Unknown>>"; 6265 } else { 6266 OS << *ExitValue; 6267 } 6268 } 6269 6270 OS << "\n"; 6271 } 6272 6273 OS << "Determining loop execution counts for: "; 6274 WriteAsOperand(OS, F, /*PrintType=*/false); 6275 OS << "\n"; 6276 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6277 PrintLoopInfo(OS, &SE, *I); 6278} 6279 6280ScalarEvolution::LoopDisposition 6281ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6282 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6283 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6284 Values.insert(std::make_pair(L, LoopVariant)); 6285 if (!Pair.second) 6286 return Pair.first->second; 6287 6288 LoopDisposition D = computeLoopDisposition(S, L); 6289 return LoopDispositions[S][L] = D; 6290} 6291 6292ScalarEvolution::LoopDisposition 6293ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6294 switch (S->getSCEVType()) { 6295 case scConstant: 6296 return LoopInvariant; 6297 case scTruncate: 6298 case scZeroExtend: 6299 case scSignExtend: 6300 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6301 case scAddRecExpr: { 6302 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6303 6304 // If L is the addrec's loop, it's computable. 6305 if (AR->getLoop() == L) 6306 return LoopComputable; 6307 6308 // Add recurrences are never invariant in the function-body (null loop). 6309 if (!L) 6310 return LoopVariant; 6311 6312 // This recurrence is variant w.r.t. L if L contains AR's loop. 6313 if (L->contains(AR->getLoop())) 6314 return LoopVariant; 6315 6316 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6317 if (AR->getLoop()->contains(L)) 6318 return LoopInvariant; 6319 6320 // This recurrence is variant w.r.t. L if any of its operands 6321 // are variant. 6322 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6323 I != E; ++I) 6324 if (!isLoopInvariant(*I, L)) 6325 return LoopVariant; 6326 6327 // Otherwise it's loop-invariant. 6328 return LoopInvariant; 6329 } 6330 case scAddExpr: 6331 case scMulExpr: 6332 case scUMaxExpr: 6333 case scSMaxExpr: { 6334 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6335 bool HasVarying = false; 6336 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6337 I != E; ++I) { 6338 LoopDisposition D = getLoopDisposition(*I, L); 6339 if (D == LoopVariant) 6340 return LoopVariant; 6341 if (D == LoopComputable) 6342 HasVarying = true; 6343 } 6344 return HasVarying ? LoopComputable : LoopInvariant; 6345 } 6346 case scUDivExpr: { 6347 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6348 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6349 if (LD == LoopVariant) 6350 return LoopVariant; 6351 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6352 if (RD == LoopVariant) 6353 return LoopVariant; 6354 return (LD == LoopInvariant && RD == LoopInvariant) ? 6355 LoopInvariant : LoopComputable; 6356 } 6357 case scUnknown: 6358 // All non-instruction values are loop invariant. All instructions are loop 6359 // invariant if they are not contained in the specified loop. 6360 // Instructions are never considered invariant in the function body 6361 // (null loop) because they are defined within the "loop". 6362 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6363 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6364 return LoopInvariant; 6365 case scCouldNotCompute: 6366 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6367 return LoopVariant; 6368 default: break; 6369 } 6370 llvm_unreachable("Unknown SCEV kind!"); 6371 return LoopVariant; 6372} 6373 6374bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6375 return getLoopDisposition(S, L) == LoopInvariant; 6376} 6377 6378bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6379 return getLoopDisposition(S, L) == LoopComputable; 6380} 6381 6382ScalarEvolution::BlockDisposition 6383ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6384 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6385 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6386 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6387 if (!Pair.second) 6388 return Pair.first->second; 6389 6390 BlockDisposition D = computeBlockDisposition(S, BB); 6391 return BlockDispositions[S][BB] = D; 6392} 6393 6394ScalarEvolution::BlockDisposition 6395ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6396 switch (S->getSCEVType()) { 6397 case scConstant: 6398 return ProperlyDominatesBlock; 6399 case scTruncate: 6400 case scZeroExtend: 6401 case scSignExtend: 6402 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6403 case scAddRecExpr: { 6404 // This uses a "dominates" query instead of "properly dominates" query 6405 // to test for proper dominance too, because the instruction which 6406 // produces the addrec's value is a PHI, and a PHI effectively properly 6407 // dominates its entire containing block. 6408 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6409 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6410 return DoesNotDominateBlock; 6411 } 6412 // FALL THROUGH into SCEVNAryExpr handling. 6413 case scAddExpr: 6414 case scMulExpr: 6415 case scUMaxExpr: 6416 case scSMaxExpr: { 6417 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6418 bool Proper = true; 6419 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6420 I != E; ++I) { 6421 BlockDisposition D = getBlockDisposition(*I, BB); 6422 if (D == DoesNotDominateBlock) 6423 return DoesNotDominateBlock; 6424 if (D == DominatesBlock) 6425 Proper = false; 6426 } 6427 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6428 } 6429 case scUDivExpr: { 6430 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6431 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6432 BlockDisposition LD = getBlockDisposition(LHS, BB); 6433 if (LD == DoesNotDominateBlock) 6434 return DoesNotDominateBlock; 6435 BlockDisposition RD = getBlockDisposition(RHS, BB); 6436 if (RD == DoesNotDominateBlock) 6437 return DoesNotDominateBlock; 6438 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6439 ProperlyDominatesBlock : DominatesBlock; 6440 } 6441 case scUnknown: 6442 if (Instruction *I = 6443 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6444 if (I->getParent() == BB) 6445 return DominatesBlock; 6446 if (DT->properlyDominates(I->getParent(), BB)) 6447 return ProperlyDominatesBlock; 6448 return DoesNotDominateBlock; 6449 } 6450 return ProperlyDominatesBlock; 6451 case scCouldNotCompute: 6452 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6453 return DoesNotDominateBlock; 6454 default: break; 6455 } 6456 llvm_unreachable("Unknown SCEV kind!"); 6457 return DoesNotDominateBlock; 6458} 6459 6460bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6461 return getBlockDisposition(S, BB) >= DominatesBlock; 6462} 6463 6464bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6465 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6466} 6467 6468bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6469 switch (S->getSCEVType()) { 6470 case scConstant: 6471 return false; 6472 case scTruncate: 6473 case scZeroExtend: 6474 case scSignExtend: { 6475 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6476 const SCEV *CastOp = Cast->getOperand(); 6477 return Op == CastOp || hasOperand(CastOp, Op); 6478 } 6479 case scAddRecExpr: 6480 case scAddExpr: 6481 case scMulExpr: 6482 case scUMaxExpr: 6483 case scSMaxExpr: { 6484 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6485 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6486 I != E; ++I) { 6487 const SCEV *NAryOp = *I; 6488 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6489 return true; 6490 } 6491 return false; 6492 } 6493 case scUDivExpr: { 6494 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6495 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6496 return LHS == Op || hasOperand(LHS, Op) || 6497 RHS == Op || hasOperand(RHS, Op); 6498 } 6499 case scUnknown: 6500 return false; 6501 case scCouldNotCompute: 6502 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6503 return false; 6504 default: break; 6505 } 6506 llvm_unreachable("Unknown SCEV kind!"); 6507 return false; 6508} 6509 6510void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6511 ValuesAtScopes.erase(S); 6512 LoopDispositions.erase(S); 6513 BlockDispositions.erase(S); 6514 UnsignedRanges.erase(S); 6515 SignedRanges.erase(S); 6516} 6517