ScalarEvolution.cpp revision 630d85a78cdebf14a6fc2a0750bf48738f26ef08
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/InstructionSimplify.h" 73#include "llvm/Analysis/LoopInfo.h" 74#include "llvm/Analysis/ValueTracking.h" 75#include "llvm/Assembly/Writer.h" 76#include "llvm/Target/TargetData.h" 77#include "llvm/Support/CommandLine.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/Debug.h" 80#include "llvm/Support/ErrorHandling.h" 81#include "llvm/Support/GetElementPtrTypeIterator.h" 82#include "llvm/Support/InstIterator.h" 83#include "llvm/Support/MathExtras.h" 84#include "llvm/Support/raw_ostream.h" 85#include "llvm/ADT/Statistic.h" 86#include "llvm/ADT/STLExtras.h" 87#include "llvm/ADT/SmallPtrSet.h" 88#include <algorithm> 89using namespace llvm; 90 91STATISTIC(NumArrayLenItCounts, 92 "Number of trip counts computed with array length"); 93STATISTIC(NumTripCountsComputed, 94 "Number of loops with predictable loop counts"); 95STATISTIC(NumTripCountsNotComputed, 96 "Number of loops without predictable loop counts"); 97STATISTIC(NumBruteForceTripCountsComputed, 98 "Number of loops with trip counts computed by force"); 99 100static cl::opt<unsigned> 101MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 102 cl::desc("Maximum number of iterations SCEV will " 103 "symbolically execute a constant " 104 "derived loop"), 105 cl::init(100)); 106 107INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 108 "Scalar Evolution Analysis", false, true) 109INITIALIZE_PASS_DEPENDENCY(LoopInfo) 110INITIALIZE_PASS_DEPENDENCY(DominatorTree) 111INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 112 "Scalar Evolution Analysis", false, true) 113char ScalarEvolution::ID = 0; 114 115//===----------------------------------------------------------------------===// 116// SCEV class definitions 117//===----------------------------------------------------------------------===// 118 119//===----------------------------------------------------------------------===// 120// Implementation of the SCEV class. 121// 122 123void SCEV::dump() const { 124 print(dbgs()); 125 dbgs() << '\n'; 126} 127 128void SCEV::print(raw_ostream &OS) const { 129 switch (getSCEVType()) { 130 case scConstant: 131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 132 return; 133 case scTruncate: { 134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 135 const SCEV *Op = Trunc->getOperand(); 136 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 137 << *Trunc->getType() << ")"; 138 return; 139 } 140 case scZeroExtend: { 141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 142 const SCEV *Op = ZExt->getOperand(); 143 OS << "(zext " << *Op->getType() << " " << *Op << " to " 144 << *ZExt->getType() << ")"; 145 return; 146 } 147 case scSignExtend: { 148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 149 const SCEV *Op = SExt->getOperand(); 150 OS << "(sext " << *Op->getType() << " " << *Op << " to " 151 << *SExt->getType() << ")"; 152 return; 153 } 154 case scAddRecExpr: { 155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 156 OS << "{" << *AR->getOperand(0); 157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 158 OS << ",+," << *AR->getOperand(i); 159 OS << "}<"; 160 if (AR->hasNoUnsignedWrap()) 161 OS << "nuw><"; 162 if (AR->hasNoSignedWrap()) 163 OS << "nsw><"; 164 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 165 OS << ">"; 166 return; 167 } 168 case scAddExpr: 169 case scMulExpr: 170 case scUMaxExpr: 171 case scSMaxExpr: { 172 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 173 const char *OpStr = 0; 174 switch (NAry->getSCEVType()) { 175 case scAddExpr: OpStr = " + "; break; 176 case scMulExpr: OpStr = " * "; break; 177 case scUMaxExpr: OpStr = " umax "; break; 178 case scSMaxExpr: OpStr = " smax "; break; 179 } 180 OS << "("; 181 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 182 I != E; ++I) { 183 OS << **I; 184 if (llvm::next(I) != E) 185 OS << OpStr; 186 } 187 OS << ")"; 188 return; 189 } 190 case scUDivExpr: { 191 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 192 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 193 return; 194 } 195 case scUnknown: { 196 const SCEVUnknown *U = cast<SCEVUnknown>(this); 197 const Type *AllocTy; 198 if (U->isSizeOf(AllocTy)) { 199 OS << "sizeof(" << *AllocTy << ")"; 200 return; 201 } 202 if (U->isAlignOf(AllocTy)) { 203 OS << "alignof(" << *AllocTy << ")"; 204 return; 205 } 206 207 const Type *CTy; 208 Constant *FieldNo; 209 if (U->isOffsetOf(CTy, FieldNo)) { 210 OS << "offsetof(" << *CTy << ", "; 211 WriteAsOperand(OS, FieldNo, false); 212 OS << ")"; 213 return; 214 } 215 216 // Otherwise just print it normally. 217 WriteAsOperand(OS, U->getValue(), false); 218 return; 219 } 220 case scCouldNotCompute: 221 OS << "***COULDNOTCOMPUTE***"; 222 return; 223 default: break; 224 } 225 llvm_unreachable("Unknown SCEV kind!"); 226} 227 228const Type *SCEV::getType() const { 229 switch (getSCEVType()) { 230 case scConstant: 231 return cast<SCEVConstant>(this)->getType(); 232 case scTruncate: 233 case scZeroExtend: 234 case scSignExtend: 235 return cast<SCEVCastExpr>(this)->getType(); 236 case scAddRecExpr: 237 case scMulExpr: 238 case scUMaxExpr: 239 case scSMaxExpr: 240 return cast<SCEVNAryExpr>(this)->getType(); 241 case scAddExpr: 242 return cast<SCEVAddExpr>(this)->getType(); 243 case scUDivExpr: 244 return cast<SCEVUDivExpr>(this)->getType(); 245 case scUnknown: 246 return cast<SCEVUnknown>(this)->getType(); 247 case scCouldNotCompute: 248 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 249 return 0; 250 default: break; 251 } 252 llvm_unreachable("Unknown SCEV kind!"); 253 return 0; 254} 255 256bool SCEV::isZero() const { 257 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 258 return SC->getValue()->isZero(); 259 return false; 260} 261 262bool SCEV::isOne() const { 263 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 264 return SC->getValue()->isOne(); 265 return false; 266} 267 268bool SCEV::isAllOnesValue() const { 269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 270 return SC->getValue()->isAllOnesValue(); 271 return false; 272} 273 274SCEVCouldNotCompute::SCEVCouldNotCompute() : 275 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 276 277bool SCEVCouldNotCompute::classof(const SCEV *S) { 278 return S->getSCEVType() == scCouldNotCompute; 279} 280 281const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 282 FoldingSetNodeID ID; 283 ID.AddInteger(scConstant); 284 ID.AddPointer(V); 285 void *IP = 0; 286 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 287 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 288 UniqueSCEVs.InsertNode(S, IP); 289 return S; 290} 291 292const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 293 return getConstant(ConstantInt::get(getContext(), Val)); 294} 295 296const SCEV * 297ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 298 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 299 return getConstant(ConstantInt::get(ITy, V, isSigned)); 300} 301 302SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 303 unsigned SCEVTy, const SCEV *op, const Type *ty) 304 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 305 306SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 307 const SCEV *op, const Type *ty) 308 : SCEVCastExpr(ID, scTruncate, op, ty) { 309 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 310 (Ty->isIntegerTy() || Ty->isPointerTy()) && 311 "Cannot truncate non-integer value!"); 312} 313 314SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 315 const SCEV *op, const Type *ty) 316 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 317 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 318 (Ty->isIntegerTy() || Ty->isPointerTy()) && 319 "Cannot zero extend non-integer value!"); 320} 321 322SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 323 const SCEV *op, const Type *ty) 324 : SCEVCastExpr(ID, scSignExtend, op, ty) { 325 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 326 (Ty->isIntegerTy() || Ty->isPointerTy()) && 327 "Cannot sign extend non-integer value!"); 328} 329 330void SCEVUnknown::deleted() { 331 // Clear this SCEVUnknown from various maps. 332 SE->forgetMemoizedResults(this); 333 334 // Remove this SCEVUnknown from the uniquing map. 335 SE->UniqueSCEVs.RemoveNode(this); 336 337 // Release the value. 338 setValPtr(0); 339} 340 341void SCEVUnknown::allUsesReplacedWith(Value *New) { 342 // Clear this SCEVUnknown from various maps. 343 SE->forgetMemoizedResults(this); 344 345 // Remove this SCEVUnknown from the uniquing map. 346 SE->UniqueSCEVs.RemoveNode(this); 347 348 // Update this SCEVUnknown to point to the new value. This is needed 349 // because there may still be outstanding SCEVs which still point to 350 // this SCEVUnknown. 351 setValPtr(New); 352} 353 354bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 355 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 356 if (VCE->getOpcode() == Instruction::PtrToInt) 357 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 358 if (CE->getOpcode() == Instruction::GetElementPtr && 359 CE->getOperand(0)->isNullValue() && 360 CE->getNumOperands() == 2) 361 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 362 if (CI->isOne()) { 363 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 364 ->getElementType(); 365 return true; 366 } 367 368 return false; 369} 370 371bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 372 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 373 if (VCE->getOpcode() == Instruction::PtrToInt) 374 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 375 if (CE->getOpcode() == Instruction::GetElementPtr && 376 CE->getOperand(0)->isNullValue()) { 377 const Type *Ty = 378 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 379 if (const StructType *STy = dyn_cast<StructType>(Ty)) 380 if (!STy->isPacked() && 381 CE->getNumOperands() == 3 && 382 CE->getOperand(1)->isNullValue()) { 383 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 384 if (CI->isOne() && 385 STy->getNumElements() == 2 && 386 STy->getElementType(0)->isIntegerTy(1)) { 387 AllocTy = STy->getElementType(1); 388 return true; 389 } 390 } 391 } 392 393 return false; 394} 395 396bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 397 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 398 if (VCE->getOpcode() == Instruction::PtrToInt) 399 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 400 if (CE->getOpcode() == Instruction::GetElementPtr && 401 CE->getNumOperands() == 3 && 402 CE->getOperand(0)->isNullValue() && 403 CE->getOperand(1)->isNullValue()) { 404 const Type *Ty = 405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 406 // Ignore vector types here so that ScalarEvolutionExpander doesn't 407 // emit getelementptrs that index into vectors. 408 if (Ty->isStructTy() || Ty->isArrayTy()) { 409 CTy = Ty; 410 FieldNo = CE->getOperand(2); 411 return true; 412 } 413 } 414 415 return false; 416} 417 418//===----------------------------------------------------------------------===// 419// SCEV Utilities 420//===----------------------------------------------------------------------===// 421 422namespace { 423 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 424 /// than the complexity of the RHS. This comparator is used to canonicalize 425 /// expressions. 426 class SCEVComplexityCompare { 427 const LoopInfo *const LI; 428 public: 429 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 430 431 // Return true or false if LHS is less than, or at least RHS, respectively. 432 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 433 return compare(LHS, RHS) < 0; 434 } 435 436 // Return negative, zero, or positive, if LHS is less than, equal to, or 437 // greater than RHS, respectively. A three-way result allows recursive 438 // comparisons to be more efficient. 439 int compare(const SCEV *LHS, const SCEV *RHS) const { 440 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 441 if (LHS == RHS) 442 return 0; 443 444 // Primarily, sort the SCEVs by their getSCEVType(). 445 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 446 if (LType != RType) 447 return (int)LType - (int)RType; 448 449 // Aside from the getSCEVType() ordering, the particular ordering 450 // isn't very important except that it's beneficial to be consistent, 451 // so that (a + b) and (b + a) don't end up as different expressions. 452 switch (LType) { 453 case scUnknown: { 454 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 455 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 456 457 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 458 // not as complete as it could be. 459 const Value *LV = LU->getValue(), *RV = RU->getValue(); 460 461 // Order pointer values after integer values. This helps SCEVExpander 462 // form GEPs. 463 bool LIsPointer = LV->getType()->isPointerTy(), 464 RIsPointer = RV->getType()->isPointerTy(); 465 if (LIsPointer != RIsPointer) 466 return (int)LIsPointer - (int)RIsPointer; 467 468 // Compare getValueID values. 469 unsigned LID = LV->getValueID(), 470 RID = RV->getValueID(); 471 if (LID != RID) 472 return (int)LID - (int)RID; 473 474 // Sort arguments by their position. 475 if (const Argument *LA = dyn_cast<Argument>(LV)) { 476 const Argument *RA = cast<Argument>(RV); 477 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 478 return (int)LArgNo - (int)RArgNo; 479 } 480 481 // For instructions, compare their loop depth, and their operand 482 // count. This is pretty loose. 483 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 484 const Instruction *RInst = cast<Instruction>(RV); 485 486 // Compare loop depths. 487 const BasicBlock *LParent = LInst->getParent(), 488 *RParent = RInst->getParent(); 489 if (LParent != RParent) { 490 unsigned LDepth = LI->getLoopDepth(LParent), 491 RDepth = LI->getLoopDepth(RParent); 492 if (LDepth != RDepth) 493 return (int)LDepth - (int)RDepth; 494 } 495 496 // Compare the number of operands. 497 unsigned LNumOps = LInst->getNumOperands(), 498 RNumOps = RInst->getNumOperands(); 499 return (int)LNumOps - (int)RNumOps; 500 } 501 502 return 0; 503 } 504 505 case scConstant: { 506 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 507 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 508 509 // Compare constant values. 510 const APInt &LA = LC->getValue()->getValue(); 511 const APInt &RA = RC->getValue()->getValue(); 512 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 513 if (LBitWidth != RBitWidth) 514 return (int)LBitWidth - (int)RBitWidth; 515 return LA.ult(RA) ? -1 : 1; 516 } 517 518 case scAddRecExpr: { 519 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 520 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 521 522 // Compare addrec loop depths. 523 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 524 if (LLoop != RLoop) { 525 unsigned LDepth = LLoop->getLoopDepth(), 526 RDepth = RLoop->getLoopDepth(); 527 if (LDepth != RDepth) 528 return (int)LDepth - (int)RDepth; 529 } 530 531 // Addrec complexity grows with operand count. 532 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 533 if (LNumOps != RNumOps) 534 return (int)LNumOps - (int)RNumOps; 535 536 // Lexicographically compare. 537 for (unsigned i = 0; i != LNumOps; ++i) { 538 long X = compare(LA->getOperand(i), RA->getOperand(i)); 539 if (X != 0) 540 return X; 541 } 542 543 return 0; 544 } 545 546 case scAddExpr: 547 case scMulExpr: 548 case scSMaxExpr: 549 case scUMaxExpr: { 550 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 551 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 552 553 // Lexicographically compare n-ary expressions. 554 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 555 for (unsigned i = 0; i != LNumOps; ++i) { 556 if (i >= RNumOps) 557 return 1; 558 long X = compare(LC->getOperand(i), RC->getOperand(i)); 559 if (X != 0) 560 return X; 561 } 562 return (int)LNumOps - (int)RNumOps; 563 } 564 565 case scUDivExpr: { 566 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 567 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 568 569 // Lexicographically compare udiv expressions. 570 long X = compare(LC->getLHS(), RC->getLHS()); 571 if (X != 0) 572 return X; 573 return compare(LC->getRHS(), RC->getRHS()); 574 } 575 576 case scTruncate: 577 case scZeroExtend: 578 case scSignExtend: { 579 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 580 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 581 582 // Compare cast expressions by operand. 583 return compare(LC->getOperand(), RC->getOperand()); 584 } 585 586 default: 587 break; 588 } 589 590 llvm_unreachable("Unknown SCEV kind!"); 591 return 0; 592 } 593 }; 594} 595 596/// GroupByComplexity - Given a list of SCEV objects, order them by their 597/// complexity, and group objects of the same complexity together by value. 598/// When this routine is finished, we know that any duplicates in the vector are 599/// consecutive and that complexity is monotonically increasing. 600/// 601/// Note that we go take special precautions to ensure that we get deterministic 602/// results from this routine. In other words, we don't want the results of 603/// this to depend on where the addresses of various SCEV objects happened to 604/// land in memory. 605/// 606static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 607 LoopInfo *LI) { 608 if (Ops.size() < 2) return; // Noop 609 if (Ops.size() == 2) { 610 // This is the common case, which also happens to be trivially simple. 611 // Special case it. 612 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 613 if (SCEVComplexityCompare(LI)(RHS, LHS)) 614 std::swap(LHS, RHS); 615 return; 616 } 617 618 // Do the rough sort by complexity. 619 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 620 621 // Now that we are sorted by complexity, group elements of the same 622 // complexity. Note that this is, at worst, N^2, but the vector is likely to 623 // be extremely short in practice. Note that we take this approach because we 624 // do not want to depend on the addresses of the objects we are grouping. 625 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 626 const SCEV *S = Ops[i]; 627 unsigned Complexity = S->getSCEVType(); 628 629 // If there are any objects of the same complexity and same value as this 630 // one, group them. 631 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 632 if (Ops[j] == S) { // Found a duplicate. 633 // Move it to immediately after i'th element. 634 std::swap(Ops[i+1], Ops[j]); 635 ++i; // no need to rescan it. 636 if (i == e-2) return; // Done! 637 } 638 } 639 } 640} 641 642 643 644//===----------------------------------------------------------------------===// 645// Simple SCEV method implementations 646//===----------------------------------------------------------------------===// 647 648/// BinomialCoefficient - Compute BC(It, K). The result has width W. 649/// Assume, K > 0. 650static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 651 ScalarEvolution &SE, 652 const Type* ResultTy) { 653 // Handle the simplest case efficiently. 654 if (K == 1) 655 return SE.getTruncateOrZeroExtend(It, ResultTy); 656 657 // We are using the following formula for BC(It, K): 658 // 659 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 660 // 661 // Suppose, W is the bitwidth of the return value. We must be prepared for 662 // overflow. Hence, we must assure that the result of our computation is 663 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 664 // safe in modular arithmetic. 665 // 666 // However, this code doesn't use exactly that formula; the formula it uses 667 // is something like the following, where T is the number of factors of 2 in 668 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 669 // exponentiation: 670 // 671 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 672 // 673 // This formula is trivially equivalent to the previous formula. However, 674 // this formula can be implemented much more efficiently. The trick is that 675 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 676 // arithmetic. To do exact division in modular arithmetic, all we have 677 // to do is multiply by the inverse. Therefore, this step can be done at 678 // width W. 679 // 680 // The next issue is how to safely do the division by 2^T. The way this 681 // is done is by doing the multiplication step at a width of at least W + T 682 // bits. This way, the bottom W+T bits of the product are accurate. Then, 683 // when we perform the division by 2^T (which is equivalent to a right shift 684 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 685 // truncated out after the division by 2^T. 686 // 687 // In comparison to just directly using the first formula, this technique 688 // is much more efficient; using the first formula requires W * K bits, 689 // but this formula less than W + K bits. Also, the first formula requires 690 // a division step, whereas this formula only requires multiplies and shifts. 691 // 692 // It doesn't matter whether the subtraction step is done in the calculation 693 // width or the input iteration count's width; if the subtraction overflows, 694 // the result must be zero anyway. We prefer here to do it in the width of 695 // the induction variable because it helps a lot for certain cases; CodeGen 696 // isn't smart enough to ignore the overflow, which leads to much less 697 // efficient code if the width of the subtraction is wider than the native 698 // register width. 699 // 700 // (It's possible to not widen at all by pulling out factors of 2 before 701 // the multiplication; for example, K=2 can be calculated as 702 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 703 // extra arithmetic, so it's not an obvious win, and it gets 704 // much more complicated for K > 3.) 705 706 // Protection from insane SCEVs; this bound is conservative, 707 // but it probably doesn't matter. 708 if (K > 1000) 709 return SE.getCouldNotCompute(); 710 711 unsigned W = SE.getTypeSizeInBits(ResultTy); 712 713 // Calculate K! / 2^T and T; we divide out the factors of two before 714 // multiplying for calculating K! / 2^T to avoid overflow. 715 // Other overflow doesn't matter because we only care about the bottom 716 // W bits of the result. 717 APInt OddFactorial(W, 1); 718 unsigned T = 1; 719 for (unsigned i = 3; i <= K; ++i) { 720 APInt Mult(W, i); 721 unsigned TwoFactors = Mult.countTrailingZeros(); 722 T += TwoFactors; 723 Mult = Mult.lshr(TwoFactors); 724 OddFactorial *= Mult; 725 } 726 727 // We need at least W + T bits for the multiplication step 728 unsigned CalculationBits = W + T; 729 730 // Calculate 2^T, at width T+W. 731 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 732 733 // Calculate the multiplicative inverse of K! / 2^T; 734 // this multiplication factor will perform the exact division by 735 // K! / 2^T. 736 APInt Mod = APInt::getSignedMinValue(W+1); 737 APInt MultiplyFactor = OddFactorial.zext(W+1); 738 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 739 MultiplyFactor = MultiplyFactor.trunc(W); 740 741 // Calculate the product, at width T+W 742 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 743 CalculationBits); 744 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 745 for (unsigned i = 1; i != K; ++i) { 746 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 747 Dividend = SE.getMulExpr(Dividend, 748 SE.getTruncateOrZeroExtend(S, CalculationTy)); 749 } 750 751 // Divide by 2^T 752 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 753 754 // Truncate the result, and divide by K! / 2^T. 755 756 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 757 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 758} 759 760/// evaluateAtIteration - Return the value of this chain of recurrences at 761/// the specified iteration number. We can evaluate this recurrence by 762/// multiplying each element in the chain by the binomial coefficient 763/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 764/// 765/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 766/// 767/// where BC(It, k) stands for binomial coefficient. 768/// 769const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 770 ScalarEvolution &SE) const { 771 const SCEV *Result = getStart(); 772 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 773 // The computation is correct in the face of overflow provided that the 774 // multiplication is performed _after_ the evaluation of the binomial 775 // coefficient. 776 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 777 if (isa<SCEVCouldNotCompute>(Coeff)) 778 return Coeff; 779 780 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 781 } 782 return Result; 783} 784 785//===----------------------------------------------------------------------===// 786// SCEV Expression folder implementations 787//===----------------------------------------------------------------------===// 788 789const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 790 const Type *Ty) { 791 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 792 "This is not a truncating conversion!"); 793 assert(isSCEVable(Ty) && 794 "This is not a conversion to a SCEVable type!"); 795 Ty = getEffectiveSCEVType(Ty); 796 797 FoldingSetNodeID ID; 798 ID.AddInteger(scTruncate); 799 ID.AddPointer(Op); 800 ID.AddPointer(Ty); 801 void *IP = 0; 802 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 803 804 // Fold if the operand is constant. 805 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 806 return getConstant( 807 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 808 getEffectiveSCEVType(Ty)))); 809 810 // trunc(trunc(x)) --> trunc(x) 811 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 812 return getTruncateExpr(ST->getOperand(), Ty); 813 814 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 815 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 816 return getTruncateOrSignExtend(SS->getOperand(), Ty); 817 818 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 819 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 820 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 821 822 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 823 // eliminate all the truncates. 824 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 825 SmallVector<const SCEV *, 4> Operands; 826 bool hasTrunc = false; 827 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 828 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 829 hasTrunc = isa<SCEVTruncateExpr>(S); 830 Operands.push_back(S); 831 } 832 if (!hasTrunc) 833 return getAddExpr(Operands, false, false); 834 } 835 836 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 837 // eliminate all the truncates. 838 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 839 SmallVector<const SCEV *, 4> Operands; 840 bool hasTrunc = false; 841 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 842 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 843 hasTrunc = isa<SCEVTruncateExpr>(S); 844 Operands.push_back(S); 845 } 846 if (!hasTrunc) 847 return getMulExpr(Operands, false, false); 848 } 849 850 // If the input value is a chrec scev, truncate the chrec's operands. 851 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 852 SmallVector<const SCEV *, 4> Operands; 853 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 854 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 855 return getAddRecExpr(Operands, AddRec->getLoop()); 856 } 857 858 // As a special case, fold trunc(undef) to undef. We don't want to 859 // know too much about SCEVUnknowns, but this special case is handy 860 // and harmless. 861 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 862 if (isa<UndefValue>(U->getValue())) 863 return getSCEV(UndefValue::get(Ty)); 864 865 // The cast wasn't folded; create an explicit cast node. We can reuse 866 // the existing insert position since if we get here, we won't have 867 // made any changes which would invalidate it. 868 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 869 Op, Ty); 870 UniqueSCEVs.InsertNode(S, IP); 871 return S; 872} 873 874const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 875 const Type *Ty) { 876 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 877 "This is not an extending conversion!"); 878 assert(isSCEVable(Ty) && 879 "This is not a conversion to a SCEVable type!"); 880 Ty = getEffectiveSCEVType(Ty); 881 882 // Fold if the operand is constant. 883 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 884 return getConstant( 885 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 886 getEffectiveSCEVType(Ty)))); 887 888 // zext(zext(x)) --> zext(x) 889 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 890 return getZeroExtendExpr(SZ->getOperand(), Ty); 891 892 // Before doing any expensive analysis, check to see if we've already 893 // computed a SCEV for this Op and Ty. 894 FoldingSetNodeID ID; 895 ID.AddInteger(scZeroExtend); 896 ID.AddPointer(Op); 897 ID.AddPointer(Ty); 898 void *IP = 0; 899 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 900 901 // zext(trunc(x)) --> zext(x) or x or trunc(x) 902 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 903 // It's possible the bits taken off by the truncate were all zero bits. If 904 // so, we should be able to simplify this further. 905 const SCEV *X = ST->getOperand(); 906 ConstantRange CR = getUnsignedRange(X); 907 unsigned OrigBits = CR.getBitWidth(); 908 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 909 unsigned NewBits = getTypeSizeInBits(Ty); 910 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 911 CR.zextOrTrunc(NewBits))) { 912 if (NewBits > OrigBits) return getZeroExtendExpr(X, Ty); 913 if (NewBits < OrigBits) return getTruncateExpr(X, Ty); 914 return X; 915 } 916 } 917 918 // If the input value is a chrec scev, and we can prove that the value 919 // did not overflow the old, smaller, value, we can zero extend all of the 920 // operands (often constants). This allows analysis of something like 921 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 922 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 923 if (AR->isAffine()) { 924 const SCEV *Start = AR->getStart(); 925 const SCEV *Step = AR->getStepRecurrence(*this); 926 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 927 const Loop *L = AR->getLoop(); 928 929 // If we have special knowledge that this addrec won't overflow, 930 // we don't need to do any further analysis. 931 if (AR->hasNoUnsignedWrap()) 932 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 933 getZeroExtendExpr(Step, Ty), 934 L); 935 936 // Check whether the backedge-taken count is SCEVCouldNotCompute. 937 // Note that this serves two purposes: It filters out loops that are 938 // simply not analyzable, and it covers the case where this code is 939 // being called from within backedge-taken count analysis, such that 940 // attempting to ask for the backedge-taken count would likely result 941 // in infinite recursion. In the later case, the analysis code will 942 // cope with a conservative value, and it will take care to purge 943 // that value once it has finished. 944 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 945 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 946 // Manually compute the final value for AR, checking for 947 // overflow. 948 949 // Check whether the backedge-taken count can be losslessly casted to 950 // the addrec's type. The count is always unsigned. 951 const SCEV *CastedMaxBECount = 952 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 953 const SCEV *RecastedMaxBECount = 954 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 955 if (MaxBECount == RecastedMaxBECount) { 956 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 957 // Check whether Start+Step*MaxBECount has no unsigned overflow. 958 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 959 const SCEV *Add = getAddExpr(Start, ZMul); 960 const SCEV *OperandExtendedAdd = 961 getAddExpr(getZeroExtendExpr(Start, WideTy), 962 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 963 getZeroExtendExpr(Step, WideTy))); 964 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 965 // Return the expression with the addrec on the outside. 966 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 967 getZeroExtendExpr(Step, Ty), 968 L); 969 970 // Similar to above, only this time treat the step value as signed. 971 // This covers loops that count down. 972 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 973 Add = getAddExpr(Start, SMul); 974 OperandExtendedAdd = 975 getAddExpr(getZeroExtendExpr(Start, WideTy), 976 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 977 getSignExtendExpr(Step, WideTy))); 978 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 979 // Return the expression with the addrec on the outside. 980 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 981 getSignExtendExpr(Step, Ty), 982 L); 983 } 984 985 // If the backedge is guarded by a comparison with the pre-inc value 986 // the addrec is safe. Also, if the entry is guarded by a comparison 987 // with the start value and the backedge is guarded by a comparison 988 // with the post-inc value, the addrec is safe. 989 if (isKnownPositive(Step)) { 990 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 991 getUnsignedRange(Step).getUnsignedMax()); 992 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 993 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 994 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 995 AR->getPostIncExpr(*this), N))) 996 // Return the expression with the addrec on the outside. 997 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 998 getZeroExtendExpr(Step, Ty), 999 L); 1000 } else if (isKnownNegative(Step)) { 1001 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1002 getSignedRange(Step).getSignedMin()); 1003 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1004 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1005 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1006 AR->getPostIncExpr(*this), N))) 1007 // Return the expression with the addrec on the outside. 1008 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1009 getSignExtendExpr(Step, Ty), 1010 L); 1011 } 1012 } 1013 } 1014 1015 // The cast wasn't folded; create an explicit cast node. 1016 // Recompute the insert position, as it may have been invalidated. 1017 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1018 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1019 Op, Ty); 1020 UniqueSCEVs.InsertNode(S, IP); 1021 return S; 1022} 1023 1024const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1025 const Type *Ty) { 1026 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1027 "This is not an extending conversion!"); 1028 assert(isSCEVable(Ty) && 1029 "This is not a conversion to a SCEVable type!"); 1030 Ty = getEffectiveSCEVType(Ty); 1031 1032 // Fold if the operand is constant. 1033 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1034 return getConstant( 1035 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1036 getEffectiveSCEVType(Ty)))); 1037 1038 // sext(sext(x)) --> sext(x) 1039 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1040 return getSignExtendExpr(SS->getOperand(), Ty); 1041 1042 // sext(zext(x)) --> zext(x) 1043 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1044 return getZeroExtendExpr(SZ->getOperand(), Ty); 1045 1046 // Before doing any expensive analysis, check to see if we've already 1047 // computed a SCEV for this Op and Ty. 1048 FoldingSetNodeID ID; 1049 ID.AddInteger(scSignExtend); 1050 ID.AddPointer(Op); 1051 ID.AddPointer(Ty); 1052 void *IP = 0; 1053 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1054 1055 // If the input value is provably positive, build a zext instead. 1056 if (isKnownNonNegative(Op)) 1057 return getZeroExtendExpr(Op, Ty); 1058 1059 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1060 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1061 // It's possible the bits taken off by the truncate were all sign bits. If 1062 // so, we should be able to simplify this further. 1063 const SCEV *X = ST->getOperand(); 1064 ConstantRange CR = getSignedRange(X); 1065 unsigned OrigBits = CR.getBitWidth(); 1066 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1067 unsigned NewBits = getTypeSizeInBits(Ty); 1068 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1069 CR.sextOrTrunc(NewBits))) { 1070 if (NewBits > OrigBits) return getSignExtendExpr(X, Ty); 1071 if (NewBits < OrigBits) return getTruncateExpr(X, Ty); 1072 return X; 1073 } 1074 } 1075 1076 // If the input value is a chrec scev, and we can prove that the value 1077 // did not overflow the old, smaller, value, we can sign extend all of the 1078 // operands (often constants). This allows analysis of something like 1079 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1080 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1081 if (AR->isAffine()) { 1082 const SCEV *Start = AR->getStart(); 1083 const SCEV *Step = AR->getStepRecurrence(*this); 1084 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1085 const Loop *L = AR->getLoop(); 1086 1087 // If we have special knowledge that this addrec won't overflow, 1088 // we don't need to do any further analysis. 1089 if (AR->hasNoSignedWrap()) 1090 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1091 getSignExtendExpr(Step, Ty), 1092 L); 1093 1094 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1095 // Note that this serves two purposes: It filters out loops that are 1096 // simply not analyzable, and it covers the case where this code is 1097 // being called from within backedge-taken count analysis, such that 1098 // attempting to ask for the backedge-taken count would likely result 1099 // in infinite recursion. In the later case, the analysis code will 1100 // cope with a conservative value, and it will take care to purge 1101 // that value once it has finished. 1102 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1103 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1104 // Manually compute the final value for AR, checking for 1105 // overflow. 1106 1107 // Check whether the backedge-taken count can be losslessly casted to 1108 // the addrec's type. The count is always unsigned. 1109 const SCEV *CastedMaxBECount = 1110 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1111 const SCEV *RecastedMaxBECount = 1112 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1113 if (MaxBECount == RecastedMaxBECount) { 1114 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1115 // Check whether Start+Step*MaxBECount has no signed overflow. 1116 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1117 const SCEV *Add = getAddExpr(Start, SMul); 1118 const SCEV *OperandExtendedAdd = 1119 getAddExpr(getSignExtendExpr(Start, WideTy), 1120 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1121 getSignExtendExpr(Step, WideTy))); 1122 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1123 // Return the expression with the addrec on the outside. 1124 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1125 getSignExtendExpr(Step, Ty), 1126 L); 1127 1128 // Similar to above, only this time treat the step value as unsigned. 1129 // This covers loops that count up with an unsigned step. 1130 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1131 Add = getAddExpr(Start, UMul); 1132 OperandExtendedAdd = 1133 getAddExpr(getSignExtendExpr(Start, WideTy), 1134 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1135 getZeroExtendExpr(Step, WideTy))); 1136 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1137 // Return the expression with the addrec on the outside. 1138 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1139 getZeroExtendExpr(Step, Ty), 1140 L); 1141 } 1142 1143 // If the backedge is guarded by a comparison with the pre-inc value 1144 // the addrec is safe. Also, if the entry is guarded by a comparison 1145 // with the start value and the backedge is guarded by a comparison 1146 // with the post-inc value, the addrec is safe. 1147 if (isKnownPositive(Step)) { 1148 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1149 getSignedRange(Step).getSignedMax()); 1150 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1151 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1152 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1153 AR->getPostIncExpr(*this), N))) 1154 // Return the expression with the addrec on the outside. 1155 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1156 getSignExtendExpr(Step, Ty), 1157 L); 1158 } else if (isKnownNegative(Step)) { 1159 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1160 getSignedRange(Step).getSignedMin()); 1161 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1162 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1163 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1164 AR->getPostIncExpr(*this), N))) 1165 // Return the expression with the addrec on the outside. 1166 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1167 getSignExtendExpr(Step, Ty), 1168 L); 1169 } 1170 } 1171 } 1172 1173 // The cast wasn't folded; create an explicit cast node. 1174 // Recompute the insert position, as it may have been invalidated. 1175 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1176 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1177 Op, Ty); 1178 UniqueSCEVs.InsertNode(S, IP); 1179 return S; 1180} 1181 1182/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1183/// unspecified bits out to the given type. 1184/// 1185const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1186 const Type *Ty) { 1187 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1188 "This is not an extending conversion!"); 1189 assert(isSCEVable(Ty) && 1190 "This is not a conversion to a SCEVable type!"); 1191 Ty = getEffectiveSCEVType(Ty); 1192 1193 // Sign-extend negative constants. 1194 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1195 if (SC->getValue()->getValue().isNegative()) 1196 return getSignExtendExpr(Op, Ty); 1197 1198 // Peel off a truncate cast. 1199 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1200 const SCEV *NewOp = T->getOperand(); 1201 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1202 return getAnyExtendExpr(NewOp, Ty); 1203 return getTruncateOrNoop(NewOp, Ty); 1204 } 1205 1206 // Next try a zext cast. If the cast is folded, use it. 1207 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1208 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1209 return ZExt; 1210 1211 // Next try a sext cast. If the cast is folded, use it. 1212 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1213 if (!isa<SCEVSignExtendExpr>(SExt)) 1214 return SExt; 1215 1216 // Force the cast to be folded into the operands of an addrec. 1217 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1218 SmallVector<const SCEV *, 4> Ops; 1219 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1220 I != E; ++I) 1221 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1222 return getAddRecExpr(Ops, AR->getLoop()); 1223 } 1224 1225 // As a special case, fold anyext(undef) to undef. We don't want to 1226 // know too much about SCEVUnknowns, but this special case is handy 1227 // and harmless. 1228 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1229 if (isa<UndefValue>(U->getValue())) 1230 return getSCEV(UndefValue::get(Ty)); 1231 1232 // If the expression is obviously signed, use the sext cast value. 1233 if (isa<SCEVSMaxExpr>(Op)) 1234 return SExt; 1235 1236 // Absent any other information, use the zext cast value. 1237 return ZExt; 1238} 1239 1240/// CollectAddOperandsWithScales - Process the given Ops list, which is 1241/// a list of operands to be added under the given scale, update the given 1242/// map. This is a helper function for getAddRecExpr. As an example of 1243/// what it does, given a sequence of operands that would form an add 1244/// expression like this: 1245/// 1246/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1247/// 1248/// where A and B are constants, update the map with these values: 1249/// 1250/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1251/// 1252/// and add 13 + A*B*29 to AccumulatedConstant. 1253/// This will allow getAddRecExpr to produce this: 1254/// 1255/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1256/// 1257/// This form often exposes folding opportunities that are hidden in 1258/// the original operand list. 1259/// 1260/// Return true iff it appears that any interesting folding opportunities 1261/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1262/// the common case where no interesting opportunities are present, and 1263/// is also used as a check to avoid infinite recursion. 1264/// 1265static bool 1266CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1267 SmallVector<const SCEV *, 8> &NewOps, 1268 APInt &AccumulatedConstant, 1269 const SCEV *const *Ops, size_t NumOperands, 1270 const APInt &Scale, 1271 ScalarEvolution &SE) { 1272 bool Interesting = false; 1273 1274 // Iterate over the add operands. They are sorted, with constants first. 1275 unsigned i = 0; 1276 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1277 ++i; 1278 // Pull a buried constant out to the outside. 1279 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1280 Interesting = true; 1281 AccumulatedConstant += Scale * C->getValue()->getValue(); 1282 } 1283 1284 // Next comes everything else. We're especially interested in multiplies 1285 // here, but they're in the middle, so just visit the rest with one loop. 1286 for (; i != NumOperands; ++i) { 1287 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1288 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1289 APInt NewScale = 1290 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1291 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1292 // A multiplication of a constant with another add; recurse. 1293 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1294 Interesting |= 1295 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1296 Add->op_begin(), Add->getNumOperands(), 1297 NewScale, SE); 1298 } else { 1299 // A multiplication of a constant with some other value. Update 1300 // the map. 1301 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1302 const SCEV *Key = SE.getMulExpr(MulOps); 1303 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1304 M.insert(std::make_pair(Key, NewScale)); 1305 if (Pair.second) { 1306 NewOps.push_back(Pair.first->first); 1307 } else { 1308 Pair.first->second += NewScale; 1309 // The map already had an entry for this value, which may indicate 1310 // a folding opportunity. 1311 Interesting = true; 1312 } 1313 } 1314 } else { 1315 // An ordinary operand. Update the map. 1316 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1317 M.insert(std::make_pair(Ops[i], Scale)); 1318 if (Pair.second) { 1319 NewOps.push_back(Pair.first->first); 1320 } else { 1321 Pair.first->second += Scale; 1322 // The map already had an entry for this value, which may indicate 1323 // a folding opportunity. 1324 Interesting = true; 1325 } 1326 } 1327 } 1328 1329 return Interesting; 1330} 1331 1332namespace { 1333 struct APIntCompare { 1334 bool operator()(const APInt &LHS, const APInt &RHS) const { 1335 return LHS.ult(RHS); 1336 } 1337 }; 1338} 1339 1340/// getAddExpr - Get a canonical add expression, or something simpler if 1341/// possible. 1342const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1343 bool HasNUW, bool HasNSW) { 1344 assert(!Ops.empty() && "Cannot get empty add!"); 1345 if (Ops.size() == 1) return Ops[0]; 1346#ifndef NDEBUG 1347 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1348 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1349 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1350 "SCEVAddExpr operand types don't match!"); 1351#endif 1352 1353 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1354 if (!HasNUW && HasNSW) { 1355 bool All = true; 1356 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1357 E = Ops.end(); I != E; ++I) 1358 if (!isKnownNonNegative(*I)) { 1359 All = false; 1360 break; 1361 } 1362 if (All) HasNUW = true; 1363 } 1364 1365 // Sort by complexity, this groups all similar expression types together. 1366 GroupByComplexity(Ops, LI); 1367 1368 // If there are any constants, fold them together. 1369 unsigned Idx = 0; 1370 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1371 ++Idx; 1372 assert(Idx < Ops.size()); 1373 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1374 // We found two constants, fold them together! 1375 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1376 RHSC->getValue()->getValue()); 1377 if (Ops.size() == 2) return Ops[0]; 1378 Ops.erase(Ops.begin()+1); // Erase the folded element 1379 LHSC = cast<SCEVConstant>(Ops[0]); 1380 } 1381 1382 // If we are left with a constant zero being added, strip it off. 1383 if (LHSC->getValue()->isZero()) { 1384 Ops.erase(Ops.begin()); 1385 --Idx; 1386 } 1387 1388 if (Ops.size() == 1) return Ops[0]; 1389 } 1390 1391 // Okay, check to see if the same value occurs in the operand list more than 1392 // once. If so, merge them together into an multiply expression. Since we 1393 // sorted the list, these values are required to be adjacent. 1394 const Type *Ty = Ops[0]->getType(); 1395 bool FoundMatch = false; 1396 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1397 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1398 // Scan ahead to count how many equal operands there are. 1399 unsigned Count = 2; 1400 while (i+Count != e && Ops[i+Count] == Ops[i]) 1401 ++Count; 1402 // Merge the values into a multiply. 1403 const SCEV *Scale = getConstant(Ty, Count); 1404 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1405 if (Ops.size() == Count) 1406 return Mul; 1407 Ops[i] = Mul; 1408 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1409 --i; e -= Count - 1; 1410 FoundMatch = true; 1411 } 1412 if (FoundMatch) 1413 return getAddExpr(Ops, HasNUW, HasNSW); 1414 1415 // Check for truncates. If all the operands are truncated from the same 1416 // type, see if factoring out the truncate would permit the result to be 1417 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1418 // if the contents of the resulting outer trunc fold to something simple. 1419 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1420 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1421 const Type *DstType = Trunc->getType(); 1422 const Type *SrcType = Trunc->getOperand()->getType(); 1423 SmallVector<const SCEV *, 8> LargeOps; 1424 bool Ok = true; 1425 // Check all the operands to see if they can be represented in the 1426 // source type of the truncate. 1427 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1428 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1429 if (T->getOperand()->getType() != SrcType) { 1430 Ok = false; 1431 break; 1432 } 1433 LargeOps.push_back(T->getOperand()); 1434 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1435 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1436 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1437 SmallVector<const SCEV *, 8> LargeMulOps; 1438 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1439 if (const SCEVTruncateExpr *T = 1440 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1441 if (T->getOperand()->getType() != SrcType) { 1442 Ok = false; 1443 break; 1444 } 1445 LargeMulOps.push_back(T->getOperand()); 1446 } else if (const SCEVConstant *C = 1447 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1448 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1449 } else { 1450 Ok = false; 1451 break; 1452 } 1453 } 1454 if (Ok) 1455 LargeOps.push_back(getMulExpr(LargeMulOps)); 1456 } else { 1457 Ok = false; 1458 break; 1459 } 1460 } 1461 if (Ok) { 1462 // Evaluate the expression in the larger type. 1463 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1464 // If it folds to something simple, use it. Otherwise, don't. 1465 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1466 return getTruncateExpr(Fold, DstType); 1467 } 1468 } 1469 1470 // Skip past any other cast SCEVs. 1471 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1472 ++Idx; 1473 1474 // If there are add operands they would be next. 1475 if (Idx < Ops.size()) { 1476 bool DeletedAdd = false; 1477 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1478 // If we have an add, expand the add operands onto the end of the operands 1479 // list. 1480 Ops.erase(Ops.begin()+Idx); 1481 Ops.append(Add->op_begin(), Add->op_end()); 1482 DeletedAdd = true; 1483 } 1484 1485 // If we deleted at least one add, we added operands to the end of the list, 1486 // and they are not necessarily sorted. Recurse to resort and resimplify 1487 // any operands we just acquired. 1488 if (DeletedAdd) 1489 return getAddExpr(Ops); 1490 } 1491 1492 // Skip over the add expression until we get to a multiply. 1493 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1494 ++Idx; 1495 1496 // Check to see if there are any folding opportunities present with 1497 // operands multiplied by constant values. 1498 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1499 uint64_t BitWidth = getTypeSizeInBits(Ty); 1500 DenseMap<const SCEV *, APInt> M; 1501 SmallVector<const SCEV *, 8> NewOps; 1502 APInt AccumulatedConstant(BitWidth, 0); 1503 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1504 Ops.data(), Ops.size(), 1505 APInt(BitWidth, 1), *this)) { 1506 // Some interesting folding opportunity is present, so its worthwhile to 1507 // re-generate the operands list. Group the operands by constant scale, 1508 // to avoid multiplying by the same constant scale multiple times. 1509 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1510 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1511 E = NewOps.end(); I != E; ++I) 1512 MulOpLists[M.find(*I)->second].push_back(*I); 1513 // Re-generate the operands list. 1514 Ops.clear(); 1515 if (AccumulatedConstant != 0) 1516 Ops.push_back(getConstant(AccumulatedConstant)); 1517 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1518 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1519 if (I->first != 0) 1520 Ops.push_back(getMulExpr(getConstant(I->first), 1521 getAddExpr(I->second))); 1522 if (Ops.empty()) 1523 return getConstant(Ty, 0); 1524 if (Ops.size() == 1) 1525 return Ops[0]; 1526 return getAddExpr(Ops); 1527 } 1528 } 1529 1530 // If we are adding something to a multiply expression, make sure the 1531 // something is not already an operand of the multiply. If so, merge it into 1532 // the multiply. 1533 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1534 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1535 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1536 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1537 if (isa<SCEVConstant>(MulOpSCEV)) 1538 continue; 1539 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1540 if (MulOpSCEV == Ops[AddOp]) { 1541 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1542 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1543 if (Mul->getNumOperands() != 2) { 1544 // If the multiply has more than two operands, we must get the 1545 // Y*Z term. 1546 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1547 Mul->op_begin()+MulOp); 1548 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1549 InnerMul = getMulExpr(MulOps); 1550 } 1551 const SCEV *One = getConstant(Ty, 1); 1552 const SCEV *AddOne = getAddExpr(One, InnerMul); 1553 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1554 if (Ops.size() == 2) return OuterMul; 1555 if (AddOp < Idx) { 1556 Ops.erase(Ops.begin()+AddOp); 1557 Ops.erase(Ops.begin()+Idx-1); 1558 } else { 1559 Ops.erase(Ops.begin()+Idx); 1560 Ops.erase(Ops.begin()+AddOp-1); 1561 } 1562 Ops.push_back(OuterMul); 1563 return getAddExpr(Ops); 1564 } 1565 1566 // Check this multiply against other multiplies being added together. 1567 for (unsigned OtherMulIdx = Idx+1; 1568 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1569 ++OtherMulIdx) { 1570 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1571 // If MulOp occurs in OtherMul, we can fold the two multiplies 1572 // together. 1573 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1574 OMulOp != e; ++OMulOp) 1575 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1576 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1577 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1578 if (Mul->getNumOperands() != 2) { 1579 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1580 Mul->op_begin()+MulOp); 1581 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1582 InnerMul1 = getMulExpr(MulOps); 1583 } 1584 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1585 if (OtherMul->getNumOperands() != 2) { 1586 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1587 OtherMul->op_begin()+OMulOp); 1588 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1589 InnerMul2 = getMulExpr(MulOps); 1590 } 1591 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1592 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1593 if (Ops.size() == 2) return OuterMul; 1594 Ops.erase(Ops.begin()+Idx); 1595 Ops.erase(Ops.begin()+OtherMulIdx-1); 1596 Ops.push_back(OuterMul); 1597 return getAddExpr(Ops); 1598 } 1599 } 1600 } 1601 } 1602 1603 // If there are any add recurrences in the operands list, see if any other 1604 // added values are loop invariant. If so, we can fold them into the 1605 // recurrence. 1606 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1607 ++Idx; 1608 1609 // Scan over all recurrences, trying to fold loop invariants into them. 1610 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1611 // Scan all of the other operands to this add and add them to the vector if 1612 // they are loop invariant w.r.t. the recurrence. 1613 SmallVector<const SCEV *, 8> LIOps; 1614 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1615 const Loop *AddRecLoop = AddRec->getLoop(); 1616 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1617 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1618 LIOps.push_back(Ops[i]); 1619 Ops.erase(Ops.begin()+i); 1620 --i; --e; 1621 } 1622 1623 // If we found some loop invariants, fold them into the recurrence. 1624 if (!LIOps.empty()) { 1625 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1626 LIOps.push_back(AddRec->getStart()); 1627 1628 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1629 AddRec->op_end()); 1630 AddRecOps[0] = getAddExpr(LIOps); 1631 1632 // Build the new addrec. Propagate the NUW and NSW flags if both the 1633 // outer add and the inner addrec are guaranteed to have no overflow. 1634 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1635 HasNUW && AddRec->hasNoUnsignedWrap(), 1636 HasNSW && AddRec->hasNoSignedWrap()); 1637 1638 // If all of the other operands were loop invariant, we are done. 1639 if (Ops.size() == 1) return NewRec; 1640 1641 // Otherwise, add the folded AddRec by the non-liv parts. 1642 for (unsigned i = 0;; ++i) 1643 if (Ops[i] == AddRec) { 1644 Ops[i] = NewRec; 1645 break; 1646 } 1647 return getAddExpr(Ops); 1648 } 1649 1650 // Okay, if there weren't any loop invariants to be folded, check to see if 1651 // there are multiple AddRec's with the same loop induction variable being 1652 // added together. If so, we can fold them. 1653 for (unsigned OtherIdx = Idx+1; 1654 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1655 ++OtherIdx) 1656 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1657 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1658 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1659 AddRec->op_end()); 1660 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1661 ++OtherIdx) 1662 if (const SCEVAddRecExpr *OtherAddRec = 1663 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1664 if (OtherAddRec->getLoop() == AddRecLoop) { 1665 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1666 i != e; ++i) { 1667 if (i >= AddRecOps.size()) { 1668 AddRecOps.append(OtherAddRec->op_begin()+i, 1669 OtherAddRec->op_end()); 1670 break; 1671 } 1672 AddRecOps[i] = getAddExpr(AddRecOps[i], 1673 OtherAddRec->getOperand(i)); 1674 } 1675 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1676 } 1677 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1678 return getAddExpr(Ops); 1679 } 1680 1681 // Otherwise couldn't fold anything into this recurrence. Move onto the 1682 // next one. 1683 } 1684 1685 // Okay, it looks like we really DO need an add expr. Check to see if we 1686 // already have one, otherwise create a new one. 1687 FoldingSetNodeID ID; 1688 ID.AddInteger(scAddExpr); 1689 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1690 ID.AddPointer(Ops[i]); 1691 void *IP = 0; 1692 SCEVAddExpr *S = 1693 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1694 if (!S) { 1695 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1696 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1697 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1698 O, Ops.size()); 1699 UniqueSCEVs.InsertNode(S, IP); 1700 } 1701 if (HasNUW) S->setHasNoUnsignedWrap(true); 1702 if (HasNSW) S->setHasNoSignedWrap(true); 1703 return S; 1704} 1705 1706/// getMulExpr - Get a canonical multiply expression, or something simpler if 1707/// possible. 1708const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1709 bool HasNUW, bool HasNSW) { 1710 assert(!Ops.empty() && "Cannot get empty mul!"); 1711 if (Ops.size() == 1) return Ops[0]; 1712#ifndef NDEBUG 1713 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1714 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1715 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1716 "SCEVMulExpr operand types don't match!"); 1717#endif 1718 1719 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1720 if (!HasNUW && HasNSW) { 1721 bool All = true; 1722 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1723 E = Ops.end(); I != E; ++I) 1724 if (!isKnownNonNegative(*I)) { 1725 All = false; 1726 break; 1727 } 1728 if (All) HasNUW = true; 1729 } 1730 1731 // Sort by complexity, this groups all similar expression types together. 1732 GroupByComplexity(Ops, LI); 1733 1734 // If there are any constants, fold them together. 1735 unsigned Idx = 0; 1736 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1737 1738 // C1*(C2+V) -> C1*C2 + C1*V 1739 if (Ops.size() == 2) 1740 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1741 if (Add->getNumOperands() == 2 && 1742 isa<SCEVConstant>(Add->getOperand(0))) 1743 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1744 getMulExpr(LHSC, Add->getOperand(1))); 1745 1746 ++Idx; 1747 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1748 // We found two constants, fold them together! 1749 ConstantInt *Fold = ConstantInt::get(getContext(), 1750 LHSC->getValue()->getValue() * 1751 RHSC->getValue()->getValue()); 1752 Ops[0] = getConstant(Fold); 1753 Ops.erase(Ops.begin()+1); // Erase the folded element 1754 if (Ops.size() == 1) return Ops[0]; 1755 LHSC = cast<SCEVConstant>(Ops[0]); 1756 } 1757 1758 // If we are left with a constant one being multiplied, strip it off. 1759 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1760 Ops.erase(Ops.begin()); 1761 --Idx; 1762 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1763 // If we have a multiply of zero, it will always be zero. 1764 return Ops[0]; 1765 } else if (Ops[0]->isAllOnesValue()) { 1766 // If we have a mul by -1 of an add, try distributing the -1 among the 1767 // add operands. 1768 if (Ops.size() == 2) 1769 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1770 SmallVector<const SCEV *, 4> NewOps; 1771 bool AnyFolded = false; 1772 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1773 I != E; ++I) { 1774 const SCEV *Mul = getMulExpr(Ops[0], *I); 1775 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1776 NewOps.push_back(Mul); 1777 } 1778 if (AnyFolded) 1779 return getAddExpr(NewOps); 1780 } 1781 } 1782 1783 if (Ops.size() == 1) 1784 return Ops[0]; 1785 } 1786 1787 // Skip over the add expression until we get to a multiply. 1788 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1789 ++Idx; 1790 1791 // If there are mul operands inline them all into this expression. 1792 if (Idx < Ops.size()) { 1793 bool DeletedMul = false; 1794 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1795 // If we have an mul, expand the mul operands onto the end of the operands 1796 // list. 1797 Ops.erase(Ops.begin()+Idx); 1798 Ops.append(Mul->op_begin(), Mul->op_end()); 1799 DeletedMul = true; 1800 } 1801 1802 // If we deleted at least one mul, we added operands to the end of the list, 1803 // and they are not necessarily sorted. Recurse to resort and resimplify 1804 // any operands we just acquired. 1805 if (DeletedMul) 1806 return getMulExpr(Ops); 1807 } 1808 1809 // If there are any add recurrences in the operands list, see if any other 1810 // added values are loop invariant. If so, we can fold them into the 1811 // recurrence. 1812 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1813 ++Idx; 1814 1815 // Scan over all recurrences, trying to fold loop invariants into them. 1816 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1817 // Scan all of the other operands to this mul and add them to the vector if 1818 // they are loop invariant w.r.t. the recurrence. 1819 SmallVector<const SCEV *, 8> LIOps; 1820 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1821 const Loop *AddRecLoop = AddRec->getLoop(); 1822 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1823 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1824 LIOps.push_back(Ops[i]); 1825 Ops.erase(Ops.begin()+i); 1826 --i; --e; 1827 } 1828 1829 // If we found some loop invariants, fold them into the recurrence. 1830 if (!LIOps.empty()) { 1831 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1832 SmallVector<const SCEV *, 4> NewOps; 1833 NewOps.reserve(AddRec->getNumOperands()); 1834 const SCEV *Scale = getMulExpr(LIOps); 1835 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1836 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1837 1838 // Build the new addrec. Propagate the NUW and NSW flags if both the 1839 // outer mul and the inner addrec are guaranteed to have no overflow. 1840 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, 1841 HasNUW && AddRec->hasNoUnsignedWrap(), 1842 HasNSW && AddRec->hasNoSignedWrap()); 1843 1844 // If all of the other operands were loop invariant, we are done. 1845 if (Ops.size() == 1) return NewRec; 1846 1847 // Otherwise, multiply the folded AddRec by the non-liv parts. 1848 for (unsigned i = 0;; ++i) 1849 if (Ops[i] == AddRec) { 1850 Ops[i] = NewRec; 1851 break; 1852 } 1853 return getMulExpr(Ops); 1854 } 1855 1856 // Okay, if there weren't any loop invariants to be folded, check to see if 1857 // there are multiple AddRec's with the same loop induction variable being 1858 // multiplied together. If so, we can fold them. 1859 for (unsigned OtherIdx = Idx+1; 1860 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1861 ++OtherIdx) 1862 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1863 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1864 // {A*C,+,F*D + G*B + B*D}<L> 1865 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1866 ++OtherIdx) 1867 if (const SCEVAddRecExpr *OtherAddRec = 1868 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1869 if (OtherAddRec->getLoop() == AddRecLoop) { 1870 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1871 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1872 const SCEV *B = F->getStepRecurrence(*this); 1873 const SCEV *D = G->getStepRecurrence(*this); 1874 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1875 getMulExpr(G, B), 1876 getMulExpr(B, D)); 1877 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1878 F->getLoop()); 1879 if (Ops.size() == 2) return NewAddRec; 1880 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1881 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1882 } 1883 return getMulExpr(Ops); 1884 } 1885 1886 // Otherwise couldn't fold anything into this recurrence. Move onto the 1887 // next one. 1888 } 1889 1890 // Okay, it looks like we really DO need an mul expr. Check to see if we 1891 // already have one, otherwise create a new one. 1892 FoldingSetNodeID ID; 1893 ID.AddInteger(scMulExpr); 1894 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1895 ID.AddPointer(Ops[i]); 1896 void *IP = 0; 1897 SCEVMulExpr *S = 1898 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1899 if (!S) { 1900 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1901 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1902 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1903 O, Ops.size()); 1904 UniqueSCEVs.InsertNode(S, IP); 1905 } 1906 if (HasNUW) S->setHasNoUnsignedWrap(true); 1907 if (HasNSW) S->setHasNoSignedWrap(true); 1908 return S; 1909} 1910 1911/// getUDivExpr - Get a canonical unsigned division expression, or something 1912/// simpler if possible. 1913const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1914 const SCEV *RHS) { 1915 assert(getEffectiveSCEVType(LHS->getType()) == 1916 getEffectiveSCEVType(RHS->getType()) && 1917 "SCEVUDivExpr operand types don't match!"); 1918 1919 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1920 if (RHSC->getValue()->equalsInt(1)) 1921 return LHS; // X udiv 1 --> x 1922 // If the denominator is zero, the result of the udiv is undefined. Don't 1923 // try to analyze it, because the resolution chosen here may differ from 1924 // the resolution chosen in other parts of the compiler. 1925 if (!RHSC->getValue()->isZero()) { 1926 // Determine if the division can be folded into the operands of 1927 // its operands. 1928 // TODO: Generalize this to non-constants by using known-bits information. 1929 const Type *Ty = LHS->getType(); 1930 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1931 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1932 // For non-power-of-two values, effectively round the value up to the 1933 // nearest power of two. 1934 if (!RHSC->getValue()->getValue().isPowerOf2()) 1935 ++MaxShiftAmt; 1936 const IntegerType *ExtTy = 1937 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1938 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1939 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1940 if (const SCEVConstant *Step = 1941 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1942 if (!Step->getValue()->getValue() 1943 .urem(RHSC->getValue()->getValue()) && 1944 getZeroExtendExpr(AR, ExtTy) == 1945 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1946 getZeroExtendExpr(Step, ExtTy), 1947 AR->getLoop())) { 1948 SmallVector<const SCEV *, 4> Operands; 1949 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1950 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1951 return getAddRecExpr(Operands, AR->getLoop()); 1952 } 1953 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1954 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1955 SmallVector<const SCEV *, 4> Operands; 1956 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1957 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1958 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1959 // Find an operand that's safely divisible. 1960 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1961 const SCEV *Op = M->getOperand(i); 1962 const SCEV *Div = getUDivExpr(Op, RHSC); 1963 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1964 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1965 M->op_end()); 1966 Operands[i] = Div; 1967 return getMulExpr(Operands); 1968 } 1969 } 1970 } 1971 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1972 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1973 SmallVector<const SCEV *, 4> Operands; 1974 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1975 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1976 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1977 Operands.clear(); 1978 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1979 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1980 if (isa<SCEVUDivExpr>(Op) || 1981 getMulExpr(Op, RHS) != A->getOperand(i)) 1982 break; 1983 Operands.push_back(Op); 1984 } 1985 if (Operands.size() == A->getNumOperands()) 1986 return getAddExpr(Operands); 1987 } 1988 } 1989 1990 // Fold if both operands are constant. 1991 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1992 Constant *LHSCV = LHSC->getValue(); 1993 Constant *RHSCV = RHSC->getValue(); 1994 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1995 RHSCV))); 1996 } 1997 } 1998 } 1999 2000 FoldingSetNodeID ID; 2001 ID.AddInteger(scUDivExpr); 2002 ID.AddPointer(LHS); 2003 ID.AddPointer(RHS); 2004 void *IP = 0; 2005 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2006 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2007 LHS, RHS); 2008 UniqueSCEVs.InsertNode(S, IP); 2009 return S; 2010} 2011 2012 2013/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2014/// Simplify the expression as much as possible. 2015const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 2016 const SCEV *Step, const Loop *L, 2017 bool HasNUW, bool HasNSW) { 2018 SmallVector<const SCEV *, 4> Operands; 2019 Operands.push_back(Start); 2020 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2021 if (StepChrec->getLoop() == L) { 2022 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2023 return getAddRecExpr(Operands, L); 2024 } 2025 2026 Operands.push_back(Step); 2027 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2028} 2029 2030/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2031/// Simplify the expression as much as possible. 2032const SCEV * 2033ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2034 const Loop *L, 2035 bool HasNUW, bool HasNSW) { 2036 if (Operands.size() == 1) return Operands[0]; 2037#ifndef NDEBUG 2038 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2039 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2040 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2041 "SCEVAddRecExpr operand types don't match!"); 2042 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2043 assert(isLoopInvariant(Operands[i], L) && 2044 "SCEVAddRecExpr operand is not loop-invariant!"); 2045#endif 2046 2047 if (Operands.back()->isZero()) { 2048 Operands.pop_back(); 2049 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2050 } 2051 2052 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2053 // use that information to infer NUW and NSW flags. However, computing a 2054 // BE count requires calling getAddRecExpr, so we may not yet have a 2055 // meaningful BE count at this point (and if we don't, we'd be stuck 2056 // with a SCEVCouldNotCompute as the cached BE count). 2057 2058 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2059 if (!HasNUW && HasNSW) { 2060 bool All = true; 2061 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2062 E = Operands.end(); I != E; ++I) 2063 if (!isKnownNonNegative(*I)) { 2064 All = false; 2065 break; 2066 } 2067 if (All) HasNUW = true; 2068 } 2069 2070 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2071 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2072 const Loop *NestedLoop = NestedAR->getLoop(); 2073 if (L->contains(NestedLoop) ? 2074 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2075 (!NestedLoop->contains(L) && 2076 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2077 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2078 NestedAR->op_end()); 2079 Operands[0] = NestedAR->getStart(); 2080 // AddRecs require their operands be loop-invariant with respect to their 2081 // loops. Don't perform this transformation if it would break this 2082 // requirement. 2083 bool AllInvariant = true; 2084 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2085 if (!isLoopInvariant(Operands[i], L)) { 2086 AllInvariant = false; 2087 break; 2088 } 2089 if (AllInvariant) { 2090 NestedOperands[0] = getAddRecExpr(Operands, L); 2091 AllInvariant = true; 2092 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2093 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2094 AllInvariant = false; 2095 break; 2096 } 2097 if (AllInvariant) 2098 // Ok, both add recurrences are valid after the transformation. 2099 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2100 } 2101 // Reset Operands to its original state. 2102 Operands[0] = NestedAR; 2103 } 2104 } 2105 2106 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2107 // already have one, otherwise create a new one. 2108 FoldingSetNodeID ID; 2109 ID.AddInteger(scAddRecExpr); 2110 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2111 ID.AddPointer(Operands[i]); 2112 ID.AddPointer(L); 2113 void *IP = 0; 2114 SCEVAddRecExpr *S = 2115 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2116 if (!S) { 2117 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2118 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2119 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2120 O, Operands.size(), L); 2121 UniqueSCEVs.InsertNode(S, IP); 2122 } 2123 if (HasNUW) S->setHasNoUnsignedWrap(true); 2124 if (HasNSW) S->setHasNoSignedWrap(true); 2125 return S; 2126} 2127 2128const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2129 const SCEV *RHS) { 2130 SmallVector<const SCEV *, 2> Ops; 2131 Ops.push_back(LHS); 2132 Ops.push_back(RHS); 2133 return getSMaxExpr(Ops); 2134} 2135 2136const SCEV * 2137ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2138 assert(!Ops.empty() && "Cannot get empty smax!"); 2139 if (Ops.size() == 1) return Ops[0]; 2140#ifndef NDEBUG 2141 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2142 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2143 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2144 "SCEVSMaxExpr operand types don't match!"); 2145#endif 2146 2147 // Sort by complexity, this groups all similar expression types together. 2148 GroupByComplexity(Ops, LI); 2149 2150 // If there are any constants, fold them together. 2151 unsigned Idx = 0; 2152 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2153 ++Idx; 2154 assert(Idx < Ops.size()); 2155 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2156 // We found two constants, fold them together! 2157 ConstantInt *Fold = ConstantInt::get(getContext(), 2158 APIntOps::smax(LHSC->getValue()->getValue(), 2159 RHSC->getValue()->getValue())); 2160 Ops[0] = getConstant(Fold); 2161 Ops.erase(Ops.begin()+1); // Erase the folded element 2162 if (Ops.size() == 1) return Ops[0]; 2163 LHSC = cast<SCEVConstant>(Ops[0]); 2164 } 2165 2166 // If we are left with a constant minimum-int, strip it off. 2167 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2168 Ops.erase(Ops.begin()); 2169 --Idx; 2170 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2171 // If we have an smax with a constant maximum-int, it will always be 2172 // maximum-int. 2173 return Ops[0]; 2174 } 2175 2176 if (Ops.size() == 1) return Ops[0]; 2177 } 2178 2179 // Find the first SMax 2180 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2181 ++Idx; 2182 2183 // Check to see if one of the operands is an SMax. If so, expand its operands 2184 // onto our operand list, and recurse to simplify. 2185 if (Idx < Ops.size()) { 2186 bool DeletedSMax = false; 2187 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2188 Ops.erase(Ops.begin()+Idx); 2189 Ops.append(SMax->op_begin(), SMax->op_end()); 2190 DeletedSMax = true; 2191 } 2192 2193 if (DeletedSMax) 2194 return getSMaxExpr(Ops); 2195 } 2196 2197 // Okay, check to see if the same value occurs in the operand list twice. If 2198 // so, delete one. Since we sorted the list, these values are required to 2199 // be adjacent. 2200 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2201 // X smax Y smax Y --> X smax Y 2202 // X smax Y --> X, if X is always greater than Y 2203 if (Ops[i] == Ops[i+1] || 2204 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2205 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2206 --i; --e; 2207 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2208 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2209 --i; --e; 2210 } 2211 2212 if (Ops.size() == 1) return Ops[0]; 2213 2214 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2215 2216 // Okay, it looks like we really DO need an smax expr. Check to see if we 2217 // already have one, otherwise create a new one. 2218 FoldingSetNodeID ID; 2219 ID.AddInteger(scSMaxExpr); 2220 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2221 ID.AddPointer(Ops[i]); 2222 void *IP = 0; 2223 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2224 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2225 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2226 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2227 O, Ops.size()); 2228 UniqueSCEVs.InsertNode(S, IP); 2229 return S; 2230} 2231 2232const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2233 const SCEV *RHS) { 2234 SmallVector<const SCEV *, 2> Ops; 2235 Ops.push_back(LHS); 2236 Ops.push_back(RHS); 2237 return getUMaxExpr(Ops); 2238} 2239 2240const SCEV * 2241ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2242 assert(!Ops.empty() && "Cannot get empty umax!"); 2243 if (Ops.size() == 1) return Ops[0]; 2244#ifndef NDEBUG 2245 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2246 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2247 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2248 "SCEVUMaxExpr operand types don't match!"); 2249#endif 2250 2251 // Sort by complexity, this groups all similar expression types together. 2252 GroupByComplexity(Ops, LI); 2253 2254 // If there are any constants, fold them together. 2255 unsigned Idx = 0; 2256 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2257 ++Idx; 2258 assert(Idx < Ops.size()); 2259 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2260 // We found two constants, fold them together! 2261 ConstantInt *Fold = ConstantInt::get(getContext(), 2262 APIntOps::umax(LHSC->getValue()->getValue(), 2263 RHSC->getValue()->getValue())); 2264 Ops[0] = getConstant(Fold); 2265 Ops.erase(Ops.begin()+1); // Erase the folded element 2266 if (Ops.size() == 1) return Ops[0]; 2267 LHSC = cast<SCEVConstant>(Ops[0]); 2268 } 2269 2270 // If we are left with a constant minimum-int, strip it off. 2271 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2272 Ops.erase(Ops.begin()); 2273 --Idx; 2274 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2275 // If we have an umax with a constant maximum-int, it will always be 2276 // maximum-int. 2277 return Ops[0]; 2278 } 2279 2280 if (Ops.size() == 1) return Ops[0]; 2281 } 2282 2283 // Find the first UMax 2284 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2285 ++Idx; 2286 2287 // Check to see if one of the operands is a UMax. If so, expand its operands 2288 // onto our operand list, and recurse to simplify. 2289 if (Idx < Ops.size()) { 2290 bool DeletedUMax = false; 2291 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2292 Ops.erase(Ops.begin()+Idx); 2293 Ops.append(UMax->op_begin(), UMax->op_end()); 2294 DeletedUMax = true; 2295 } 2296 2297 if (DeletedUMax) 2298 return getUMaxExpr(Ops); 2299 } 2300 2301 // Okay, check to see if the same value occurs in the operand list twice. If 2302 // so, delete one. Since we sorted the list, these values are required to 2303 // be adjacent. 2304 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2305 // X umax Y umax Y --> X umax Y 2306 // X umax Y --> X, if X is always greater than Y 2307 if (Ops[i] == Ops[i+1] || 2308 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2309 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2310 --i; --e; 2311 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2312 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2313 --i; --e; 2314 } 2315 2316 if (Ops.size() == 1) return Ops[0]; 2317 2318 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2319 2320 // Okay, it looks like we really DO need a umax expr. Check to see if we 2321 // already have one, otherwise create a new one. 2322 FoldingSetNodeID ID; 2323 ID.AddInteger(scUMaxExpr); 2324 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2325 ID.AddPointer(Ops[i]); 2326 void *IP = 0; 2327 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2328 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2329 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2330 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2331 O, Ops.size()); 2332 UniqueSCEVs.InsertNode(S, IP); 2333 return S; 2334} 2335 2336const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2337 const SCEV *RHS) { 2338 // ~smax(~x, ~y) == smin(x, y). 2339 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2340} 2341 2342const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2343 const SCEV *RHS) { 2344 // ~umax(~x, ~y) == umin(x, y) 2345 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2346} 2347 2348const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2349 // If we have TargetData, we can bypass creating a target-independent 2350 // constant expression and then folding it back into a ConstantInt. 2351 // This is just a compile-time optimization. 2352 if (TD) 2353 return getConstant(TD->getIntPtrType(getContext()), 2354 TD->getTypeAllocSize(AllocTy)); 2355 2356 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2357 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2358 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2359 C = Folded; 2360 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2361 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2362} 2363 2364const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2365 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2366 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2367 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2368 C = Folded; 2369 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2370 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2371} 2372 2373const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2374 unsigned FieldNo) { 2375 // If we have TargetData, we can bypass creating a target-independent 2376 // constant expression and then folding it back into a ConstantInt. 2377 // This is just a compile-time optimization. 2378 if (TD) 2379 return getConstant(TD->getIntPtrType(getContext()), 2380 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2381 2382 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2383 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2384 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2385 C = Folded; 2386 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2387 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2388} 2389 2390const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2391 Constant *FieldNo) { 2392 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2393 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2394 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2395 C = Folded; 2396 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2397 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2398} 2399 2400const SCEV *ScalarEvolution::getUnknown(Value *V) { 2401 // Don't attempt to do anything other than create a SCEVUnknown object 2402 // here. createSCEV only calls getUnknown after checking for all other 2403 // interesting possibilities, and any other code that calls getUnknown 2404 // is doing so in order to hide a value from SCEV canonicalization. 2405 2406 FoldingSetNodeID ID; 2407 ID.AddInteger(scUnknown); 2408 ID.AddPointer(V); 2409 void *IP = 0; 2410 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2411 assert(cast<SCEVUnknown>(S)->getValue() == V && 2412 "Stale SCEVUnknown in uniquing map!"); 2413 return S; 2414 } 2415 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2416 FirstUnknown); 2417 FirstUnknown = cast<SCEVUnknown>(S); 2418 UniqueSCEVs.InsertNode(S, IP); 2419 return S; 2420} 2421 2422//===----------------------------------------------------------------------===// 2423// Basic SCEV Analysis and PHI Idiom Recognition Code 2424// 2425 2426/// isSCEVable - Test if values of the given type are analyzable within 2427/// the SCEV framework. This primarily includes integer types, and it 2428/// can optionally include pointer types if the ScalarEvolution class 2429/// has access to target-specific information. 2430bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2431 // Integers and pointers are always SCEVable. 2432 return Ty->isIntegerTy() || Ty->isPointerTy(); 2433} 2434 2435/// getTypeSizeInBits - Return the size in bits of the specified type, 2436/// for which isSCEVable must return true. 2437uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2438 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2439 2440 // If we have a TargetData, use it! 2441 if (TD) 2442 return TD->getTypeSizeInBits(Ty); 2443 2444 // Integer types have fixed sizes. 2445 if (Ty->isIntegerTy()) 2446 return Ty->getPrimitiveSizeInBits(); 2447 2448 // The only other support type is pointer. Without TargetData, conservatively 2449 // assume pointers are 64-bit. 2450 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2451 return 64; 2452} 2453 2454/// getEffectiveSCEVType - Return a type with the same bitwidth as 2455/// the given type and which represents how SCEV will treat the given 2456/// type, for which isSCEVable must return true. For pointer types, 2457/// this is the pointer-sized integer type. 2458const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2459 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2460 2461 if (Ty->isIntegerTy()) 2462 return Ty; 2463 2464 // The only other support type is pointer. 2465 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2466 if (TD) return TD->getIntPtrType(getContext()); 2467 2468 // Without TargetData, conservatively assume pointers are 64-bit. 2469 return Type::getInt64Ty(getContext()); 2470} 2471 2472const SCEV *ScalarEvolution::getCouldNotCompute() { 2473 return &CouldNotCompute; 2474} 2475 2476/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2477/// expression and create a new one. 2478const SCEV *ScalarEvolution::getSCEV(Value *V) { 2479 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2480 2481 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2482 if (I != ValueExprMap.end()) return I->second; 2483 const SCEV *S = createSCEV(V); 2484 2485 // The process of creating a SCEV for V may have caused other SCEVs 2486 // to have been created, so it's necessary to insert the new entry 2487 // from scratch, rather than trying to remember the insert position 2488 // above. 2489 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2490 return S; 2491} 2492 2493/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2494/// 2495const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2496 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2497 return getConstant( 2498 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2499 2500 const Type *Ty = V->getType(); 2501 Ty = getEffectiveSCEVType(Ty); 2502 return getMulExpr(V, 2503 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2504} 2505 2506/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2507const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2508 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2509 return getConstant( 2510 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2511 2512 const Type *Ty = V->getType(); 2513 Ty = getEffectiveSCEVType(Ty); 2514 const SCEV *AllOnes = 2515 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2516 return getMinusSCEV(AllOnes, V); 2517} 2518 2519/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1, 2520/// and thus the HasNUW and HasNSW bits apply to the resultant add, not 2521/// whether the sub would have overflowed. 2522const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2523 bool HasNUW, bool HasNSW) { 2524 // Fast path: X - X --> 0. 2525 if (LHS == RHS) 2526 return getConstant(LHS->getType(), 0); 2527 2528 // X - Y --> X + -Y 2529 return getAddExpr(LHS, getNegativeSCEV(RHS), HasNUW, HasNSW); 2530} 2531 2532/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2533/// input value to the specified type. If the type must be extended, it is zero 2534/// extended. 2535const SCEV * 2536ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) { 2537 const Type *SrcTy = V->getType(); 2538 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2539 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2540 "Cannot truncate or zero extend with non-integer arguments!"); 2541 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2542 return V; // No conversion 2543 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2544 return getTruncateExpr(V, Ty); 2545 return getZeroExtendExpr(V, Ty); 2546} 2547 2548/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2549/// input value to the specified type. If the type must be extended, it is sign 2550/// extended. 2551const SCEV * 2552ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2553 const Type *Ty) { 2554 const Type *SrcTy = V->getType(); 2555 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2556 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2557 "Cannot truncate or zero extend with non-integer arguments!"); 2558 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2559 return V; // No conversion 2560 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2561 return getTruncateExpr(V, Ty); 2562 return getSignExtendExpr(V, Ty); 2563} 2564 2565/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2566/// input value to the specified type. If the type must be extended, it is zero 2567/// extended. The conversion must not be narrowing. 2568const SCEV * 2569ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2570 const Type *SrcTy = V->getType(); 2571 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2572 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2573 "Cannot noop or zero extend with non-integer arguments!"); 2574 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2575 "getNoopOrZeroExtend cannot truncate!"); 2576 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2577 return V; // No conversion 2578 return getZeroExtendExpr(V, Ty); 2579} 2580 2581/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2582/// input value to the specified type. If the type must be extended, it is sign 2583/// extended. The conversion must not be narrowing. 2584const SCEV * 2585ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2586 const Type *SrcTy = V->getType(); 2587 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2588 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2589 "Cannot noop or sign extend with non-integer arguments!"); 2590 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2591 "getNoopOrSignExtend cannot truncate!"); 2592 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2593 return V; // No conversion 2594 return getSignExtendExpr(V, Ty); 2595} 2596 2597/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2598/// the input value to the specified type. If the type must be extended, 2599/// it is extended with unspecified bits. The conversion must not be 2600/// narrowing. 2601const SCEV * 2602ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2603 const Type *SrcTy = V->getType(); 2604 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2605 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2606 "Cannot noop or any extend with non-integer arguments!"); 2607 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2608 "getNoopOrAnyExtend cannot truncate!"); 2609 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2610 return V; // No conversion 2611 return getAnyExtendExpr(V, Ty); 2612} 2613 2614/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2615/// input value to the specified type. The conversion must not be widening. 2616const SCEV * 2617ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2618 const Type *SrcTy = V->getType(); 2619 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2620 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2621 "Cannot truncate or noop with non-integer arguments!"); 2622 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2623 "getTruncateOrNoop cannot extend!"); 2624 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2625 return V; // No conversion 2626 return getTruncateExpr(V, Ty); 2627} 2628 2629/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2630/// the types using zero-extension, and then perform a umax operation 2631/// with them. 2632const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2633 const SCEV *RHS) { 2634 const SCEV *PromotedLHS = LHS; 2635 const SCEV *PromotedRHS = RHS; 2636 2637 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2638 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2639 else 2640 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2641 2642 return getUMaxExpr(PromotedLHS, PromotedRHS); 2643} 2644 2645/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2646/// the types using zero-extension, and then perform a umin operation 2647/// with them. 2648const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2649 const SCEV *RHS) { 2650 const SCEV *PromotedLHS = LHS; 2651 const SCEV *PromotedRHS = RHS; 2652 2653 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2654 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2655 else 2656 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2657 2658 return getUMinExpr(PromotedLHS, PromotedRHS); 2659} 2660 2661/// PushDefUseChildren - Push users of the given Instruction 2662/// onto the given Worklist. 2663static void 2664PushDefUseChildren(Instruction *I, 2665 SmallVectorImpl<Instruction *> &Worklist) { 2666 // Push the def-use children onto the Worklist stack. 2667 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2668 UI != UE; ++UI) 2669 Worklist.push_back(cast<Instruction>(*UI)); 2670} 2671 2672/// ForgetSymbolicValue - This looks up computed SCEV values for all 2673/// instructions that depend on the given instruction and removes them from 2674/// the ValueExprMapType map if they reference SymName. This is used during PHI 2675/// resolution. 2676void 2677ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2678 SmallVector<Instruction *, 16> Worklist; 2679 PushDefUseChildren(PN, Worklist); 2680 2681 SmallPtrSet<Instruction *, 8> Visited; 2682 Visited.insert(PN); 2683 while (!Worklist.empty()) { 2684 Instruction *I = Worklist.pop_back_val(); 2685 if (!Visited.insert(I)) continue; 2686 2687 ValueExprMapType::iterator It = 2688 ValueExprMap.find(static_cast<Value *>(I)); 2689 if (It != ValueExprMap.end()) { 2690 const SCEV *Old = It->second; 2691 2692 // Short-circuit the def-use traversal if the symbolic name 2693 // ceases to appear in expressions. 2694 if (Old != SymName && !hasOperand(Old, SymName)) 2695 continue; 2696 2697 // SCEVUnknown for a PHI either means that it has an unrecognized 2698 // structure, it's a PHI that's in the progress of being computed 2699 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2700 // additional loop trip count information isn't going to change anything. 2701 // In the second case, createNodeForPHI will perform the necessary 2702 // updates on its own when it gets to that point. In the third, we do 2703 // want to forget the SCEVUnknown. 2704 if (!isa<PHINode>(I) || 2705 !isa<SCEVUnknown>(Old) || 2706 (I != PN && Old == SymName)) { 2707 forgetMemoizedResults(Old); 2708 ValueExprMap.erase(It); 2709 } 2710 } 2711 2712 PushDefUseChildren(I, Worklist); 2713 } 2714} 2715 2716/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2717/// a loop header, making it a potential recurrence, or it doesn't. 2718/// 2719const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2720 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2721 if (L->getHeader() == PN->getParent()) { 2722 // The loop may have multiple entrances or multiple exits; we can analyze 2723 // this phi as an addrec if it has a unique entry value and a unique 2724 // backedge value. 2725 Value *BEValueV = 0, *StartValueV = 0; 2726 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2727 Value *V = PN->getIncomingValue(i); 2728 if (L->contains(PN->getIncomingBlock(i))) { 2729 if (!BEValueV) { 2730 BEValueV = V; 2731 } else if (BEValueV != V) { 2732 BEValueV = 0; 2733 break; 2734 } 2735 } else if (!StartValueV) { 2736 StartValueV = V; 2737 } else if (StartValueV != V) { 2738 StartValueV = 0; 2739 break; 2740 } 2741 } 2742 if (BEValueV && StartValueV) { 2743 // While we are analyzing this PHI node, handle its value symbolically. 2744 const SCEV *SymbolicName = getUnknown(PN); 2745 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2746 "PHI node already processed?"); 2747 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2748 2749 // Using this symbolic name for the PHI, analyze the value coming around 2750 // the back-edge. 2751 const SCEV *BEValue = getSCEV(BEValueV); 2752 2753 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2754 // has a special value for the first iteration of the loop. 2755 2756 // If the value coming around the backedge is an add with the symbolic 2757 // value we just inserted, then we found a simple induction variable! 2758 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2759 // If there is a single occurrence of the symbolic value, replace it 2760 // with a recurrence. 2761 unsigned FoundIndex = Add->getNumOperands(); 2762 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2763 if (Add->getOperand(i) == SymbolicName) 2764 if (FoundIndex == e) { 2765 FoundIndex = i; 2766 break; 2767 } 2768 2769 if (FoundIndex != Add->getNumOperands()) { 2770 // Create an add with everything but the specified operand. 2771 SmallVector<const SCEV *, 8> Ops; 2772 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2773 if (i != FoundIndex) 2774 Ops.push_back(Add->getOperand(i)); 2775 const SCEV *Accum = getAddExpr(Ops); 2776 2777 // This is not a valid addrec if the step amount is varying each 2778 // loop iteration, but is not itself an addrec in this loop. 2779 if (isLoopInvariant(Accum, L) || 2780 (isa<SCEVAddRecExpr>(Accum) && 2781 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2782 bool HasNUW = false; 2783 bool HasNSW = false; 2784 2785 // If the increment doesn't overflow, then neither the addrec nor 2786 // the post-increment will overflow. 2787 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2788 if (OBO->hasNoUnsignedWrap()) 2789 HasNUW = true; 2790 if (OBO->hasNoSignedWrap()) 2791 HasNSW = true; 2792 } else if (const GEPOperator *GEP = 2793 dyn_cast<GEPOperator>(BEValueV)) { 2794 // If the increment is a GEP, then we know it won't perform an 2795 // unsigned overflow, because the address space cannot be 2796 // wrapped around. 2797 HasNUW |= GEP->isInBounds(); 2798 } 2799 2800 const SCEV *StartVal = getSCEV(StartValueV); 2801 const SCEV *PHISCEV = 2802 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2803 2804 // Since the no-wrap flags are on the increment, they apply to the 2805 // post-incremented value as well. 2806 if (isLoopInvariant(Accum, L)) 2807 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2808 Accum, L, HasNUW, HasNSW); 2809 2810 // Okay, for the entire analysis of this edge we assumed the PHI 2811 // to be symbolic. We now need to go back and purge all of the 2812 // entries for the scalars that use the symbolic expression. 2813 ForgetSymbolicName(PN, SymbolicName); 2814 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2815 return PHISCEV; 2816 } 2817 } 2818 } else if (const SCEVAddRecExpr *AddRec = 2819 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2820 // Otherwise, this could be a loop like this: 2821 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2822 // In this case, j = {1,+,1} and BEValue is j. 2823 // Because the other in-value of i (0) fits the evolution of BEValue 2824 // i really is an addrec evolution. 2825 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2826 const SCEV *StartVal = getSCEV(StartValueV); 2827 2828 // If StartVal = j.start - j.stride, we can use StartVal as the 2829 // initial step of the addrec evolution. 2830 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2831 AddRec->getOperand(1))) { 2832 const SCEV *PHISCEV = 2833 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2834 2835 // Okay, for the entire analysis of this edge we assumed the PHI 2836 // to be symbolic. We now need to go back and purge all of the 2837 // entries for the scalars that use the symbolic expression. 2838 ForgetSymbolicName(PN, SymbolicName); 2839 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2840 return PHISCEV; 2841 } 2842 } 2843 } 2844 } 2845 } 2846 2847 // If the PHI has a single incoming value, follow that value, unless the 2848 // PHI's incoming blocks are in a different loop, in which case doing so 2849 // risks breaking LCSSA form. Instcombine would normally zap these, but 2850 // it doesn't have DominatorTree information, so it may miss cases. 2851 if (Value *V = SimplifyInstruction(PN, TD, DT)) 2852 if (LI->replacementPreservesLCSSAForm(PN, V)) 2853 return getSCEV(V); 2854 2855 // If it's not a loop phi, we can't handle it yet. 2856 return getUnknown(PN); 2857} 2858 2859/// createNodeForGEP - Expand GEP instructions into add and multiply 2860/// operations. This allows them to be analyzed by regular SCEV code. 2861/// 2862const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2863 2864 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2865 // Add expression, because the Instruction may be guarded by control flow 2866 // and the no-overflow bits may not be valid for the expression in any 2867 // context. 2868 2869 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2870 Value *Base = GEP->getOperand(0); 2871 // Don't attempt to analyze GEPs over unsized objects. 2872 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2873 return getUnknown(GEP); 2874 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2875 gep_type_iterator GTI = gep_type_begin(GEP); 2876 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2877 E = GEP->op_end(); 2878 I != E; ++I) { 2879 Value *Index = *I; 2880 // Compute the (potentially symbolic) offset in bytes for this index. 2881 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2882 // For a struct, add the member offset. 2883 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2884 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2885 2886 // Add the field offset to the running total offset. 2887 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2888 } else { 2889 // For an array, add the element offset, explicitly scaled. 2890 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2891 const SCEV *IndexS = getSCEV(Index); 2892 // Getelementptr indices are signed. 2893 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2894 2895 // Multiply the index by the element size to compute the element offset. 2896 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2897 2898 // Add the element offset to the running total offset. 2899 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2900 } 2901 } 2902 2903 // Get the SCEV for the GEP base. 2904 const SCEV *BaseS = getSCEV(Base); 2905 2906 // Add the total offset from all the GEP indices to the base. 2907 return getAddExpr(BaseS, TotalOffset); 2908} 2909 2910/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2911/// guaranteed to end in (at every loop iteration). It is, at the same time, 2912/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2913/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2914uint32_t 2915ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2916 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2917 return C->getValue()->getValue().countTrailingZeros(); 2918 2919 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2920 return std::min(GetMinTrailingZeros(T->getOperand()), 2921 (uint32_t)getTypeSizeInBits(T->getType())); 2922 2923 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2924 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2925 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2926 getTypeSizeInBits(E->getType()) : OpRes; 2927 } 2928 2929 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2930 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2931 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2932 getTypeSizeInBits(E->getType()) : OpRes; 2933 } 2934 2935 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2936 // The result is the min of all operands results. 2937 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2938 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2939 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2940 return MinOpRes; 2941 } 2942 2943 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2944 // The result is the sum of all operands results. 2945 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2946 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2947 for (unsigned i = 1, e = M->getNumOperands(); 2948 SumOpRes != BitWidth && i != e; ++i) 2949 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2950 BitWidth); 2951 return SumOpRes; 2952 } 2953 2954 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2955 // The result is the min of all operands results. 2956 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2957 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2958 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2959 return MinOpRes; 2960 } 2961 2962 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2963 // The result is the min of all operands results. 2964 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2965 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2966 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2967 return MinOpRes; 2968 } 2969 2970 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2971 // The result is the min of all operands results. 2972 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2973 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2974 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2975 return MinOpRes; 2976 } 2977 2978 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2979 // For a SCEVUnknown, ask ValueTracking. 2980 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2981 APInt Mask = APInt::getAllOnesValue(BitWidth); 2982 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2983 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2984 return Zeros.countTrailingOnes(); 2985 } 2986 2987 // SCEVUDivExpr 2988 return 0; 2989} 2990 2991/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2992/// 2993ConstantRange 2994ScalarEvolution::getUnsignedRange(const SCEV *S) { 2995 // See if we've computed this range already. 2996 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 2997 if (I != UnsignedRanges.end()) 2998 return I->second; 2999 3000 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3001 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3002 3003 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3004 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3005 3006 // If the value has known zeros, the maximum unsigned value will have those 3007 // known zeros as well. 3008 uint32_t TZ = GetMinTrailingZeros(S); 3009 if (TZ != 0) 3010 ConservativeResult = 3011 ConstantRange(APInt::getMinValue(BitWidth), 3012 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3013 3014 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3015 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3016 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3017 X = X.add(getUnsignedRange(Add->getOperand(i))); 3018 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3019 } 3020 3021 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3022 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3023 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3024 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3025 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3026 } 3027 3028 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3029 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3030 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3031 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3032 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3033 } 3034 3035 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3036 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3037 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3038 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3039 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3040 } 3041 3042 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3043 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3044 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3045 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3046 } 3047 3048 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3049 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3050 return setUnsignedRange(ZExt, 3051 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3052 } 3053 3054 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3055 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3056 return setUnsignedRange(SExt, 3057 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3058 } 3059 3060 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3061 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3062 return setUnsignedRange(Trunc, 3063 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3064 } 3065 3066 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3067 // If there's no unsigned wrap, the value will never be less than its 3068 // initial value. 3069 if (AddRec->hasNoUnsignedWrap()) 3070 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3071 if (!C->getValue()->isZero()) 3072 ConservativeResult = 3073 ConservativeResult.intersectWith( 3074 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3075 3076 // TODO: non-affine addrec 3077 if (AddRec->isAffine()) { 3078 const Type *Ty = AddRec->getType(); 3079 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3080 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3081 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3082 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3083 3084 const SCEV *Start = AddRec->getStart(); 3085 const SCEV *Step = AddRec->getStepRecurrence(*this); 3086 3087 ConstantRange StartRange = getUnsignedRange(Start); 3088 ConstantRange StepRange = getSignedRange(Step); 3089 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3090 ConstantRange EndRange = 3091 StartRange.add(MaxBECountRange.multiply(StepRange)); 3092 3093 // Check for overflow. This must be done with ConstantRange arithmetic 3094 // because we could be called from within the ScalarEvolution overflow 3095 // checking code. 3096 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3097 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3098 ConstantRange ExtMaxBECountRange = 3099 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3100 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3101 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3102 ExtEndRange) 3103 return setUnsignedRange(AddRec, ConservativeResult); 3104 3105 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3106 EndRange.getUnsignedMin()); 3107 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3108 EndRange.getUnsignedMax()); 3109 if (Min.isMinValue() && Max.isMaxValue()) 3110 return setUnsignedRange(AddRec, ConservativeResult); 3111 return setUnsignedRange(AddRec, 3112 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3113 } 3114 } 3115 3116 return setUnsignedRange(AddRec, ConservativeResult); 3117 } 3118 3119 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3120 // For a SCEVUnknown, ask ValueTracking. 3121 APInt Mask = APInt::getAllOnesValue(BitWidth); 3122 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3123 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3124 if (Ones == ~Zeros + 1) 3125 return setUnsignedRange(U, ConservativeResult); 3126 return setUnsignedRange(U, 3127 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3128 } 3129 3130 return setUnsignedRange(S, ConservativeResult); 3131} 3132 3133/// getSignedRange - Determine the signed range for a particular SCEV. 3134/// 3135ConstantRange 3136ScalarEvolution::getSignedRange(const SCEV *S) { 3137 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3138 if (I != SignedRanges.end()) 3139 return I->second; 3140 3141 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3142 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3143 3144 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3145 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3146 3147 // If the value has known zeros, the maximum signed value will have those 3148 // known zeros as well. 3149 uint32_t TZ = GetMinTrailingZeros(S); 3150 if (TZ != 0) 3151 ConservativeResult = 3152 ConstantRange(APInt::getSignedMinValue(BitWidth), 3153 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3154 3155 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3156 ConstantRange X = getSignedRange(Add->getOperand(0)); 3157 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3158 X = X.add(getSignedRange(Add->getOperand(i))); 3159 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3160 } 3161 3162 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3163 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3164 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3165 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3166 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3167 } 3168 3169 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3170 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3171 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3172 X = X.smax(getSignedRange(SMax->getOperand(i))); 3173 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3174 } 3175 3176 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3177 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3178 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3179 X = X.umax(getSignedRange(UMax->getOperand(i))); 3180 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3181 } 3182 3183 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3184 ConstantRange X = getSignedRange(UDiv->getLHS()); 3185 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3186 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3187 } 3188 3189 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3190 ConstantRange X = getSignedRange(ZExt->getOperand()); 3191 return setSignedRange(ZExt, 3192 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3193 } 3194 3195 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3196 ConstantRange X = getSignedRange(SExt->getOperand()); 3197 return setSignedRange(SExt, 3198 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3199 } 3200 3201 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3202 ConstantRange X = getSignedRange(Trunc->getOperand()); 3203 return setSignedRange(Trunc, 3204 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3205 } 3206 3207 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3208 // If there's no signed wrap, and all the operands have the same sign or 3209 // zero, the value won't ever change sign. 3210 if (AddRec->hasNoSignedWrap()) { 3211 bool AllNonNeg = true; 3212 bool AllNonPos = true; 3213 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3214 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3215 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3216 } 3217 if (AllNonNeg) 3218 ConservativeResult = ConservativeResult.intersectWith( 3219 ConstantRange(APInt(BitWidth, 0), 3220 APInt::getSignedMinValue(BitWidth))); 3221 else if (AllNonPos) 3222 ConservativeResult = ConservativeResult.intersectWith( 3223 ConstantRange(APInt::getSignedMinValue(BitWidth), 3224 APInt(BitWidth, 1))); 3225 } 3226 3227 // TODO: non-affine addrec 3228 if (AddRec->isAffine()) { 3229 const Type *Ty = AddRec->getType(); 3230 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3231 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3232 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3233 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3234 3235 const SCEV *Start = AddRec->getStart(); 3236 const SCEV *Step = AddRec->getStepRecurrence(*this); 3237 3238 ConstantRange StartRange = getSignedRange(Start); 3239 ConstantRange StepRange = getSignedRange(Step); 3240 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3241 ConstantRange EndRange = 3242 StartRange.add(MaxBECountRange.multiply(StepRange)); 3243 3244 // Check for overflow. This must be done with ConstantRange arithmetic 3245 // because we could be called from within the ScalarEvolution overflow 3246 // checking code. 3247 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3248 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3249 ConstantRange ExtMaxBECountRange = 3250 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3251 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3252 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3253 ExtEndRange) 3254 return setSignedRange(AddRec, ConservativeResult); 3255 3256 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3257 EndRange.getSignedMin()); 3258 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3259 EndRange.getSignedMax()); 3260 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3261 return setSignedRange(AddRec, ConservativeResult); 3262 return setSignedRange(AddRec, 3263 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3264 } 3265 } 3266 3267 return setSignedRange(AddRec, ConservativeResult); 3268 } 3269 3270 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3271 // For a SCEVUnknown, ask ValueTracking. 3272 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3273 return setSignedRange(U, ConservativeResult); 3274 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3275 if (NS == 1) 3276 return setSignedRange(U, ConservativeResult); 3277 return setSignedRange(U, ConservativeResult.intersectWith( 3278 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3279 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3280 } 3281 3282 return setSignedRange(S, ConservativeResult); 3283} 3284 3285/// createSCEV - We know that there is no SCEV for the specified value. 3286/// Analyze the expression. 3287/// 3288const SCEV *ScalarEvolution::createSCEV(Value *V) { 3289 if (!isSCEVable(V->getType())) 3290 return getUnknown(V); 3291 3292 unsigned Opcode = Instruction::UserOp1; 3293 if (Instruction *I = dyn_cast<Instruction>(V)) { 3294 Opcode = I->getOpcode(); 3295 3296 // Don't attempt to analyze instructions in blocks that aren't 3297 // reachable. Such instructions don't matter, and they aren't required 3298 // to obey basic rules for definitions dominating uses which this 3299 // analysis depends on. 3300 if (!DT->isReachableFromEntry(I->getParent())) 3301 return getUnknown(V); 3302 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3303 Opcode = CE->getOpcode(); 3304 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3305 return getConstant(CI); 3306 else if (isa<ConstantPointerNull>(V)) 3307 return getConstant(V->getType(), 0); 3308 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3309 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3310 else 3311 return getUnknown(V); 3312 3313 Operator *U = cast<Operator>(V); 3314 switch (Opcode) { 3315 case Instruction::Add: { 3316 // The simple thing to do would be to just call getSCEV on both operands 3317 // and call getAddExpr with the result. However if we're looking at a 3318 // bunch of things all added together, this can be quite inefficient, 3319 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3320 // Instead, gather up all the operands and make a single getAddExpr call. 3321 // LLVM IR canonical form means we need only traverse the left operands. 3322 SmallVector<const SCEV *, 4> AddOps; 3323 AddOps.push_back(getSCEV(U->getOperand(1))); 3324 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3325 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3326 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3327 break; 3328 U = cast<Operator>(Op); 3329 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3330 if (Opcode == Instruction::Sub) 3331 AddOps.push_back(getNegativeSCEV(Op1)); 3332 else 3333 AddOps.push_back(Op1); 3334 } 3335 AddOps.push_back(getSCEV(U->getOperand(0))); 3336 return getAddExpr(AddOps); 3337 } 3338 case Instruction::Mul: { 3339 // See the Add code above. 3340 SmallVector<const SCEV *, 4> MulOps; 3341 MulOps.push_back(getSCEV(U->getOperand(1))); 3342 for (Value *Op = U->getOperand(0); 3343 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3344 Op = U->getOperand(0)) { 3345 U = cast<Operator>(Op); 3346 MulOps.push_back(getSCEV(U->getOperand(1))); 3347 } 3348 MulOps.push_back(getSCEV(U->getOperand(0))); 3349 return getMulExpr(MulOps); 3350 } 3351 case Instruction::UDiv: 3352 return getUDivExpr(getSCEV(U->getOperand(0)), 3353 getSCEV(U->getOperand(1))); 3354 case Instruction::Sub: 3355 return getMinusSCEV(getSCEV(U->getOperand(0)), 3356 getSCEV(U->getOperand(1))); 3357 case Instruction::And: 3358 // For an expression like x&255 that merely masks off the high bits, 3359 // use zext(trunc(x)) as the SCEV expression. 3360 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3361 if (CI->isNullValue()) 3362 return getSCEV(U->getOperand(1)); 3363 if (CI->isAllOnesValue()) 3364 return getSCEV(U->getOperand(0)); 3365 const APInt &A = CI->getValue(); 3366 3367 // Instcombine's ShrinkDemandedConstant may strip bits out of 3368 // constants, obscuring what would otherwise be a low-bits mask. 3369 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3370 // knew about to reconstruct a low-bits mask value. 3371 unsigned LZ = A.countLeadingZeros(); 3372 unsigned BitWidth = A.getBitWidth(); 3373 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3374 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3375 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3376 3377 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3378 3379 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3380 return 3381 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3382 IntegerType::get(getContext(), BitWidth - LZ)), 3383 U->getType()); 3384 } 3385 break; 3386 3387 case Instruction::Or: 3388 // If the RHS of the Or is a constant, we may have something like: 3389 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3390 // optimizations will transparently handle this case. 3391 // 3392 // In order for this transformation to be safe, the LHS must be of the 3393 // form X*(2^n) and the Or constant must be less than 2^n. 3394 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3395 const SCEV *LHS = getSCEV(U->getOperand(0)); 3396 const APInt &CIVal = CI->getValue(); 3397 if (GetMinTrailingZeros(LHS) >= 3398 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3399 // Build a plain add SCEV. 3400 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3401 // If the LHS of the add was an addrec and it has no-wrap flags, 3402 // transfer the no-wrap flags, since an or won't introduce a wrap. 3403 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3404 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3405 if (OldAR->hasNoUnsignedWrap()) 3406 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3407 if (OldAR->hasNoSignedWrap()) 3408 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3409 } 3410 return S; 3411 } 3412 } 3413 break; 3414 case Instruction::Xor: 3415 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3416 // If the RHS of the xor is a signbit, then this is just an add. 3417 // Instcombine turns add of signbit into xor as a strength reduction step. 3418 if (CI->getValue().isSignBit()) 3419 return getAddExpr(getSCEV(U->getOperand(0)), 3420 getSCEV(U->getOperand(1))); 3421 3422 // If the RHS of xor is -1, then this is a not operation. 3423 if (CI->isAllOnesValue()) 3424 return getNotSCEV(getSCEV(U->getOperand(0))); 3425 3426 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3427 // This is a variant of the check for xor with -1, and it handles 3428 // the case where instcombine has trimmed non-demanded bits out 3429 // of an xor with -1. 3430 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3431 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3432 if (BO->getOpcode() == Instruction::And && 3433 LCI->getValue() == CI->getValue()) 3434 if (const SCEVZeroExtendExpr *Z = 3435 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3436 const Type *UTy = U->getType(); 3437 const SCEV *Z0 = Z->getOperand(); 3438 const Type *Z0Ty = Z0->getType(); 3439 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3440 3441 // If C is a low-bits mask, the zero extend is serving to 3442 // mask off the high bits. Complement the operand and 3443 // re-apply the zext. 3444 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3445 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3446 3447 // If C is a single bit, it may be in the sign-bit position 3448 // before the zero-extend. In this case, represent the xor 3449 // using an add, which is equivalent, and re-apply the zext. 3450 APInt Trunc = CI->getValue().trunc(Z0TySize); 3451 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3452 Trunc.isSignBit()) 3453 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3454 UTy); 3455 } 3456 } 3457 break; 3458 3459 case Instruction::Shl: 3460 // Turn shift left of a constant amount into a multiply. 3461 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3462 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3463 3464 // If the shift count is not less than the bitwidth, the result of 3465 // the shift is undefined. Don't try to analyze it, because the 3466 // resolution chosen here may differ from the resolution chosen in 3467 // other parts of the compiler. 3468 if (SA->getValue().uge(BitWidth)) 3469 break; 3470 3471 Constant *X = ConstantInt::get(getContext(), 3472 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3473 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3474 } 3475 break; 3476 3477 case Instruction::LShr: 3478 // Turn logical shift right of a constant into a unsigned divide. 3479 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3480 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3481 3482 // If the shift count is not less than the bitwidth, the result of 3483 // the shift is undefined. Don't try to analyze it, because the 3484 // resolution chosen here may differ from the resolution chosen in 3485 // other parts of the compiler. 3486 if (SA->getValue().uge(BitWidth)) 3487 break; 3488 3489 Constant *X = ConstantInt::get(getContext(), 3490 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3491 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3492 } 3493 break; 3494 3495 case Instruction::AShr: 3496 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3497 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3498 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3499 if (L->getOpcode() == Instruction::Shl && 3500 L->getOperand(1) == U->getOperand(1)) { 3501 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3502 3503 // If the shift count is not less than the bitwidth, the result of 3504 // the shift is undefined. Don't try to analyze it, because the 3505 // resolution chosen here may differ from the resolution chosen in 3506 // other parts of the compiler. 3507 if (CI->getValue().uge(BitWidth)) 3508 break; 3509 3510 uint64_t Amt = BitWidth - CI->getZExtValue(); 3511 if (Amt == BitWidth) 3512 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3513 return 3514 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3515 IntegerType::get(getContext(), 3516 Amt)), 3517 U->getType()); 3518 } 3519 break; 3520 3521 case Instruction::Trunc: 3522 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3523 3524 case Instruction::ZExt: 3525 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3526 3527 case Instruction::SExt: 3528 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3529 3530 case Instruction::BitCast: 3531 // BitCasts are no-op casts so we just eliminate the cast. 3532 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3533 return getSCEV(U->getOperand(0)); 3534 break; 3535 3536 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3537 // lead to pointer expressions which cannot safely be expanded to GEPs, 3538 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3539 // simplifying integer expressions. 3540 3541 case Instruction::GetElementPtr: 3542 return createNodeForGEP(cast<GEPOperator>(U)); 3543 3544 case Instruction::PHI: 3545 return createNodeForPHI(cast<PHINode>(U)); 3546 3547 case Instruction::Select: 3548 // This could be a smax or umax that was lowered earlier. 3549 // Try to recover it. 3550 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3551 Value *LHS = ICI->getOperand(0); 3552 Value *RHS = ICI->getOperand(1); 3553 switch (ICI->getPredicate()) { 3554 case ICmpInst::ICMP_SLT: 3555 case ICmpInst::ICMP_SLE: 3556 std::swap(LHS, RHS); 3557 // fall through 3558 case ICmpInst::ICMP_SGT: 3559 case ICmpInst::ICMP_SGE: 3560 // a >s b ? a+x : b+x -> smax(a, b)+x 3561 // a >s b ? b+x : a+x -> smin(a, b)+x 3562 if (LHS->getType() == U->getType()) { 3563 const SCEV *LS = getSCEV(LHS); 3564 const SCEV *RS = getSCEV(RHS); 3565 const SCEV *LA = getSCEV(U->getOperand(1)); 3566 const SCEV *RA = getSCEV(U->getOperand(2)); 3567 const SCEV *LDiff = getMinusSCEV(LA, LS); 3568 const SCEV *RDiff = getMinusSCEV(RA, RS); 3569 if (LDiff == RDiff) 3570 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3571 LDiff = getMinusSCEV(LA, RS); 3572 RDiff = getMinusSCEV(RA, LS); 3573 if (LDiff == RDiff) 3574 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3575 } 3576 break; 3577 case ICmpInst::ICMP_ULT: 3578 case ICmpInst::ICMP_ULE: 3579 std::swap(LHS, RHS); 3580 // fall through 3581 case ICmpInst::ICMP_UGT: 3582 case ICmpInst::ICMP_UGE: 3583 // a >u b ? a+x : b+x -> umax(a, b)+x 3584 // a >u b ? b+x : a+x -> umin(a, b)+x 3585 if (LHS->getType() == U->getType()) { 3586 const SCEV *LS = getSCEV(LHS); 3587 const SCEV *RS = getSCEV(RHS); 3588 const SCEV *LA = getSCEV(U->getOperand(1)); 3589 const SCEV *RA = getSCEV(U->getOperand(2)); 3590 const SCEV *LDiff = getMinusSCEV(LA, LS); 3591 const SCEV *RDiff = getMinusSCEV(RA, RS); 3592 if (LDiff == RDiff) 3593 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3594 LDiff = getMinusSCEV(LA, RS); 3595 RDiff = getMinusSCEV(RA, LS); 3596 if (LDiff == RDiff) 3597 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3598 } 3599 break; 3600 case ICmpInst::ICMP_NE: 3601 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3602 if (LHS->getType() == U->getType() && 3603 isa<ConstantInt>(RHS) && 3604 cast<ConstantInt>(RHS)->isZero()) { 3605 const SCEV *One = getConstant(LHS->getType(), 1); 3606 const SCEV *LS = getSCEV(LHS); 3607 const SCEV *LA = getSCEV(U->getOperand(1)); 3608 const SCEV *RA = getSCEV(U->getOperand(2)); 3609 const SCEV *LDiff = getMinusSCEV(LA, LS); 3610 const SCEV *RDiff = getMinusSCEV(RA, One); 3611 if (LDiff == RDiff) 3612 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3613 } 3614 break; 3615 case ICmpInst::ICMP_EQ: 3616 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3617 if (LHS->getType() == U->getType() && 3618 isa<ConstantInt>(RHS) && 3619 cast<ConstantInt>(RHS)->isZero()) { 3620 const SCEV *One = getConstant(LHS->getType(), 1); 3621 const SCEV *LS = getSCEV(LHS); 3622 const SCEV *LA = getSCEV(U->getOperand(1)); 3623 const SCEV *RA = getSCEV(U->getOperand(2)); 3624 const SCEV *LDiff = getMinusSCEV(LA, One); 3625 const SCEV *RDiff = getMinusSCEV(RA, LS); 3626 if (LDiff == RDiff) 3627 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3628 } 3629 break; 3630 default: 3631 break; 3632 } 3633 } 3634 3635 default: // We cannot analyze this expression. 3636 break; 3637 } 3638 3639 return getUnknown(V); 3640} 3641 3642 3643 3644//===----------------------------------------------------------------------===// 3645// Iteration Count Computation Code 3646// 3647 3648/// getBackedgeTakenCount - If the specified loop has a predictable 3649/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3650/// object. The backedge-taken count is the number of times the loop header 3651/// will be branched to from within the loop. This is one less than the 3652/// trip count of the loop, since it doesn't count the first iteration, 3653/// when the header is branched to from outside the loop. 3654/// 3655/// Note that it is not valid to call this method on a loop without a 3656/// loop-invariant backedge-taken count (see 3657/// hasLoopInvariantBackedgeTakenCount). 3658/// 3659const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3660 return getBackedgeTakenInfo(L).Exact; 3661} 3662 3663/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3664/// return the least SCEV value that is known never to be less than the 3665/// actual backedge taken count. 3666const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3667 return getBackedgeTakenInfo(L).Max; 3668} 3669 3670/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3671/// onto the given Worklist. 3672static void 3673PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3674 BasicBlock *Header = L->getHeader(); 3675 3676 // Push all Loop-header PHIs onto the Worklist stack. 3677 for (BasicBlock::iterator I = Header->begin(); 3678 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3679 Worklist.push_back(PN); 3680} 3681 3682const ScalarEvolution::BackedgeTakenInfo & 3683ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3684 // Initially insert a CouldNotCompute for this loop. If the insertion 3685 // succeeds, proceed to actually compute a backedge-taken count and 3686 // update the value. The temporary CouldNotCompute value tells SCEV 3687 // code elsewhere that it shouldn't attempt to request a new 3688 // backedge-taken count, which could result in infinite recursion. 3689 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3690 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3691 if (!Pair.second) 3692 return Pair.first->second; 3693 3694 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3695 if (BECount.Exact != getCouldNotCompute()) { 3696 assert(isLoopInvariant(BECount.Exact, L) && 3697 isLoopInvariant(BECount.Max, L) && 3698 "Computed backedge-taken count isn't loop invariant for loop!"); 3699 ++NumTripCountsComputed; 3700 3701 // Update the value in the map. 3702 Pair.first->second = BECount; 3703 } else { 3704 if (BECount.Max != getCouldNotCompute()) 3705 // Update the value in the map. 3706 Pair.first->second = BECount; 3707 if (isa<PHINode>(L->getHeader()->begin())) 3708 // Only count loops that have phi nodes as not being computable. 3709 ++NumTripCountsNotComputed; 3710 } 3711 3712 // Now that we know more about the trip count for this loop, forget any 3713 // existing SCEV values for PHI nodes in this loop since they are only 3714 // conservative estimates made without the benefit of trip count 3715 // information. This is similar to the code in forgetLoop, except that 3716 // it handles SCEVUnknown PHI nodes specially. 3717 if (BECount.hasAnyInfo()) { 3718 SmallVector<Instruction *, 16> Worklist; 3719 PushLoopPHIs(L, Worklist); 3720 3721 SmallPtrSet<Instruction *, 8> Visited; 3722 while (!Worklist.empty()) { 3723 Instruction *I = Worklist.pop_back_val(); 3724 if (!Visited.insert(I)) continue; 3725 3726 ValueExprMapType::iterator It = 3727 ValueExprMap.find(static_cast<Value *>(I)); 3728 if (It != ValueExprMap.end()) { 3729 const SCEV *Old = It->second; 3730 3731 // SCEVUnknown for a PHI either means that it has an unrecognized 3732 // structure, or it's a PHI that's in the progress of being computed 3733 // by createNodeForPHI. In the former case, additional loop trip 3734 // count information isn't going to change anything. In the later 3735 // case, createNodeForPHI will perform the necessary updates on its 3736 // own when it gets to that point. 3737 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3738 forgetMemoizedResults(Old); 3739 ValueExprMap.erase(It); 3740 } 3741 if (PHINode *PN = dyn_cast<PHINode>(I)) 3742 ConstantEvolutionLoopExitValue.erase(PN); 3743 } 3744 3745 PushDefUseChildren(I, Worklist); 3746 } 3747 } 3748 return Pair.first->second; 3749} 3750 3751/// forgetLoop - This method should be called by the client when it has 3752/// changed a loop in a way that may effect ScalarEvolution's ability to 3753/// compute a trip count, or if the loop is deleted. 3754void ScalarEvolution::forgetLoop(const Loop *L) { 3755 // Drop any stored trip count value. 3756 BackedgeTakenCounts.erase(L); 3757 3758 // Drop information about expressions based on loop-header PHIs. 3759 SmallVector<Instruction *, 16> Worklist; 3760 PushLoopPHIs(L, Worklist); 3761 3762 SmallPtrSet<Instruction *, 8> Visited; 3763 while (!Worklist.empty()) { 3764 Instruction *I = Worklist.pop_back_val(); 3765 if (!Visited.insert(I)) continue; 3766 3767 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3768 if (It != ValueExprMap.end()) { 3769 forgetMemoizedResults(It->second); 3770 ValueExprMap.erase(It); 3771 if (PHINode *PN = dyn_cast<PHINode>(I)) 3772 ConstantEvolutionLoopExitValue.erase(PN); 3773 } 3774 3775 PushDefUseChildren(I, Worklist); 3776 } 3777 3778 // Forget all contained loops too, to avoid dangling entries in the 3779 // ValuesAtScopes map. 3780 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3781 forgetLoop(*I); 3782} 3783 3784/// forgetValue - This method should be called by the client when it has 3785/// changed a value in a way that may effect its value, or which may 3786/// disconnect it from a def-use chain linking it to a loop. 3787void ScalarEvolution::forgetValue(Value *V) { 3788 Instruction *I = dyn_cast<Instruction>(V); 3789 if (!I) return; 3790 3791 // Drop information about expressions based on loop-header PHIs. 3792 SmallVector<Instruction *, 16> Worklist; 3793 Worklist.push_back(I); 3794 3795 SmallPtrSet<Instruction *, 8> Visited; 3796 while (!Worklist.empty()) { 3797 I = Worklist.pop_back_val(); 3798 if (!Visited.insert(I)) continue; 3799 3800 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3801 if (It != ValueExprMap.end()) { 3802 forgetMemoizedResults(It->second); 3803 ValueExprMap.erase(It); 3804 if (PHINode *PN = dyn_cast<PHINode>(I)) 3805 ConstantEvolutionLoopExitValue.erase(PN); 3806 } 3807 3808 PushDefUseChildren(I, Worklist); 3809 } 3810} 3811 3812/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3813/// of the specified loop will execute. 3814ScalarEvolution::BackedgeTakenInfo 3815ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3816 SmallVector<BasicBlock *, 8> ExitingBlocks; 3817 L->getExitingBlocks(ExitingBlocks); 3818 3819 // Examine all exits and pick the most conservative values. 3820 const SCEV *BECount = getCouldNotCompute(); 3821 const SCEV *MaxBECount = getCouldNotCompute(); 3822 bool CouldNotComputeBECount = false; 3823 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3824 BackedgeTakenInfo NewBTI = 3825 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3826 3827 if (NewBTI.Exact == getCouldNotCompute()) { 3828 // We couldn't compute an exact value for this exit, so 3829 // we won't be able to compute an exact value for the loop. 3830 CouldNotComputeBECount = true; 3831 BECount = getCouldNotCompute(); 3832 } else if (!CouldNotComputeBECount) { 3833 if (BECount == getCouldNotCompute()) 3834 BECount = NewBTI.Exact; 3835 else 3836 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3837 } 3838 if (MaxBECount == getCouldNotCompute()) 3839 MaxBECount = NewBTI.Max; 3840 else if (NewBTI.Max != getCouldNotCompute()) 3841 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3842 } 3843 3844 return BackedgeTakenInfo(BECount, MaxBECount); 3845} 3846 3847/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3848/// of the specified loop will execute if it exits via the specified block. 3849ScalarEvolution::BackedgeTakenInfo 3850ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3851 BasicBlock *ExitingBlock) { 3852 3853 // Okay, we've chosen an exiting block. See what condition causes us to 3854 // exit at this block. 3855 // 3856 // FIXME: we should be able to handle switch instructions (with a single exit) 3857 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3858 if (ExitBr == 0) return getCouldNotCompute(); 3859 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3860 3861 // At this point, we know we have a conditional branch that determines whether 3862 // the loop is exited. However, we don't know if the branch is executed each 3863 // time through the loop. If not, then the execution count of the branch will 3864 // not be equal to the trip count of the loop. 3865 // 3866 // Currently we check for this by checking to see if the Exit branch goes to 3867 // the loop header. If so, we know it will always execute the same number of 3868 // times as the loop. We also handle the case where the exit block *is* the 3869 // loop header. This is common for un-rotated loops. 3870 // 3871 // If both of those tests fail, walk up the unique predecessor chain to the 3872 // header, stopping if there is an edge that doesn't exit the loop. If the 3873 // header is reached, the execution count of the branch will be equal to the 3874 // trip count of the loop. 3875 // 3876 // More extensive analysis could be done to handle more cases here. 3877 // 3878 if (ExitBr->getSuccessor(0) != L->getHeader() && 3879 ExitBr->getSuccessor(1) != L->getHeader() && 3880 ExitBr->getParent() != L->getHeader()) { 3881 // The simple checks failed, try climbing the unique predecessor chain 3882 // up to the header. 3883 bool Ok = false; 3884 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3885 BasicBlock *Pred = BB->getUniquePredecessor(); 3886 if (!Pred) 3887 return getCouldNotCompute(); 3888 TerminatorInst *PredTerm = Pred->getTerminator(); 3889 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3890 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3891 if (PredSucc == BB) 3892 continue; 3893 // If the predecessor has a successor that isn't BB and isn't 3894 // outside the loop, assume the worst. 3895 if (L->contains(PredSucc)) 3896 return getCouldNotCompute(); 3897 } 3898 if (Pred == L->getHeader()) { 3899 Ok = true; 3900 break; 3901 } 3902 BB = Pred; 3903 } 3904 if (!Ok) 3905 return getCouldNotCompute(); 3906 } 3907 3908 // Proceed to the next level to examine the exit condition expression. 3909 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3910 ExitBr->getSuccessor(0), 3911 ExitBr->getSuccessor(1)); 3912} 3913 3914/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3915/// backedge of the specified loop will execute if its exit condition 3916/// were a conditional branch of ExitCond, TBB, and FBB. 3917ScalarEvolution::BackedgeTakenInfo 3918ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3919 Value *ExitCond, 3920 BasicBlock *TBB, 3921 BasicBlock *FBB) { 3922 // Check if the controlling expression for this loop is an And or Or. 3923 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3924 if (BO->getOpcode() == Instruction::And) { 3925 // Recurse on the operands of the and. 3926 BackedgeTakenInfo BTI0 = 3927 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3928 BackedgeTakenInfo BTI1 = 3929 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3930 const SCEV *BECount = getCouldNotCompute(); 3931 const SCEV *MaxBECount = getCouldNotCompute(); 3932 if (L->contains(TBB)) { 3933 // Both conditions must be true for the loop to continue executing. 3934 // Choose the less conservative count. 3935 if (BTI0.Exact == getCouldNotCompute() || 3936 BTI1.Exact == getCouldNotCompute()) 3937 BECount = getCouldNotCompute(); 3938 else 3939 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3940 if (BTI0.Max == getCouldNotCompute()) 3941 MaxBECount = BTI1.Max; 3942 else if (BTI1.Max == getCouldNotCompute()) 3943 MaxBECount = BTI0.Max; 3944 else 3945 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3946 } else { 3947 // Both conditions must be true at the same time for the loop to exit. 3948 // For now, be conservative. 3949 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3950 if (BTI0.Max == BTI1.Max) 3951 MaxBECount = BTI0.Max; 3952 if (BTI0.Exact == BTI1.Exact) 3953 BECount = BTI0.Exact; 3954 } 3955 3956 return BackedgeTakenInfo(BECount, MaxBECount); 3957 } 3958 if (BO->getOpcode() == Instruction::Or) { 3959 // Recurse on the operands of the or. 3960 BackedgeTakenInfo BTI0 = 3961 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3962 BackedgeTakenInfo BTI1 = 3963 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3964 const SCEV *BECount = getCouldNotCompute(); 3965 const SCEV *MaxBECount = getCouldNotCompute(); 3966 if (L->contains(FBB)) { 3967 // Both conditions must be false for the loop to continue executing. 3968 // Choose the less conservative count. 3969 if (BTI0.Exact == getCouldNotCompute() || 3970 BTI1.Exact == getCouldNotCompute()) 3971 BECount = getCouldNotCompute(); 3972 else 3973 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3974 if (BTI0.Max == getCouldNotCompute()) 3975 MaxBECount = BTI1.Max; 3976 else if (BTI1.Max == getCouldNotCompute()) 3977 MaxBECount = BTI0.Max; 3978 else 3979 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3980 } else { 3981 // Both conditions must be false at the same time for the loop to exit. 3982 // For now, be conservative. 3983 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3984 if (BTI0.Max == BTI1.Max) 3985 MaxBECount = BTI0.Max; 3986 if (BTI0.Exact == BTI1.Exact) 3987 BECount = BTI0.Exact; 3988 } 3989 3990 return BackedgeTakenInfo(BECount, MaxBECount); 3991 } 3992 } 3993 3994 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3995 // Proceed to the next level to examine the icmp. 3996 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3997 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3998 3999 // Check for a constant condition. These are normally stripped out by 4000 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4001 // preserve the CFG and is temporarily leaving constant conditions 4002 // in place. 4003 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4004 if (L->contains(FBB) == !CI->getZExtValue()) 4005 // The backedge is always taken. 4006 return getCouldNotCompute(); 4007 else 4008 // The backedge is never taken. 4009 return getConstant(CI->getType(), 0); 4010 } 4011 4012 // If it's not an integer or pointer comparison then compute it the hard way. 4013 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4014} 4015 4016static const SCEVAddRecExpr * 4017isSimpleUnwrappingAddRec(const SCEV *S, const Loop *L) { 4018 const SCEVAddRecExpr *SA = dyn_cast<SCEVAddRecExpr>(S); 4019 4020 // The SCEV must be an addrec of this loop. 4021 if (!SA || SA->getLoop() != L || !SA->isAffine()) 4022 return 0; 4023 4024 // The SCEV must be known to not wrap in some way to be interesting. 4025 if (!SA->hasNoUnsignedWrap() && !SA->hasNoSignedWrap()) 4026 return 0; 4027 4028 // The stride must be a constant so that we know if it is striding up or down. 4029 if (!isa<SCEVConstant>(SA->getOperand(1))) 4030 return 0; 4031 return SA; 4032} 4033 4034/// getMinusSCEVForExitTest - When considering an exit test for a loop with a 4035/// "x != y" exit test, we turn this into a computation that evaluates x-y != 0, 4036/// and this function returns the expression to use for x-y. We know and take 4037/// advantage of the fact that this subtraction is only being used in a 4038/// comparison by zero context. 4039/// 4040static const SCEV *getMinusSCEVForExitTest(const SCEV *LHS, const SCEV *RHS, 4041 const Loop *L, ScalarEvolution &SE) { 4042 // If either LHS or RHS is an AddRec SCEV (of this loop) that is known to not 4043 // wrap (either NSW or NUW), then we know that the value will either become 4044 // the other one (and thus the loop terminates), that the loop will terminate 4045 // through some other exit condition first, or that the loop has undefined 4046 // behavior. This information is useful when the addrec has a stride that is 4047 // != 1 or -1, because it means we can't "miss" the exit value. 4048 // 4049 // In any of these three cases, it is safe to turn the exit condition into a 4050 // "counting down" AddRec (to zero) by subtracting the two inputs as normal, 4051 // but since we know that the "end cannot be missed" we can force the 4052 // resulting AddRec to be a NUW addrec. Since it is counting down, this means 4053 // that the AddRec *cannot* pass zero. 4054 4055 // See if LHS and RHS are addrec's we can handle. 4056 const SCEVAddRecExpr *LHSA = isSimpleUnwrappingAddRec(LHS, L); 4057 const SCEVAddRecExpr *RHSA = isSimpleUnwrappingAddRec(RHS, L); 4058 4059 // If neither addrec is interesting, just return a minus. 4060 if (RHSA == 0 && LHSA == 0) 4061 return SE.getMinusSCEV(LHS, RHS); 4062 4063 // If only one of LHS and RHS are an AddRec of this loop, make sure it is LHS. 4064 if (RHSA && LHSA == 0) { 4065 // Safe because a-b === b-a for comparisons against zero. 4066 std::swap(LHS, RHS); 4067 std::swap(LHSA, RHSA); 4068 } 4069 4070 // Handle the case when only one is advancing in a non-overflowing way. 4071 if (RHSA == 0) { 4072 // If RHS is loop varying, then we can't predict when LHS will cross it. 4073 if (!SE.isLoopInvariant(RHS, L)) 4074 return SE.getMinusSCEV(LHS, RHS); 4075 4076 // If LHS has a positive stride, then we compute RHS-LHS, because the loop 4077 // is counting up until it crosses RHS (which must be larger than LHS). If 4078 // it is negative, we compute LHS-RHS because we're counting down to RHS. 4079 const ConstantInt *Stride = 4080 cast<SCEVConstant>(LHSA->getOperand(1))->getValue(); 4081 if (Stride->getValue().isNegative()) 4082 std::swap(LHS, RHS); 4083 4084 return SE.getMinusSCEV(RHS, LHS, true /*HasNUW*/); 4085 } 4086 4087 // If both LHS and RHS are interesting, we have something like: 4088 // a+i*4 != b+i*8. 4089 const ConstantInt *LHSStride = 4090 cast<SCEVConstant>(LHSA->getOperand(1))->getValue(); 4091 const ConstantInt *RHSStride = 4092 cast<SCEVConstant>(RHSA->getOperand(1))->getValue(); 4093 4094 // If the strides are equal, then this is just a (complex) loop invariant 4095 // comparison of a and b. 4096 if (LHSStride == RHSStride) 4097 return SE.getMinusSCEV(LHSA->getStart(), RHSA->getStart()); 4098 4099 // If the signs of the strides differ, then the negative stride is counting 4100 // down to the positive stride. 4101 if (LHSStride->getValue().isNegative() != RHSStride->getValue().isNegative()){ 4102 if (RHSStride->getValue().isNegative()) 4103 std::swap(LHS, RHS); 4104 } else { 4105 // If LHS's stride is smaller than RHS's stride, then "b" must be less than 4106 // "a" and "b" is RHS is counting up (catching up) to LHS. This is true 4107 // whether the strides are positive or negative. 4108 if (RHSStride->getValue().slt(LHSStride->getValue())) 4109 std::swap(LHS, RHS); 4110 } 4111 4112 return SE.getMinusSCEV(LHS, RHS, true /*HasNUW*/); 4113} 4114 4115/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4116/// backedge of the specified loop will execute if its exit condition 4117/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4118ScalarEvolution::BackedgeTakenInfo 4119ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4120 ICmpInst *ExitCond, 4121 BasicBlock *TBB, 4122 BasicBlock *FBB) { 4123 4124 // If the condition was exit on true, convert the condition to exit on false 4125 ICmpInst::Predicate Cond; 4126 if (!L->contains(FBB)) 4127 Cond = ExitCond->getPredicate(); 4128 else 4129 Cond = ExitCond->getInversePredicate(); 4130 4131 // Handle common loops like: for (X = "string"; *X; ++X) 4132 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4133 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4134 BackedgeTakenInfo ItCnt = 4135 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4136 if (ItCnt.hasAnyInfo()) 4137 return ItCnt; 4138 } 4139 4140 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4141 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4142 4143 // Try to evaluate any dependencies out of the loop. 4144 LHS = getSCEVAtScope(LHS, L); 4145 RHS = getSCEVAtScope(RHS, L); 4146 4147 // At this point, we would like to compute how many iterations of the 4148 // loop the predicate will return true for these inputs. 4149 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4150 // If there is a loop-invariant, force it into the RHS. 4151 std::swap(LHS, RHS); 4152 Cond = ICmpInst::getSwappedPredicate(Cond); 4153 } 4154 4155 // Simplify the operands before analyzing them. 4156 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4157 4158 // If we have a comparison of a chrec against a constant, try to use value 4159 // ranges to answer this query. 4160 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4161 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4162 if (AddRec->getLoop() == L) { 4163 // Form the constant range. 4164 ConstantRange CompRange( 4165 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4166 4167 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4168 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4169 } 4170 4171 switch (Cond) { 4172 case ICmpInst::ICMP_NE: { // while (X != Y) 4173 // Convert to: while (X-Y != 0) 4174 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEVForExitTest(LHS, RHS, L, 4175 *this), L); 4176 if (BTI.hasAnyInfo()) return BTI; 4177 break; 4178 } 4179 case ICmpInst::ICMP_EQ: { // while (X == Y) 4180 // Convert to: while (X-Y == 0) 4181 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4182 if (BTI.hasAnyInfo()) return BTI; 4183 break; 4184 } 4185 case ICmpInst::ICMP_SLT: { 4186 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4187 if (BTI.hasAnyInfo()) return BTI; 4188 break; 4189 } 4190 case ICmpInst::ICMP_SGT: { 4191 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4192 getNotSCEV(RHS), L, true); 4193 if (BTI.hasAnyInfo()) return BTI; 4194 break; 4195 } 4196 case ICmpInst::ICMP_ULT: { 4197 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4198 if (BTI.hasAnyInfo()) return BTI; 4199 break; 4200 } 4201 case ICmpInst::ICMP_UGT: { 4202 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4203 getNotSCEV(RHS), L, false); 4204 if (BTI.hasAnyInfo()) return BTI; 4205 break; 4206 } 4207 default: 4208#if 0 4209 dbgs() << "ComputeBackedgeTakenCount "; 4210 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4211 dbgs() << "[unsigned] "; 4212 dbgs() << *LHS << " " 4213 << Instruction::getOpcodeName(Instruction::ICmp) 4214 << " " << *RHS << "\n"; 4215#endif 4216 break; 4217 } 4218 return 4219 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4220} 4221 4222static ConstantInt * 4223EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4224 ScalarEvolution &SE) { 4225 const SCEV *InVal = SE.getConstant(C); 4226 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4227 assert(isa<SCEVConstant>(Val) && 4228 "Evaluation of SCEV at constant didn't fold correctly?"); 4229 return cast<SCEVConstant>(Val)->getValue(); 4230} 4231 4232/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4233/// and a GEP expression (missing the pointer index) indexing into it, return 4234/// the addressed element of the initializer or null if the index expression is 4235/// invalid. 4236static Constant * 4237GetAddressedElementFromGlobal(GlobalVariable *GV, 4238 const std::vector<ConstantInt*> &Indices) { 4239 Constant *Init = GV->getInitializer(); 4240 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4241 uint64_t Idx = Indices[i]->getZExtValue(); 4242 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4243 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4244 Init = cast<Constant>(CS->getOperand(Idx)); 4245 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4246 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4247 Init = cast<Constant>(CA->getOperand(Idx)); 4248 } else if (isa<ConstantAggregateZero>(Init)) { 4249 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4250 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4251 Init = Constant::getNullValue(STy->getElementType(Idx)); 4252 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4253 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4254 Init = Constant::getNullValue(ATy->getElementType()); 4255 } else { 4256 llvm_unreachable("Unknown constant aggregate type!"); 4257 } 4258 return 0; 4259 } else { 4260 return 0; // Unknown initializer type 4261 } 4262 } 4263 return Init; 4264} 4265 4266/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4267/// 'icmp op load X, cst', try to see if we can compute the backedge 4268/// execution count. 4269ScalarEvolution::BackedgeTakenInfo 4270ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4271 LoadInst *LI, 4272 Constant *RHS, 4273 const Loop *L, 4274 ICmpInst::Predicate predicate) { 4275 if (LI->isVolatile()) return getCouldNotCompute(); 4276 4277 // Check to see if the loaded pointer is a getelementptr of a global. 4278 // TODO: Use SCEV instead of manually grubbing with GEPs. 4279 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4280 if (!GEP) return getCouldNotCompute(); 4281 4282 // Make sure that it is really a constant global we are gepping, with an 4283 // initializer, and make sure the first IDX is really 0. 4284 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4285 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4286 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4287 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4288 return getCouldNotCompute(); 4289 4290 // Okay, we allow one non-constant index into the GEP instruction. 4291 Value *VarIdx = 0; 4292 std::vector<ConstantInt*> Indexes; 4293 unsigned VarIdxNum = 0; 4294 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4295 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4296 Indexes.push_back(CI); 4297 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4298 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4299 VarIdx = GEP->getOperand(i); 4300 VarIdxNum = i-2; 4301 Indexes.push_back(0); 4302 } 4303 4304 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4305 // Check to see if X is a loop variant variable value now. 4306 const SCEV *Idx = getSCEV(VarIdx); 4307 Idx = getSCEVAtScope(Idx, L); 4308 4309 // We can only recognize very limited forms of loop index expressions, in 4310 // particular, only affine AddRec's like {C1,+,C2}. 4311 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4312 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4313 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4314 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4315 return getCouldNotCompute(); 4316 4317 unsigned MaxSteps = MaxBruteForceIterations; 4318 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4319 ConstantInt *ItCst = ConstantInt::get( 4320 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4321 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4322 4323 // Form the GEP offset. 4324 Indexes[VarIdxNum] = Val; 4325 4326 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4327 if (Result == 0) break; // Cannot compute! 4328 4329 // Evaluate the condition for this iteration. 4330 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4331 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4332 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4333#if 0 4334 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4335 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4336 << "***\n"; 4337#endif 4338 ++NumArrayLenItCounts; 4339 return getConstant(ItCst); // Found terminating iteration! 4340 } 4341 } 4342 return getCouldNotCompute(); 4343} 4344 4345 4346/// CanConstantFold - Return true if we can constant fold an instruction of the 4347/// specified type, assuming that all operands were constants. 4348static bool CanConstantFold(const Instruction *I) { 4349 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4350 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4351 return true; 4352 4353 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4354 if (const Function *F = CI->getCalledFunction()) 4355 return canConstantFoldCallTo(F); 4356 return false; 4357} 4358 4359/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4360/// in the loop that V is derived from. We allow arbitrary operations along the 4361/// way, but the operands of an operation must either be constants or a value 4362/// derived from a constant PHI. If this expression does not fit with these 4363/// constraints, return null. 4364static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4365 // If this is not an instruction, or if this is an instruction outside of the 4366 // loop, it can't be derived from a loop PHI. 4367 Instruction *I = dyn_cast<Instruction>(V); 4368 if (I == 0 || !L->contains(I)) return 0; 4369 4370 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4371 if (L->getHeader() == I->getParent()) 4372 return PN; 4373 else 4374 // We don't currently keep track of the control flow needed to evaluate 4375 // PHIs, so we cannot handle PHIs inside of loops. 4376 return 0; 4377 } 4378 4379 // If we won't be able to constant fold this expression even if the operands 4380 // are constants, return early. 4381 if (!CanConstantFold(I)) return 0; 4382 4383 // Otherwise, we can evaluate this instruction if all of its operands are 4384 // constant or derived from a PHI node themselves. 4385 PHINode *PHI = 0; 4386 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4387 if (!isa<Constant>(I->getOperand(Op))) { 4388 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4389 if (P == 0) return 0; // Not evolving from PHI 4390 if (PHI == 0) 4391 PHI = P; 4392 else if (PHI != P) 4393 return 0; // Evolving from multiple different PHIs. 4394 } 4395 4396 // This is a expression evolving from a constant PHI! 4397 return PHI; 4398} 4399 4400/// EvaluateExpression - Given an expression that passes the 4401/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4402/// in the loop has the value PHIVal. If we can't fold this expression for some 4403/// reason, return null. 4404static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4405 const TargetData *TD) { 4406 if (isa<PHINode>(V)) return PHIVal; 4407 if (Constant *C = dyn_cast<Constant>(V)) return C; 4408 Instruction *I = cast<Instruction>(V); 4409 4410 std::vector<Constant*> Operands(I->getNumOperands()); 4411 4412 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4413 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4414 if (Operands[i] == 0) return 0; 4415 } 4416 4417 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4418 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4419 Operands[1], TD); 4420 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4421 &Operands[0], Operands.size(), TD); 4422} 4423 4424/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4425/// in the header of its containing loop, we know the loop executes a 4426/// constant number of times, and the PHI node is just a recurrence 4427/// involving constants, fold it. 4428Constant * 4429ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4430 const APInt &BEs, 4431 const Loop *L) { 4432 std::map<PHINode*, Constant*>::const_iterator I = 4433 ConstantEvolutionLoopExitValue.find(PN); 4434 if (I != ConstantEvolutionLoopExitValue.end()) 4435 return I->second; 4436 4437 if (BEs.ugt(MaxBruteForceIterations)) 4438 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4439 4440 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4441 4442 // Since the loop is canonicalized, the PHI node must have two entries. One 4443 // entry must be a constant (coming in from outside of the loop), and the 4444 // second must be derived from the same PHI. 4445 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4446 Constant *StartCST = 4447 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4448 if (StartCST == 0) 4449 return RetVal = 0; // Must be a constant. 4450 4451 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4452 if (getConstantEvolvingPHI(BEValue, L) != PN && 4453 !isa<Constant>(BEValue)) 4454 return RetVal = 0; // Not derived from same PHI. 4455 4456 // Execute the loop symbolically to determine the exit value. 4457 if (BEs.getActiveBits() >= 32) 4458 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4459 4460 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4461 unsigned IterationNum = 0; 4462 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4463 if (IterationNum == NumIterations) 4464 return RetVal = PHIVal; // Got exit value! 4465 4466 // Compute the value of the PHI node for the next iteration. 4467 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4468 if (NextPHI == PHIVal) 4469 return RetVal = NextPHI; // Stopped evolving! 4470 if (NextPHI == 0) 4471 return 0; // Couldn't evaluate! 4472 PHIVal = NextPHI; 4473 } 4474} 4475 4476/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4477/// constant number of times (the condition evolves only from constants), 4478/// try to evaluate a few iterations of the loop until we get the exit 4479/// condition gets a value of ExitWhen (true or false). If we cannot 4480/// evaluate the trip count of the loop, return getCouldNotCompute(). 4481const SCEV * 4482ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4483 Value *Cond, 4484 bool ExitWhen) { 4485 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4486 if (PN == 0) return getCouldNotCompute(); 4487 4488 // If the loop is canonicalized, the PHI will have exactly two entries. 4489 // That's the only form we support here. 4490 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4491 4492 // One entry must be a constant (coming in from outside of the loop), and the 4493 // second must be derived from the same PHI. 4494 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4495 Constant *StartCST = 4496 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4497 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4498 4499 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4500 if (getConstantEvolvingPHI(BEValue, L) != PN && 4501 !isa<Constant>(BEValue)) 4502 return getCouldNotCompute(); // Not derived from same PHI. 4503 4504 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4505 // the loop symbolically to determine when the condition gets a value of 4506 // "ExitWhen". 4507 unsigned IterationNum = 0; 4508 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4509 for (Constant *PHIVal = StartCST; 4510 IterationNum != MaxIterations; ++IterationNum) { 4511 ConstantInt *CondVal = 4512 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4513 4514 // Couldn't symbolically evaluate. 4515 if (!CondVal) return getCouldNotCompute(); 4516 4517 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4518 ++NumBruteForceTripCountsComputed; 4519 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4520 } 4521 4522 // Compute the value of the PHI node for the next iteration. 4523 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4524 if (NextPHI == 0 || NextPHI == PHIVal) 4525 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4526 PHIVal = NextPHI; 4527 } 4528 4529 // Too many iterations were needed to evaluate. 4530 return getCouldNotCompute(); 4531} 4532 4533/// getSCEVAtScope - Return a SCEV expression for the specified value 4534/// at the specified scope in the program. The L value specifies a loop 4535/// nest to evaluate the expression at, where null is the top-level or a 4536/// specified loop is immediately inside of the loop. 4537/// 4538/// This method can be used to compute the exit value for a variable defined 4539/// in a loop by querying what the value will hold in the parent loop. 4540/// 4541/// In the case that a relevant loop exit value cannot be computed, the 4542/// original value V is returned. 4543const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4544 // Check to see if we've folded this expression at this loop before. 4545 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4546 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4547 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4548 if (!Pair.second) 4549 return Pair.first->second ? Pair.first->second : V; 4550 4551 // Otherwise compute it. 4552 const SCEV *C = computeSCEVAtScope(V, L); 4553 ValuesAtScopes[V][L] = C; 4554 return C; 4555} 4556 4557const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4558 if (isa<SCEVConstant>(V)) return V; 4559 4560 // If this instruction is evolved from a constant-evolving PHI, compute the 4561 // exit value from the loop without using SCEVs. 4562 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4563 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4564 const Loop *LI = (*this->LI)[I->getParent()]; 4565 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4566 if (PHINode *PN = dyn_cast<PHINode>(I)) 4567 if (PN->getParent() == LI->getHeader()) { 4568 // Okay, there is no closed form solution for the PHI node. Check 4569 // to see if the loop that contains it has a known backedge-taken 4570 // count. If so, we may be able to force computation of the exit 4571 // value. 4572 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4573 if (const SCEVConstant *BTCC = 4574 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4575 // Okay, we know how many times the containing loop executes. If 4576 // this is a constant evolving PHI node, get the final value at 4577 // the specified iteration number. 4578 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4579 BTCC->getValue()->getValue(), 4580 LI); 4581 if (RV) return getSCEV(RV); 4582 } 4583 } 4584 4585 // Okay, this is an expression that we cannot symbolically evaluate 4586 // into a SCEV. Check to see if it's possible to symbolically evaluate 4587 // the arguments into constants, and if so, try to constant propagate the 4588 // result. This is particularly useful for computing loop exit values. 4589 if (CanConstantFold(I)) { 4590 SmallVector<Constant *, 4> Operands; 4591 bool MadeImprovement = false; 4592 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4593 Value *Op = I->getOperand(i); 4594 if (Constant *C = dyn_cast<Constant>(Op)) { 4595 Operands.push_back(C); 4596 continue; 4597 } 4598 4599 // If any of the operands is non-constant and if they are 4600 // non-integer and non-pointer, don't even try to analyze them 4601 // with scev techniques. 4602 if (!isSCEVable(Op->getType())) 4603 return V; 4604 4605 const SCEV *OrigV = getSCEV(Op); 4606 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4607 MadeImprovement |= OrigV != OpV; 4608 4609 Constant *C = 0; 4610 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4611 C = SC->getValue(); 4612 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4613 C = dyn_cast<Constant>(SU->getValue()); 4614 if (!C) return V; 4615 if (C->getType() != Op->getType()) 4616 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4617 Op->getType(), 4618 false), 4619 C, Op->getType()); 4620 Operands.push_back(C); 4621 } 4622 4623 // Check to see if getSCEVAtScope actually made an improvement. 4624 if (MadeImprovement) { 4625 Constant *C = 0; 4626 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4627 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4628 Operands[0], Operands[1], TD); 4629 else 4630 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4631 &Operands[0], Operands.size(), TD); 4632 if (!C) return V; 4633 return getSCEV(C); 4634 } 4635 } 4636 } 4637 4638 // This is some other type of SCEVUnknown, just return it. 4639 return V; 4640 } 4641 4642 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4643 // Avoid performing the look-up in the common case where the specified 4644 // expression has no loop-variant portions. 4645 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4646 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4647 if (OpAtScope != Comm->getOperand(i)) { 4648 // Okay, at least one of these operands is loop variant but might be 4649 // foldable. Build a new instance of the folded commutative expression. 4650 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4651 Comm->op_begin()+i); 4652 NewOps.push_back(OpAtScope); 4653 4654 for (++i; i != e; ++i) { 4655 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4656 NewOps.push_back(OpAtScope); 4657 } 4658 if (isa<SCEVAddExpr>(Comm)) 4659 return getAddExpr(NewOps); 4660 if (isa<SCEVMulExpr>(Comm)) 4661 return getMulExpr(NewOps); 4662 if (isa<SCEVSMaxExpr>(Comm)) 4663 return getSMaxExpr(NewOps); 4664 if (isa<SCEVUMaxExpr>(Comm)) 4665 return getUMaxExpr(NewOps); 4666 llvm_unreachable("Unknown commutative SCEV type!"); 4667 } 4668 } 4669 // If we got here, all operands are loop invariant. 4670 return Comm; 4671 } 4672 4673 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4674 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4675 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4676 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4677 return Div; // must be loop invariant 4678 return getUDivExpr(LHS, RHS); 4679 } 4680 4681 // If this is a loop recurrence for a loop that does not contain L, then we 4682 // are dealing with the final value computed by the loop. 4683 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4684 // First, attempt to evaluate each operand. 4685 // Avoid performing the look-up in the common case where the specified 4686 // expression has no loop-variant portions. 4687 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4688 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4689 if (OpAtScope == AddRec->getOperand(i)) 4690 continue; 4691 4692 // Okay, at least one of these operands is loop variant but might be 4693 // foldable. Build a new instance of the folded commutative expression. 4694 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4695 AddRec->op_begin()+i); 4696 NewOps.push_back(OpAtScope); 4697 for (++i; i != e; ++i) 4698 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4699 4700 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4701 break; 4702 } 4703 4704 // If the scope is outside the addrec's loop, evaluate it by using the 4705 // loop exit value of the addrec. 4706 if (!AddRec->getLoop()->contains(L)) { 4707 // To evaluate this recurrence, we need to know how many times the AddRec 4708 // loop iterates. Compute this now. 4709 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4710 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4711 4712 // Then, evaluate the AddRec. 4713 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4714 } 4715 4716 return AddRec; 4717 } 4718 4719 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4720 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4721 if (Op == Cast->getOperand()) 4722 return Cast; // must be loop invariant 4723 return getZeroExtendExpr(Op, Cast->getType()); 4724 } 4725 4726 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4727 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4728 if (Op == Cast->getOperand()) 4729 return Cast; // must be loop invariant 4730 return getSignExtendExpr(Op, Cast->getType()); 4731 } 4732 4733 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4734 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4735 if (Op == Cast->getOperand()) 4736 return Cast; // must be loop invariant 4737 return getTruncateExpr(Op, Cast->getType()); 4738 } 4739 4740 llvm_unreachable("Unknown SCEV type!"); 4741 return 0; 4742} 4743 4744/// getSCEVAtScope - This is a convenience function which does 4745/// getSCEVAtScope(getSCEV(V), L). 4746const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4747 return getSCEVAtScope(getSCEV(V), L); 4748} 4749 4750/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4751/// following equation: 4752/// 4753/// A * X = B (mod N) 4754/// 4755/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4756/// A and B isn't important. 4757/// 4758/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4759static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4760 ScalarEvolution &SE) { 4761 uint32_t BW = A.getBitWidth(); 4762 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4763 assert(A != 0 && "A must be non-zero."); 4764 4765 // 1. D = gcd(A, N) 4766 // 4767 // The gcd of A and N may have only one prime factor: 2. The number of 4768 // trailing zeros in A is its multiplicity 4769 uint32_t Mult2 = A.countTrailingZeros(); 4770 // D = 2^Mult2 4771 4772 // 2. Check if B is divisible by D. 4773 // 4774 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4775 // is not less than multiplicity of this prime factor for D. 4776 if (B.countTrailingZeros() < Mult2) 4777 return SE.getCouldNotCompute(); 4778 4779 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4780 // modulo (N / D). 4781 // 4782 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4783 // bit width during computations. 4784 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4785 APInt Mod(BW + 1, 0); 4786 Mod.setBit(BW - Mult2); // Mod = N / D 4787 APInt I = AD.multiplicativeInverse(Mod); 4788 4789 // 4. Compute the minimum unsigned root of the equation: 4790 // I * (B / D) mod (N / D) 4791 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4792 4793 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4794 // bits. 4795 return SE.getConstant(Result.trunc(BW)); 4796} 4797 4798/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4799/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4800/// might be the same) or two SCEVCouldNotCompute objects. 4801/// 4802static std::pair<const SCEV *,const SCEV *> 4803SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4804 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4805 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4806 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4807 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4808 4809 // We currently can only solve this if the coefficients are constants. 4810 if (!LC || !MC || !NC) { 4811 const SCEV *CNC = SE.getCouldNotCompute(); 4812 return std::make_pair(CNC, CNC); 4813 } 4814 4815 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4816 const APInt &L = LC->getValue()->getValue(); 4817 const APInt &M = MC->getValue()->getValue(); 4818 const APInt &N = NC->getValue()->getValue(); 4819 APInt Two(BitWidth, 2); 4820 APInt Four(BitWidth, 4); 4821 4822 { 4823 using namespace APIntOps; 4824 const APInt& C = L; 4825 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4826 // The B coefficient is M-N/2 4827 APInt B(M); 4828 B -= sdiv(N,Two); 4829 4830 // The A coefficient is N/2 4831 APInt A(N.sdiv(Two)); 4832 4833 // Compute the B^2-4ac term. 4834 APInt SqrtTerm(B); 4835 SqrtTerm *= B; 4836 SqrtTerm -= Four * (A * C); 4837 4838 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4839 // integer value or else APInt::sqrt() will assert. 4840 APInt SqrtVal(SqrtTerm.sqrt()); 4841 4842 // Compute the two solutions for the quadratic formula. 4843 // The divisions must be performed as signed divisions. 4844 APInt NegB(-B); 4845 APInt TwoA( A << 1 ); 4846 if (TwoA.isMinValue()) { 4847 const SCEV *CNC = SE.getCouldNotCompute(); 4848 return std::make_pair(CNC, CNC); 4849 } 4850 4851 LLVMContext &Context = SE.getContext(); 4852 4853 ConstantInt *Solution1 = 4854 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4855 ConstantInt *Solution2 = 4856 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4857 4858 return std::make_pair(SE.getConstant(Solution1), 4859 SE.getConstant(Solution2)); 4860 } // end APIntOps namespace 4861} 4862 4863/// HowFarToZero - Return the number of times a backedge comparing the specified 4864/// value to zero will execute. If not computable, return CouldNotCompute. 4865ScalarEvolution::BackedgeTakenInfo 4866ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4867 // If the value is a constant 4868 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4869 // If the value is already zero, the branch will execute zero times. 4870 if (C->getValue()->isZero()) return C; 4871 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4872 } 4873 4874 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4875 if (!AddRec || AddRec->getLoop() != L) 4876 return getCouldNotCompute(); 4877 4878 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4879 // the quadratic equation to solve it. 4880 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4881 std::pair<const SCEV *,const SCEV *> Roots = 4882 SolveQuadraticEquation(AddRec, *this); 4883 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4884 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4885 if (R1 && R2) { 4886#if 0 4887 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4888 << " sol#2: " << *R2 << "\n"; 4889#endif 4890 // Pick the smallest positive root value. 4891 if (ConstantInt *CB = 4892 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 4893 R1->getValue(), 4894 R2->getValue()))) { 4895 if (CB->getZExtValue() == false) 4896 std::swap(R1, R2); // R1 is the minimum root now. 4897 4898 // We can only use this value if the chrec ends up with an exact zero 4899 // value at this index. When solving for "X*X != 5", for example, we 4900 // should not accept a root of 2. 4901 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4902 if (Val->isZero()) 4903 return R1; // We found a quadratic root! 4904 } 4905 } 4906 return getCouldNotCompute(); 4907 } 4908 4909 // Otherwise we can only handle this if it is affine. 4910 if (!AddRec->isAffine()) 4911 return getCouldNotCompute(); 4912 4913 // If this is an affine expression, the execution count of this branch is 4914 // the minimum unsigned root of the following equation: 4915 // 4916 // Start + Step*N = 0 (mod 2^BW) 4917 // 4918 // equivalent to: 4919 // 4920 // Step*N = -Start (mod 2^BW) 4921 // 4922 // where BW is the common bit width of Start and Step. 4923 4924 // Get the initial value for the loop. 4925 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 4926 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 4927 4928 // If the AddRec is NUW, then (in an unsigned sense) it cannot be counting up 4929 // to wrap to 0, it must be counting down to equal 0. Also, while counting 4930 // down, it cannot "miss" 0 (which would cause it to wrap), regardless of what 4931 // the stride is. As such, NUW addrec's will always become zero in 4932 // "start / -stride" steps, and we know that the division is exact. 4933 if (AddRec->hasNoUnsignedWrap()) 4934 // FIXME: We really want an "isexact" bit for udiv. 4935 return getUDivExpr(Start, getNegativeSCEV(Step)); 4936 4937 // For now we handle only constant steps. 4938 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 4939 if (StepC == 0) 4940 return getCouldNotCompute(); 4941 4942 // First, handle unitary steps. 4943 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4944 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4945 4946 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4947 return Start; // N = Start (as unsigned) 4948 4949 // Then, try to solve the above equation provided that Start is constant. 4950 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4951 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4952 -StartC->getValue()->getValue(), 4953 *this); 4954 return getCouldNotCompute(); 4955} 4956 4957/// HowFarToNonZero - Return the number of times a backedge checking the 4958/// specified value for nonzero will execute. If not computable, return 4959/// CouldNotCompute 4960ScalarEvolution::BackedgeTakenInfo 4961ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4962 // Loops that look like: while (X == 0) are very strange indeed. We don't 4963 // handle them yet except for the trivial case. This could be expanded in the 4964 // future as needed. 4965 4966 // If the value is a constant, check to see if it is known to be non-zero 4967 // already. If so, the backedge will execute zero times. 4968 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4969 if (!C->getValue()->isNullValue()) 4970 return getConstant(C->getType(), 0); 4971 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4972 } 4973 4974 // We could implement others, but I really doubt anyone writes loops like 4975 // this, and if they did, they would already be constant folded. 4976 return getCouldNotCompute(); 4977} 4978 4979/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4980/// (which may not be an immediate predecessor) which has exactly one 4981/// successor from which BB is reachable, or null if no such block is 4982/// found. 4983/// 4984std::pair<BasicBlock *, BasicBlock *> 4985ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4986 // If the block has a unique predecessor, then there is no path from the 4987 // predecessor to the block that does not go through the direct edge 4988 // from the predecessor to the block. 4989 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4990 return std::make_pair(Pred, BB); 4991 4992 // A loop's header is defined to be a block that dominates the loop. 4993 // If the header has a unique predecessor outside the loop, it must be 4994 // a block that has exactly one successor that can reach the loop. 4995 if (Loop *L = LI->getLoopFor(BB)) 4996 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4997 4998 return std::pair<BasicBlock *, BasicBlock *>(); 4999} 5000 5001/// HasSameValue - SCEV structural equivalence is usually sufficient for 5002/// testing whether two expressions are equal, however for the purposes of 5003/// looking for a condition guarding a loop, it can be useful to be a little 5004/// more general, since a front-end may have replicated the controlling 5005/// expression. 5006/// 5007static bool HasSameValue(const SCEV *A, const SCEV *B) { 5008 // Quick check to see if they are the same SCEV. 5009 if (A == B) return true; 5010 5011 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5012 // two different instructions with the same value. Check for this case. 5013 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5014 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5015 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5016 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5017 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5018 return true; 5019 5020 // Otherwise assume they may have a different value. 5021 return false; 5022} 5023 5024/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5025/// predicate Pred. Return true iff any changes were made. 5026/// 5027bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5028 const SCEV *&LHS, const SCEV *&RHS) { 5029 bool Changed = false; 5030 5031 // Canonicalize a constant to the right side. 5032 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5033 // Check for both operands constant. 5034 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5035 if (ConstantExpr::getICmp(Pred, 5036 LHSC->getValue(), 5037 RHSC->getValue())->isNullValue()) 5038 goto trivially_false; 5039 else 5040 goto trivially_true; 5041 } 5042 // Otherwise swap the operands to put the constant on the right. 5043 std::swap(LHS, RHS); 5044 Pred = ICmpInst::getSwappedPredicate(Pred); 5045 Changed = true; 5046 } 5047 5048 // If we're comparing an addrec with a value which is loop-invariant in the 5049 // addrec's loop, put the addrec on the left. Also make a dominance check, 5050 // as both operands could be addrecs loop-invariant in each other's loop. 5051 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5052 const Loop *L = AR->getLoop(); 5053 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5054 std::swap(LHS, RHS); 5055 Pred = ICmpInst::getSwappedPredicate(Pred); 5056 Changed = true; 5057 } 5058 } 5059 5060 // If there's a constant operand, canonicalize comparisons with boundary 5061 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5062 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5063 const APInt &RA = RC->getValue()->getValue(); 5064 switch (Pred) { 5065 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5066 case ICmpInst::ICMP_EQ: 5067 case ICmpInst::ICMP_NE: 5068 break; 5069 case ICmpInst::ICMP_UGE: 5070 if ((RA - 1).isMinValue()) { 5071 Pred = ICmpInst::ICMP_NE; 5072 RHS = getConstant(RA - 1); 5073 Changed = true; 5074 break; 5075 } 5076 if (RA.isMaxValue()) { 5077 Pred = ICmpInst::ICMP_EQ; 5078 Changed = true; 5079 break; 5080 } 5081 if (RA.isMinValue()) goto trivially_true; 5082 5083 Pred = ICmpInst::ICMP_UGT; 5084 RHS = getConstant(RA - 1); 5085 Changed = true; 5086 break; 5087 case ICmpInst::ICMP_ULE: 5088 if ((RA + 1).isMaxValue()) { 5089 Pred = ICmpInst::ICMP_NE; 5090 RHS = getConstant(RA + 1); 5091 Changed = true; 5092 break; 5093 } 5094 if (RA.isMinValue()) { 5095 Pred = ICmpInst::ICMP_EQ; 5096 Changed = true; 5097 break; 5098 } 5099 if (RA.isMaxValue()) goto trivially_true; 5100 5101 Pred = ICmpInst::ICMP_ULT; 5102 RHS = getConstant(RA + 1); 5103 Changed = true; 5104 break; 5105 case ICmpInst::ICMP_SGE: 5106 if ((RA - 1).isMinSignedValue()) { 5107 Pred = ICmpInst::ICMP_NE; 5108 RHS = getConstant(RA - 1); 5109 Changed = true; 5110 break; 5111 } 5112 if (RA.isMaxSignedValue()) { 5113 Pred = ICmpInst::ICMP_EQ; 5114 Changed = true; 5115 break; 5116 } 5117 if (RA.isMinSignedValue()) goto trivially_true; 5118 5119 Pred = ICmpInst::ICMP_SGT; 5120 RHS = getConstant(RA - 1); 5121 Changed = true; 5122 break; 5123 case ICmpInst::ICMP_SLE: 5124 if ((RA + 1).isMaxSignedValue()) { 5125 Pred = ICmpInst::ICMP_NE; 5126 RHS = getConstant(RA + 1); 5127 Changed = true; 5128 break; 5129 } 5130 if (RA.isMinSignedValue()) { 5131 Pred = ICmpInst::ICMP_EQ; 5132 Changed = true; 5133 break; 5134 } 5135 if (RA.isMaxSignedValue()) goto trivially_true; 5136 5137 Pred = ICmpInst::ICMP_SLT; 5138 RHS = getConstant(RA + 1); 5139 Changed = true; 5140 break; 5141 case ICmpInst::ICMP_UGT: 5142 if (RA.isMinValue()) { 5143 Pred = ICmpInst::ICMP_NE; 5144 Changed = true; 5145 break; 5146 } 5147 if ((RA + 1).isMaxValue()) { 5148 Pred = ICmpInst::ICMP_EQ; 5149 RHS = getConstant(RA + 1); 5150 Changed = true; 5151 break; 5152 } 5153 if (RA.isMaxValue()) goto trivially_false; 5154 break; 5155 case ICmpInst::ICMP_ULT: 5156 if (RA.isMaxValue()) { 5157 Pred = ICmpInst::ICMP_NE; 5158 Changed = true; 5159 break; 5160 } 5161 if ((RA - 1).isMinValue()) { 5162 Pred = ICmpInst::ICMP_EQ; 5163 RHS = getConstant(RA - 1); 5164 Changed = true; 5165 break; 5166 } 5167 if (RA.isMinValue()) goto trivially_false; 5168 break; 5169 case ICmpInst::ICMP_SGT: 5170 if (RA.isMinSignedValue()) { 5171 Pred = ICmpInst::ICMP_NE; 5172 Changed = true; 5173 break; 5174 } 5175 if ((RA + 1).isMaxSignedValue()) { 5176 Pred = ICmpInst::ICMP_EQ; 5177 RHS = getConstant(RA + 1); 5178 Changed = true; 5179 break; 5180 } 5181 if (RA.isMaxSignedValue()) goto trivially_false; 5182 break; 5183 case ICmpInst::ICMP_SLT: 5184 if (RA.isMaxSignedValue()) { 5185 Pred = ICmpInst::ICMP_NE; 5186 Changed = true; 5187 break; 5188 } 5189 if ((RA - 1).isMinSignedValue()) { 5190 Pred = ICmpInst::ICMP_EQ; 5191 RHS = getConstant(RA - 1); 5192 Changed = true; 5193 break; 5194 } 5195 if (RA.isMinSignedValue()) goto trivially_false; 5196 break; 5197 } 5198 } 5199 5200 // Check for obvious equality. 5201 if (HasSameValue(LHS, RHS)) { 5202 if (ICmpInst::isTrueWhenEqual(Pred)) 5203 goto trivially_true; 5204 if (ICmpInst::isFalseWhenEqual(Pred)) 5205 goto trivially_false; 5206 } 5207 5208 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5209 // adding or subtracting 1 from one of the operands. 5210 switch (Pred) { 5211 case ICmpInst::ICMP_SLE: 5212 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5213 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5214 /*HasNUW=*/false, /*HasNSW=*/true); 5215 Pred = ICmpInst::ICMP_SLT; 5216 Changed = true; 5217 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5218 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5219 /*HasNUW=*/false, /*HasNSW=*/true); 5220 Pred = ICmpInst::ICMP_SLT; 5221 Changed = true; 5222 } 5223 break; 5224 case ICmpInst::ICMP_SGE: 5225 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5226 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5227 /*HasNUW=*/false, /*HasNSW=*/true); 5228 Pred = ICmpInst::ICMP_SGT; 5229 Changed = true; 5230 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5231 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5232 /*HasNUW=*/false, /*HasNSW=*/true); 5233 Pred = ICmpInst::ICMP_SGT; 5234 Changed = true; 5235 } 5236 break; 5237 case ICmpInst::ICMP_ULE: 5238 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5239 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5240 /*HasNUW=*/true, /*HasNSW=*/false); 5241 Pred = ICmpInst::ICMP_ULT; 5242 Changed = true; 5243 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5244 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5245 /*HasNUW=*/true, /*HasNSW=*/false); 5246 Pred = ICmpInst::ICMP_ULT; 5247 Changed = true; 5248 } 5249 break; 5250 case ICmpInst::ICMP_UGE: 5251 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5252 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5253 /*HasNUW=*/true, /*HasNSW=*/false); 5254 Pred = ICmpInst::ICMP_UGT; 5255 Changed = true; 5256 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5257 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5258 /*HasNUW=*/true, /*HasNSW=*/false); 5259 Pred = ICmpInst::ICMP_UGT; 5260 Changed = true; 5261 } 5262 break; 5263 default: 5264 break; 5265 } 5266 5267 // TODO: More simplifications are possible here. 5268 5269 return Changed; 5270 5271trivially_true: 5272 // Return 0 == 0. 5273 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5274 Pred = ICmpInst::ICMP_EQ; 5275 return true; 5276 5277trivially_false: 5278 // Return 0 != 0. 5279 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5280 Pred = ICmpInst::ICMP_NE; 5281 return true; 5282} 5283 5284bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5285 return getSignedRange(S).getSignedMax().isNegative(); 5286} 5287 5288bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5289 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5290} 5291 5292bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5293 return !getSignedRange(S).getSignedMin().isNegative(); 5294} 5295 5296bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5297 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5298} 5299 5300bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5301 return isKnownNegative(S) || isKnownPositive(S); 5302} 5303 5304bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5305 const SCEV *LHS, const SCEV *RHS) { 5306 // Canonicalize the inputs first. 5307 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5308 5309 // If LHS or RHS is an addrec, check to see if the condition is true in 5310 // every iteration of the loop. 5311 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5312 if (isLoopEntryGuardedByCond( 5313 AR->getLoop(), Pred, AR->getStart(), RHS) && 5314 isLoopBackedgeGuardedByCond( 5315 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5316 return true; 5317 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5318 if (isLoopEntryGuardedByCond( 5319 AR->getLoop(), Pred, LHS, AR->getStart()) && 5320 isLoopBackedgeGuardedByCond( 5321 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5322 return true; 5323 5324 // Otherwise see what can be done with known constant ranges. 5325 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5326} 5327 5328bool 5329ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5330 const SCEV *LHS, const SCEV *RHS) { 5331 if (HasSameValue(LHS, RHS)) 5332 return ICmpInst::isTrueWhenEqual(Pred); 5333 5334 // This code is split out from isKnownPredicate because it is called from 5335 // within isLoopEntryGuardedByCond. 5336 switch (Pred) { 5337 default: 5338 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5339 break; 5340 case ICmpInst::ICMP_SGT: 5341 Pred = ICmpInst::ICMP_SLT; 5342 std::swap(LHS, RHS); 5343 case ICmpInst::ICMP_SLT: { 5344 ConstantRange LHSRange = getSignedRange(LHS); 5345 ConstantRange RHSRange = getSignedRange(RHS); 5346 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5347 return true; 5348 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5349 return false; 5350 break; 5351 } 5352 case ICmpInst::ICMP_SGE: 5353 Pred = ICmpInst::ICMP_SLE; 5354 std::swap(LHS, RHS); 5355 case ICmpInst::ICMP_SLE: { 5356 ConstantRange LHSRange = getSignedRange(LHS); 5357 ConstantRange RHSRange = getSignedRange(RHS); 5358 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5359 return true; 5360 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5361 return false; 5362 break; 5363 } 5364 case ICmpInst::ICMP_UGT: 5365 Pred = ICmpInst::ICMP_ULT; 5366 std::swap(LHS, RHS); 5367 case ICmpInst::ICMP_ULT: { 5368 ConstantRange LHSRange = getUnsignedRange(LHS); 5369 ConstantRange RHSRange = getUnsignedRange(RHS); 5370 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5371 return true; 5372 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5373 return false; 5374 break; 5375 } 5376 case ICmpInst::ICMP_UGE: 5377 Pred = ICmpInst::ICMP_ULE; 5378 std::swap(LHS, RHS); 5379 case ICmpInst::ICMP_ULE: { 5380 ConstantRange LHSRange = getUnsignedRange(LHS); 5381 ConstantRange RHSRange = getUnsignedRange(RHS); 5382 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5383 return true; 5384 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5385 return false; 5386 break; 5387 } 5388 case ICmpInst::ICMP_NE: { 5389 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5390 return true; 5391 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5392 return true; 5393 5394 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5395 if (isKnownNonZero(Diff)) 5396 return true; 5397 break; 5398 } 5399 case ICmpInst::ICMP_EQ: 5400 // The check at the top of the function catches the case where 5401 // the values are known to be equal. 5402 break; 5403 } 5404 return false; 5405} 5406 5407/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5408/// protected by a conditional between LHS and RHS. This is used to 5409/// to eliminate casts. 5410bool 5411ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5412 ICmpInst::Predicate Pred, 5413 const SCEV *LHS, const SCEV *RHS) { 5414 // Interpret a null as meaning no loop, where there is obviously no guard 5415 // (interprocedural conditions notwithstanding). 5416 if (!L) return true; 5417 5418 BasicBlock *Latch = L->getLoopLatch(); 5419 if (!Latch) 5420 return false; 5421 5422 BranchInst *LoopContinuePredicate = 5423 dyn_cast<BranchInst>(Latch->getTerminator()); 5424 if (!LoopContinuePredicate || 5425 LoopContinuePredicate->isUnconditional()) 5426 return false; 5427 5428 return isImpliedCond(Pred, LHS, RHS, 5429 LoopContinuePredicate->getCondition(), 5430 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5431} 5432 5433/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5434/// by a conditional between LHS and RHS. This is used to help avoid max 5435/// expressions in loop trip counts, and to eliminate casts. 5436bool 5437ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5438 ICmpInst::Predicate Pred, 5439 const SCEV *LHS, const SCEV *RHS) { 5440 // Interpret a null as meaning no loop, where there is obviously no guard 5441 // (interprocedural conditions notwithstanding). 5442 if (!L) return false; 5443 5444 // Starting at the loop predecessor, climb up the predecessor chain, as long 5445 // as there are predecessors that can be found that have unique successors 5446 // leading to the original header. 5447 for (std::pair<BasicBlock *, BasicBlock *> 5448 Pair(L->getLoopPredecessor(), L->getHeader()); 5449 Pair.first; 5450 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5451 5452 BranchInst *LoopEntryPredicate = 5453 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5454 if (!LoopEntryPredicate || 5455 LoopEntryPredicate->isUnconditional()) 5456 continue; 5457 5458 if (isImpliedCond(Pred, LHS, RHS, 5459 LoopEntryPredicate->getCondition(), 5460 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5461 return true; 5462 } 5463 5464 return false; 5465} 5466 5467/// isImpliedCond - Test whether the condition described by Pred, LHS, 5468/// and RHS is true whenever the given Cond value evaluates to true. 5469bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5470 const SCEV *LHS, const SCEV *RHS, 5471 Value *FoundCondValue, 5472 bool Inverse) { 5473 // Recursively handle And and Or conditions. 5474 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5475 if (BO->getOpcode() == Instruction::And) { 5476 if (!Inverse) 5477 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5478 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5479 } else if (BO->getOpcode() == Instruction::Or) { 5480 if (Inverse) 5481 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5482 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5483 } 5484 } 5485 5486 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5487 if (!ICI) return false; 5488 5489 // Bail if the ICmp's operands' types are wider than the needed type 5490 // before attempting to call getSCEV on them. This avoids infinite 5491 // recursion, since the analysis of widening casts can require loop 5492 // exit condition information for overflow checking, which would 5493 // lead back here. 5494 if (getTypeSizeInBits(LHS->getType()) < 5495 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5496 return false; 5497 5498 // Now that we found a conditional branch that dominates the loop, check to 5499 // see if it is the comparison we are looking for. 5500 ICmpInst::Predicate FoundPred; 5501 if (Inverse) 5502 FoundPred = ICI->getInversePredicate(); 5503 else 5504 FoundPred = ICI->getPredicate(); 5505 5506 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5507 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5508 5509 // Balance the types. The case where FoundLHS' type is wider than 5510 // LHS' type is checked for above. 5511 if (getTypeSizeInBits(LHS->getType()) > 5512 getTypeSizeInBits(FoundLHS->getType())) { 5513 if (CmpInst::isSigned(Pred)) { 5514 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5515 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5516 } else { 5517 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5518 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5519 } 5520 } 5521 5522 // Canonicalize the query to match the way instcombine will have 5523 // canonicalized the comparison. 5524 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5525 if (LHS == RHS) 5526 return CmpInst::isTrueWhenEqual(Pred); 5527 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5528 if (FoundLHS == FoundRHS) 5529 return CmpInst::isFalseWhenEqual(Pred); 5530 5531 // Check to see if we can make the LHS or RHS match. 5532 if (LHS == FoundRHS || RHS == FoundLHS) { 5533 if (isa<SCEVConstant>(RHS)) { 5534 std::swap(FoundLHS, FoundRHS); 5535 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5536 } else { 5537 std::swap(LHS, RHS); 5538 Pred = ICmpInst::getSwappedPredicate(Pred); 5539 } 5540 } 5541 5542 // Check whether the found predicate is the same as the desired predicate. 5543 if (FoundPred == Pred) 5544 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5545 5546 // Check whether swapping the found predicate makes it the same as the 5547 // desired predicate. 5548 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5549 if (isa<SCEVConstant>(RHS)) 5550 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5551 else 5552 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5553 RHS, LHS, FoundLHS, FoundRHS); 5554 } 5555 5556 // Check whether the actual condition is beyond sufficient. 5557 if (FoundPred == ICmpInst::ICMP_EQ) 5558 if (ICmpInst::isTrueWhenEqual(Pred)) 5559 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5560 return true; 5561 if (Pred == ICmpInst::ICMP_NE) 5562 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5563 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5564 return true; 5565 5566 // Otherwise assume the worst. 5567 return false; 5568} 5569 5570/// isImpliedCondOperands - Test whether the condition described by Pred, 5571/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5572/// and FoundRHS is true. 5573bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5574 const SCEV *LHS, const SCEV *RHS, 5575 const SCEV *FoundLHS, 5576 const SCEV *FoundRHS) { 5577 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5578 FoundLHS, FoundRHS) || 5579 // ~x < ~y --> x > y 5580 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5581 getNotSCEV(FoundRHS), 5582 getNotSCEV(FoundLHS)); 5583} 5584 5585/// isImpliedCondOperandsHelper - Test whether the condition described by 5586/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5587/// FoundLHS, and FoundRHS is true. 5588bool 5589ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5590 const SCEV *LHS, const SCEV *RHS, 5591 const SCEV *FoundLHS, 5592 const SCEV *FoundRHS) { 5593 switch (Pred) { 5594 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5595 case ICmpInst::ICMP_EQ: 5596 case ICmpInst::ICMP_NE: 5597 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5598 return true; 5599 break; 5600 case ICmpInst::ICMP_SLT: 5601 case ICmpInst::ICMP_SLE: 5602 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5603 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5604 return true; 5605 break; 5606 case ICmpInst::ICMP_SGT: 5607 case ICmpInst::ICMP_SGE: 5608 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5609 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5610 return true; 5611 break; 5612 case ICmpInst::ICMP_ULT: 5613 case ICmpInst::ICMP_ULE: 5614 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5615 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5616 return true; 5617 break; 5618 case ICmpInst::ICMP_UGT: 5619 case ICmpInst::ICMP_UGE: 5620 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5621 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5622 return true; 5623 break; 5624 } 5625 5626 return false; 5627} 5628 5629/// getBECount - Subtract the end and start values and divide by the step, 5630/// rounding up, to get the number of times the backedge is executed. Return 5631/// CouldNotCompute if an intermediate computation overflows. 5632const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5633 const SCEV *End, 5634 const SCEV *Step, 5635 bool NoWrap) { 5636 assert(!isKnownNegative(Step) && 5637 "This code doesn't handle negative strides yet!"); 5638 5639 const Type *Ty = Start->getType(); 5640 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5641 const SCEV *Diff = getMinusSCEV(End, Start); 5642 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5643 5644 // Add an adjustment to the difference between End and Start so that 5645 // the division will effectively round up. 5646 const SCEV *Add = getAddExpr(Diff, RoundUp); 5647 5648 if (!NoWrap) { 5649 // Check Add for unsigned overflow. 5650 // TODO: More sophisticated things could be done here. 5651 const Type *WideTy = IntegerType::get(getContext(), 5652 getTypeSizeInBits(Ty) + 1); 5653 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5654 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5655 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5656 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5657 return getCouldNotCompute(); 5658 } 5659 5660 return getUDivExpr(Add, Step); 5661} 5662 5663/// HowManyLessThans - Return the number of times a backedge containing the 5664/// specified less-than comparison will execute. If not computable, return 5665/// CouldNotCompute. 5666ScalarEvolution::BackedgeTakenInfo 5667ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5668 const Loop *L, bool isSigned) { 5669 // Only handle: "ADDREC < LoopInvariant". 5670 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5671 5672 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5673 if (!AddRec || AddRec->getLoop() != L) 5674 return getCouldNotCompute(); 5675 5676 // Check to see if we have a flag which makes analysis easy. 5677 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5678 AddRec->hasNoUnsignedWrap(); 5679 5680 if (AddRec->isAffine()) { 5681 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5682 const SCEV *Step = AddRec->getStepRecurrence(*this); 5683 5684 if (Step->isZero()) 5685 return getCouldNotCompute(); 5686 if (Step->isOne()) { 5687 // With unit stride, the iteration never steps past the limit value. 5688 } else if (isKnownPositive(Step)) { 5689 // Test whether a positive iteration can step past the limit 5690 // value and past the maximum value for its type in a single step. 5691 // Note that it's not sufficient to check NoWrap here, because even 5692 // though the value after a wrap is undefined, it's not undefined 5693 // behavior, so if wrap does occur, the loop could either terminate or 5694 // loop infinitely, but in either case, the loop is guaranteed to 5695 // iterate at least until the iteration where the wrapping occurs. 5696 const SCEV *One = getConstant(Step->getType(), 1); 5697 if (isSigned) { 5698 APInt Max = APInt::getSignedMaxValue(BitWidth); 5699 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5700 .slt(getSignedRange(RHS).getSignedMax())) 5701 return getCouldNotCompute(); 5702 } else { 5703 APInt Max = APInt::getMaxValue(BitWidth); 5704 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5705 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5706 return getCouldNotCompute(); 5707 } 5708 } else 5709 // TODO: Handle negative strides here and below. 5710 return getCouldNotCompute(); 5711 5712 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5713 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5714 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5715 // treat m-n as signed nor unsigned due to overflow possibility. 5716 5717 // First, we get the value of the LHS in the first iteration: n 5718 const SCEV *Start = AddRec->getOperand(0); 5719 5720 // Determine the minimum constant start value. 5721 const SCEV *MinStart = getConstant(isSigned ? 5722 getSignedRange(Start).getSignedMin() : 5723 getUnsignedRange(Start).getUnsignedMin()); 5724 5725 // If we know that the condition is true in order to enter the loop, 5726 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5727 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5728 // the division must round up. 5729 const SCEV *End = RHS; 5730 if (!isLoopEntryGuardedByCond(L, 5731 isSigned ? ICmpInst::ICMP_SLT : 5732 ICmpInst::ICMP_ULT, 5733 getMinusSCEV(Start, Step), RHS)) 5734 End = isSigned ? getSMaxExpr(RHS, Start) 5735 : getUMaxExpr(RHS, Start); 5736 5737 // Determine the maximum constant end value. 5738 const SCEV *MaxEnd = getConstant(isSigned ? 5739 getSignedRange(End).getSignedMax() : 5740 getUnsignedRange(End).getUnsignedMax()); 5741 5742 // If MaxEnd is within a step of the maximum integer value in its type, 5743 // adjust it down to the minimum value which would produce the same effect. 5744 // This allows the subsequent ceiling division of (N+(step-1))/step to 5745 // compute the correct value. 5746 const SCEV *StepMinusOne = getMinusSCEV(Step, 5747 getConstant(Step->getType(), 1)); 5748 MaxEnd = isSigned ? 5749 getSMinExpr(MaxEnd, 5750 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5751 StepMinusOne)) : 5752 getUMinExpr(MaxEnd, 5753 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5754 StepMinusOne)); 5755 5756 // Finally, we subtract these two values and divide, rounding up, to get 5757 // the number of times the backedge is executed. 5758 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5759 5760 // The maximum backedge count is similar, except using the minimum start 5761 // value and the maximum end value. 5762 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5763 5764 return BackedgeTakenInfo(BECount, MaxBECount); 5765 } 5766 5767 return getCouldNotCompute(); 5768} 5769 5770/// getNumIterationsInRange - Return the number of iterations of this loop that 5771/// produce values in the specified constant range. Another way of looking at 5772/// this is that it returns the first iteration number where the value is not in 5773/// the condition, thus computing the exit count. If the iteration count can't 5774/// be computed, an instance of SCEVCouldNotCompute is returned. 5775const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5776 ScalarEvolution &SE) const { 5777 if (Range.isFullSet()) // Infinite loop. 5778 return SE.getCouldNotCompute(); 5779 5780 // If the start is a non-zero constant, shift the range to simplify things. 5781 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5782 if (!SC->getValue()->isZero()) { 5783 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5784 Operands[0] = SE.getConstant(SC->getType(), 0); 5785 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5786 if (const SCEVAddRecExpr *ShiftedAddRec = 5787 dyn_cast<SCEVAddRecExpr>(Shifted)) 5788 return ShiftedAddRec->getNumIterationsInRange( 5789 Range.subtract(SC->getValue()->getValue()), SE); 5790 // This is strange and shouldn't happen. 5791 return SE.getCouldNotCompute(); 5792 } 5793 5794 // The only time we can solve this is when we have all constant indices. 5795 // Otherwise, we cannot determine the overflow conditions. 5796 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5797 if (!isa<SCEVConstant>(getOperand(i))) 5798 return SE.getCouldNotCompute(); 5799 5800 5801 // Okay at this point we know that all elements of the chrec are constants and 5802 // that the start element is zero. 5803 5804 // First check to see if the range contains zero. If not, the first 5805 // iteration exits. 5806 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5807 if (!Range.contains(APInt(BitWidth, 0))) 5808 return SE.getConstant(getType(), 0); 5809 5810 if (isAffine()) { 5811 // If this is an affine expression then we have this situation: 5812 // Solve {0,+,A} in Range === Ax in Range 5813 5814 // We know that zero is in the range. If A is positive then we know that 5815 // the upper value of the range must be the first possible exit value. 5816 // If A is negative then the lower of the range is the last possible loop 5817 // value. Also note that we already checked for a full range. 5818 APInt One(BitWidth,1); 5819 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5820 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5821 5822 // The exit value should be (End+A)/A. 5823 APInt ExitVal = (End + A).udiv(A); 5824 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5825 5826 // Evaluate at the exit value. If we really did fall out of the valid 5827 // range, then we computed our trip count, otherwise wrap around or other 5828 // things must have happened. 5829 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5830 if (Range.contains(Val->getValue())) 5831 return SE.getCouldNotCompute(); // Something strange happened 5832 5833 // Ensure that the previous value is in the range. This is a sanity check. 5834 assert(Range.contains( 5835 EvaluateConstantChrecAtConstant(this, 5836 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5837 "Linear scev computation is off in a bad way!"); 5838 return SE.getConstant(ExitValue); 5839 } else if (isQuadratic()) { 5840 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5841 // quadratic equation to solve it. To do this, we must frame our problem in 5842 // terms of figuring out when zero is crossed, instead of when 5843 // Range.getUpper() is crossed. 5844 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5845 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5846 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5847 5848 // Next, solve the constructed addrec 5849 std::pair<const SCEV *,const SCEV *> Roots = 5850 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5851 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5852 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5853 if (R1) { 5854 // Pick the smallest positive root value. 5855 if (ConstantInt *CB = 5856 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5857 R1->getValue(), R2->getValue()))) { 5858 if (CB->getZExtValue() == false) 5859 std::swap(R1, R2); // R1 is the minimum root now. 5860 5861 // Make sure the root is not off by one. The returned iteration should 5862 // not be in the range, but the previous one should be. When solving 5863 // for "X*X < 5", for example, we should not return a root of 2. 5864 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5865 R1->getValue(), 5866 SE); 5867 if (Range.contains(R1Val->getValue())) { 5868 // The next iteration must be out of the range... 5869 ConstantInt *NextVal = 5870 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5871 5872 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5873 if (!Range.contains(R1Val->getValue())) 5874 return SE.getConstant(NextVal); 5875 return SE.getCouldNotCompute(); // Something strange happened 5876 } 5877 5878 // If R1 was not in the range, then it is a good return value. Make 5879 // sure that R1-1 WAS in the range though, just in case. 5880 ConstantInt *NextVal = 5881 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5882 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5883 if (Range.contains(R1Val->getValue())) 5884 return R1; 5885 return SE.getCouldNotCompute(); // Something strange happened 5886 } 5887 } 5888 } 5889 5890 return SE.getCouldNotCompute(); 5891} 5892 5893 5894 5895//===----------------------------------------------------------------------===// 5896// SCEVCallbackVH Class Implementation 5897//===----------------------------------------------------------------------===// 5898 5899void ScalarEvolution::SCEVCallbackVH::deleted() { 5900 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5901 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5902 SE->ConstantEvolutionLoopExitValue.erase(PN); 5903 SE->ValueExprMap.erase(getValPtr()); 5904 // this now dangles! 5905} 5906 5907void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5908 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5909 5910 // Forget all the expressions associated with users of the old value, 5911 // so that future queries will recompute the expressions using the new 5912 // value. 5913 Value *Old = getValPtr(); 5914 SmallVector<User *, 16> Worklist; 5915 SmallPtrSet<User *, 8> Visited; 5916 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5917 UI != UE; ++UI) 5918 Worklist.push_back(*UI); 5919 while (!Worklist.empty()) { 5920 User *U = Worklist.pop_back_val(); 5921 // Deleting the Old value will cause this to dangle. Postpone 5922 // that until everything else is done. 5923 if (U == Old) 5924 continue; 5925 if (!Visited.insert(U)) 5926 continue; 5927 if (PHINode *PN = dyn_cast<PHINode>(U)) 5928 SE->ConstantEvolutionLoopExitValue.erase(PN); 5929 SE->ValueExprMap.erase(U); 5930 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5931 UI != UE; ++UI) 5932 Worklist.push_back(*UI); 5933 } 5934 // Delete the Old value. 5935 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5936 SE->ConstantEvolutionLoopExitValue.erase(PN); 5937 SE->ValueExprMap.erase(Old); 5938 // this now dangles! 5939} 5940 5941ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5942 : CallbackVH(V), SE(se) {} 5943 5944//===----------------------------------------------------------------------===// 5945// ScalarEvolution Class Implementation 5946//===----------------------------------------------------------------------===// 5947 5948ScalarEvolution::ScalarEvolution() 5949 : FunctionPass(ID), FirstUnknown(0) { 5950 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 5951} 5952 5953bool ScalarEvolution::runOnFunction(Function &F) { 5954 this->F = &F; 5955 LI = &getAnalysis<LoopInfo>(); 5956 TD = getAnalysisIfAvailable<TargetData>(); 5957 DT = &getAnalysis<DominatorTree>(); 5958 return false; 5959} 5960 5961void ScalarEvolution::releaseMemory() { 5962 // Iterate through all the SCEVUnknown instances and call their 5963 // destructors, so that they release their references to their values. 5964 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5965 U->~SCEVUnknown(); 5966 FirstUnknown = 0; 5967 5968 ValueExprMap.clear(); 5969 BackedgeTakenCounts.clear(); 5970 ConstantEvolutionLoopExitValue.clear(); 5971 ValuesAtScopes.clear(); 5972 LoopDispositions.clear(); 5973 BlockDispositions.clear(); 5974 UnsignedRanges.clear(); 5975 SignedRanges.clear(); 5976 UniqueSCEVs.clear(); 5977 SCEVAllocator.Reset(); 5978} 5979 5980void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5981 AU.setPreservesAll(); 5982 AU.addRequiredTransitive<LoopInfo>(); 5983 AU.addRequiredTransitive<DominatorTree>(); 5984} 5985 5986bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5987 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5988} 5989 5990static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5991 const Loop *L) { 5992 // Print all inner loops first 5993 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5994 PrintLoopInfo(OS, SE, *I); 5995 5996 OS << "Loop "; 5997 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5998 OS << ": "; 5999 6000 SmallVector<BasicBlock *, 8> ExitBlocks; 6001 L->getExitBlocks(ExitBlocks); 6002 if (ExitBlocks.size() != 1) 6003 OS << "<multiple exits> "; 6004 6005 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6006 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6007 } else { 6008 OS << "Unpredictable backedge-taken count. "; 6009 } 6010 6011 OS << "\n" 6012 "Loop "; 6013 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6014 OS << ": "; 6015 6016 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6017 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6018 } else { 6019 OS << "Unpredictable max backedge-taken count. "; 6020 } 6021 6022 OS << "\n"; 6023} 6024 6025void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6026 // ScalarEvolution's implementation of the print method is to print 6027 // out SCEV values of all instructions that are interesting. Doing 6028 // this potentially causes it to create new SCEV objects though, 6029 // which technically conflicts with the const qualifier. This isn't 6030 // observable from outside the class though, so casting away the 6031 // const isn't dangerous. 6032 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6033 6034 OS << "Classifying expressions for: "; 6035 WriteAsOperand(OS, F, /*PrintType=*/false); 6036 OS << "\n"; 6037 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6038 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6039 OS << *I << '\n'; 6040 OS << " --> "; 6041 const SCEV *SV = SE.getSCEV(&*I); 6042 SV->print(OS); 6043 6044 const Loop *L = LI->getLoopFor((*I).getParent()); 6045 6046 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6047 if (AtUse != SV) { 6048 OS << " --> "; 6049 AtUse->print(OS); 6050 } 6051 6052 if (L) { 6053 OS << "\t\t" "Exits: "; 6054 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6055 if (!SE.isLoopInvariant(ExitValue, L)) { 6056 OS << "<<Unknown>>"; 6057 } else { 6058 OS << *ExitValue; 6059 } 6060 } 6061 6062 OS << "\n"; 6063 } 6064 6065 OS << "Determining loop execution counts for: "; 6066 WriteAsOperand(OS, F, /*PrintType=*/false); 6067 OS << "\n"; 6068 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6069 PrintLoopInfo(OS, &SE, *I); 6070} 6071 6072ScalarEvolution::LoopDisposition 6073ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6074 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6075 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6076 Values.insert(std::make_pair(L, LoopVariant)); 6077 if (!Pair.second) 6078 return Pair.first->second; 6079 6080 LoopDisposition D = computeLoopDisposition(S, L); 6081 return LoopDispositions[S][L] = D; 6082} 6083 6084ScalarEvolution::LoopDisposition 6085ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6086 switch (S->getSCEVType()) { 6087 case scConstant: 6088 return LoopInvariant; 6089 case scTruncate: 6090 case scZeroExtend: 6091 case scSignExtend: 6092 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6093 case scAddRecExpr: { 6094 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6095 6096 // If L is the addrec's loop, it's computable. 6097 if (AR->getLoop() == L) 6098 return LoopComputable; 6099 6100 // Add recurrences are never invariant in the function-body (null loop). 6101 if (!L) 6102 return LoopVariant; 6103 6104 // This recurrence is variant w.r.t. L if L contains AR's loop. 6105 if (L->contains(AR->getLoop())) 6106 return LoopVariant; 6107 6108 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6109 if (AR->getLoop()->contains(L)) 6110 return LoopInvariant; 6111 6112 // This recurrence is variant w.r.t. L if any of its operands 6113 // are variant. 6114 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6115 I != E; ++I) 6116 if (!isLoopInvariant(*I, L)) 6117 return LoopVariant; 6118 6119 // Otherwise it's loop-invariant. 6120 return LoopInvariant; 6121 } 6122 case scAddExpr: 6123 case scMulExpr: 6124 case scUMaxExpr: 6125 case scSMaxExpr: { 6126 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6127 bool HasVarying = false; 6128 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6129 I != E; ++I) { 6130 LoopDisposition D = getLoopDisposition(*I, L); 6131 if (D == LoopVariant) 6132 return LoopVariant; 6133 if (D == LoopComputable) 6134 HasVarying = true; 6135 } 6136 return HasVarying ? LoopComputable : LoopInvariant; 6137 } 6138 case scUDivExpr: { 6139 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6140 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6141 if (LD == LoopVariant) 6142 return LoopVariant; 6143 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6144 if (RD == LoopVariant) 6145 return LoopVariant; 6146 return (LD == LoopInvariant && RD == LoopInvariant) ? 6147 LoopInvariant : LoopComputable; 6148 } 6149 case scUnknown: 6150 // All non-instruction values are loop invariant. All instructions are loop 6151 // invariant if they are not contained in the specified loop. 6152 // Instructions are never considered invariant in the function body 6153 // (null loop) because they are defined within the "loop". 6154 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6155 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6156 return LoopInvariant; 6157 case scCouldNotCompute: 6158 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6159 return LoopVariant; 6160 default: break; 6161 } 6162 llvm_unreachable("Unknown SCEV kind!"); 6163 return LoopVariant; 6164} 6165 6166bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6167 return getLoopDisposition(S, L) == LoopInvariant; 6168} 6169 6170bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6171 return getLoopDisposition(S, L) == LoopComputable; 6172} 6173 6174ScalarEvolution::BlockDisposition 6175ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6176 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6177 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6178 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6179 if (!Pair.second) 6180 return Pair.first->second; 6181 6182 BlockDisposition D = computeBlockDisposition(S, BB); 6183 return BlockDispositions[S][BB] = D; 6184} 6185 6186ScalarEvolution::BlockDisposition 6187ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6188 switch (S->getSCEVType()) { 6189 case scConstant: 6190 return ProperlyDominatesBlock; 6191 case scTruncate: 6192 case scZeroExtend: 6193 case scSignExtend: 6194 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6195 case scAddRecExpr: { 6196 // This uses a "dominates" query instead of "properly dominates" query 6197 // to test for proper dominance too, because the instruction which 6198 // produces the addrec's value is a PHI, and a PHI effectively properly 6199 // dominates its entire containing block. 6200 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6201 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6202 return DoesNotDominateBlock; 6203 } 6204 // FALL THROUGH into SCEVNAryExpr handling. 6205 case scAddExpr: 6206 case scMulExpr: 6207 case scUMaxExpr: 6208 case scSMaxExpr: { 6209 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6210 bool Proper = true; 6211 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6212 I != E; ++I) { 6213 BlockDisposition D = getBlockDisposition(*I, BB); 6214 if (D == DoesNotDominateBlock) 6215 return DoesNotDominateBlock; 6216 if (D == DominatesBlock) 6217 Proper = false; 6218 } 6219 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6220 } 6221 case scUDivExpr: { 6222 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6223 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6224 BlockDisposition LD = getBlockDisposition(LHS, BB); 6225 if (LD == DoesNotDominateBlock) 6226 return DoesNotDominateBlock; 6227 BlockDisposition RD = getBlockDisposition(RHS, BB); 6228 if (RD == DoesNotDominateBlock) 6229 return DoesNotDominateBlock; 6230 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6231 ProperlyDominatesBlock : DominatesBlock; 6232 } 6233 case scUnknown: 6234 if (Instruction *I = 6235 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6236 if (I->getParent() == BB) 6237 return DominatesBlock; 6238 if (DT->properlyDominates(I->getParent(), BB)) 6239 return ProperlyDominatesBlock; 6240 return DoesNotDominateBlock; 6241 } 6242 return ProperlyDominatesBlock; 6243 case scCouldNotCompute: 6244 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6245 return DoesNotDominateBlock; 6246 default: break; 6247 } 6248 llvm_unreachable("Unknown SCEV kind!"); 6249 return DoesNotDominateBlock; 6250} 6251 6252bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6253 return getBlockDisposition(S, BB) >= DominatesBlock; 6254} 6255 6256bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6257 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6258} 6259 6260bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6261 switch (S->getSCEVType()) { 6262 case scConstant: 6263 return false; 6264 case scTruncate: 6265 case scZeroExtend: 6266 case scSignExtend: { 6267 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6268 const SCEV *CastOp = Cast->getOperand(); 6269 return Op == CastOp || hasOperand(CastOp, Op); 6270 } 6271 case scAddRecExpr: 6272 case scAddExpr: 6273 case scMulExpr: 6274 case scUMaxExpr: 6275 case scSMaxExpr: { 6276 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6277 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6278 I != E; ++I) { 6279 const SCEV *NAryOp = *I; 6280 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6281 return true; 6282 } 6283 return false; 6284 } 6285 case scUDivExpr: { 6286 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6287 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6288 return LHS == Op || hasOperand(LHS, Op) || 6289 RHS == Op || hasOperand(RHS, Op); 6290 } 6291 case scUnknown: 6292 return false; 6293 case scCouldNotCompute: 6294 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6295 return false; 6296 default: break; 6297 } 6298 llvm_unreachable("Unknown SCEV kind!"); 6299 return false; 6300} 6301 6302void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6303 ValuesAtScopes.erase(S); 6304 LoopDispositions.erase(S); 6305 BlockDispositions.erase(S); 6306 UnsignedRanges.erase(S); 6307 SignedRanges.erase(S); 6308} 6309