ScalarEvolution.cpp revision 308bec390f4e6cba04ae06e2ca1a274c91a14f41
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/InstructionSimplify.h" 73#include "llvm/Analysis/LoopInfo.h" 74#include "llvm/Analysis/ValueTracking.h" 75#include "llvm/Assembly/Writer.h" 76#include "llvm/Target/TargetData.h" 77#include "llvm/Support/CommandLine.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/Debug.h" 80#include "llvm/Support/ErrorHandling.h" 81#include "llvm/Support/GetElementPtrTypeIterator.h" 82#include "llvm/Support/InstIterator.h" 83#include "llvm/Support/MathExtras.h" 84#include "llvm/Support/raw_ostream.h" 85#include "llvm/ADT/Statistic.h" 86#include "llvm/ADT/STLExtras.h" 87#include "llvm/ADT/SmallPtrSet.h" 88#include <algorithm> 89using namespace llvm; 90 91STATISTIC(NumArrayLenItCounts, 92 "Number of trip counts computed with array length"); 93STATISTIC(NumTripCountsComputed, 94 "Number of loops with predictable loop counts"); 95STATISTIC(NumTripCountsNotComputed, 96 "Number of loops without predictable loop counts"); 97STATISTIC(NumBruteForceTripCountsComputed, 98 "Number of loops with trip counts computed by force"); 99 100static cl::opt<unsigned> 101MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 102 cl::desc("Maximum number of iterations SCEV will " 103 "symbolically execute a constant " 104 "derived loop"), 105 cl::init(100)); 106 107INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 108 "Scalar Evolution Analysis", false, true) 109INITIALIZE_PASS_DEPENDENCY(LoopInfo) 110INITIALIZE_PASS_DEPENDENCY(DominatorTree) 111INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 112 "Scalar Evolution Analysis", false, true) 113char ScalarEvolution::ID = 0; 114 115//===----------------------------------------------------------------------===// 116// SCEV class definitions 117//===----------------------------------------------------------------------===// 118 119//===----------------------------------------------------------------------===// 120// Implementation of the SCEV class. 121// 122 123void SCEV::dump() const { 124 print(dbgs()); 125 dbgs() << '\n'; 126} 127 128void SCEV::print(raw_ostream &OS) const { 129 switch (getSCEVType()) { 130 case scConstant: 131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 132 return; 133 case scTruncate: { 134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 135 const SCEV *Op = Trunc->getOperand(); 136 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 137 << *Trunc->getType() << ")"; 138 return; 139 } 140 case scZeroExtend: { 141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 142 const SCEV *Op = ZExt->getOperand(); 143 OS << "(zext " << *Op->getType() << " " << *Op << " to " 144 << *ZExt->getType() << ")"; 145 return; 146 } 147 case scSignExtend: { 148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 149 const SCEV *Op = SExt->getOperand(); 150 OS << "(sext " << *Op->getType() << " " << *Op << " to " 151 << *SExt->getType() << ")"; 152 return; 153 } 154 case scAddRecExpr: { 155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 156 OS << "{" << *AR->getOperand(0); 157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 158 OS << ",+," << *AR->getOperand(i); 159 OS << "}<"; 160 if (AR->getNoWrapFlags(FlagNUW)) 161 OS << "nuw><"; 162 if (AR->getNoWrapFlags(FlagNSW)) 163 OS << "nsw><"; 164 if (AR->getNoWrapFlags(FlagNW) && 165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 166 OS << "nw><"; 167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 168 OS << ">"; 169 return; 170 } 171 case scAddExpr: 172 case scMulExpr: 173 case scUMaxExpr: 174 case scSMaxExpr: { 175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 176 const char *OpStr = 0; 177 switch (NAry->getSCEVType()) { 178 case scAddExpr: OpStr = " + "; break; 179 case scMulExpr: OpStr = " * "; break; 180 case scUMaxExpr: OpStr = " umax "; break; 181 case scSMaxExpr: OpStr = " smax "; break; 182 } 183 OS << "("; 184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 185 I != E; ++I) { 186 OS << **I; 187 if (llvm::next(I) != E) 188 OS << OpStr; 189 } 190 OS << ")"; 191 return; 192 } 193 case scUDivExpr: { 194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 196 return; 197 } 198 case scUnknown: { 199 const SCEVUnknown *U = cast<SCEVUnknown>(this); 200 const Type *AllocTy; 201 if (U->isSizeOf(AllocTy)) { 202 OS << "sizeof(" << *AllocTy << ")"; 203 return; 204 } 205 if (U->isAlignOf(AllocTy)) { 206 OS << "alignof(" << *AllocTy << ")"; 207 return; 208 } 209 210 const Type *CTy; 211 Constant *FieldNo; 212 if (U->isOffsetOf(CTy, FieldNo)) { 213 OS << "offsetof(" << *CTy << ", "; 214 WriteAsOperand(OS, FieldNo, false); 215 OS << ")"; 216 return; 217 } 218 219 // Otherwise just print it normally. 220 WriteAsOperand(OS, U->getValue(), false); 221 return; 222 } 223 case scCouldNotCompute: 224 OS << "***COULDNOTCOMPUTE***"; 225 return; 226 default: break; 227 } 228 llvm_unreachable("Unknown SCEV kind!"); 229} 230 231const Type *SCEV::getType() const { 232 switch (getSCEVType()) { 233 case scConstant: 234 return cast<SCEVConstant>(this)->getType(); 235 case scTruncate: 236 case scZeroExtend: 237 case scSignExtend: 238 return cast<SCEVCastExpr>(this)->getType(); 239 case scAddRecExpr: 240 case scMulExpr: 241 case scUMaxExpr: 242 case scSMaxExpr: 243 return cast<SCEVNAryExpr>(this)->getType(); 244 case scAddExpr: 245 return cast<SCEVAddExpr>(this)->getType(); 246 case scUDivExpr: 247 return cast<SCEVUDivExpr>(this)->getType(); 248 case scUnknown: 249 return cast<SCEVUnknown>(this)->getType(); 250 case scCouldNotCompute: 251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 252 return 0; 253 default: break; 254 } 255 llvm_unreachable("Unknown SCEV kind!"); 256 return 0; 257} 258 259bool SCEV::isZero() const { 260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 261 return SC->getValue()->isZero(); 262 return false; 263} 264 265bool SCEV::isOne() const { 266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 267 return SC->getValue()->isOne(); 268 return false; 269} 270 271bool SCEV::isAllOnesValue() const { 272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 273 return SC->getValue()->isAllOnesValue(); 274 return false; 275} 276 277SCEVCouldNotCompute::SCEVCouldNotCompute() : 278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 279 280bool SCEVCouldNotCompute::classof(const SCEV *S) { 281 return S->getSCEVType() == scCouldNotCompute; 282} 283 284const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 285 FoldingSetNodeID ID; 286 ID.AddInteger(scConstant); 287 ID.AddPointer(V); 288 void *IP = 0; 289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 291 UniqueSCEVs.InsertNode(S, IP); 292 return S; 293} 294 295const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 296 return getConstant(ConstantInt::get(getContext(), Val)); 297} 298 299const SCEV * 300ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 301 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 302 return getConstant(ConstantInt::get(ITy, V, isSigned)); 303} 304 305SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 306 unsigned SCEVTy, const SCEV *op, const Type *ty) 307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 308 309SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 310 const SCEV *op, const Type *ty) 311 : SCEVCastExpr(ID, scTruncate, op, ty) { 312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 313 (Ty->isIntegerTy() || Ty->isPointerTy()) && 314 "Cannot truncate non-integer value!"); 315} 316 317SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 318 const SCEV *op, const Type *ty) 319 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 321 (Ty->isIntegerTy() || Ty->isPointerTy()) && 322 "Cannot zero extend non-integer value!"); 323} 324 325SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 326 const SCEV *op, const Type *ty) 327 : SCEVCastExpr(ID, scSignExtend, op, ty) { 328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 329 (Ty->isIntegerTy() || Ty->isPointerTy()) && 330 "Cannot sign extend non-integer value!"); 331} 332 333void SCEVUnknown::deleted() { 334 // Clear this SCEVUnknown from various maps. 335 SE->forgetMemoizedResults(this); 336 337 // Remove this SCEVUnknown from the uniquing map. 338 SE->UniqueSCEVs.RemoveNode(this); 339 340 // Release the value. 341 setValPtr(0); 342} 343 344void SCEVUnknown::allUsesReplacedWith(Value *New) { 345 // Clear this SCEVUnknown from various maps. 346 SE->forgetMemoizedResults(this); 347 348 // Remove this SCEVUnknown from the uniquing map. 349 SE->UniqueSCEVs.RemoveNode(this); 350 351 // Update this SCEVUnknown to point to the new value. This is needed 352 // because there may still be outstanding SCEVs which still point to 353 // this SCEVUnknown. 354 setValPtr(New); 355} 356 357bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 359 if (VCE->getOpcode() == Instruction::PtrToInt) 360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 361 if (CE->getOpcode() == Instruction::GetElementPtr && 362 CE->getOperand(0)->isNullValue() && 363 CE->getNumOperands() == 2) 364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 365 if (CI->isOne()) { 366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 367 ->getElementType(); 368 return true; 369 } 370 371 return false; 372} 373 374bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 376 if (VCE->getOpcode() == Instruction::PtrToInt) 377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 378 if (CE->getOpcode() == Instruction::GetElementPtr && 379 CE->getOperand(0)->isNullValue()) { 380 const Type *Ty = 381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 382 if (const StructType *STy = dyn_cast<StructType>(Ty)) 383 if (!STy->isPacked() && 384 CE->getNumOperands() == 3 && 385 CE->getOperand(1)->isNullValue()) { 386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 387 if (CI->isOne() && 388 STy->getNumElements() == 2 && 389 STy->getElementType(0)->isIntegerTy(1)) { 390 AllocTy = STy->getElementType(1); 391 return true; 392 } 393 } 394 } 395 396 return false; 397} 398 399bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 401 if (VCE->getOpcode() == Instruction::PtrToInt) 402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 403 if (CE->getOpcode() == Instruction::GetElementPtr && 404 CE->getNumOperands() == 3 && 405 CE->getOperand(0)->isNullValue() && 406 CE->getOperand(1)->isNullValue()) { 407 const Type *Ty = 408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 409 // Ignore vector types here so that ScalarEvolutionExpander doesn't 410 // emit getelementptrs that index into vectors. 411 if (Ty->isStructTy() || Ty->isArrayTy()) { 412 CTy = Ty; 413 FieldNo = CE->getOperand(2); 414 return true; 415 } 416 } 417 418 return false; 419} 420 421//===----------------------------------------------------------------------===// 422// SCEV Utilities 423//===----------------------------------------------------------------------===// 424 425namespace { 426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 427 /// than the complexity of the RHS. This comparator is used to canonicalize 428 /// expressions. 429 class SCEVComplexityCompare { 430 const LoopInfo *const LI; 431 public: 432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 433 434 // Return true or false if LHS is less than, or at least RHS, respectively. 435 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 436 return compare(LHS, RHS) < 0; 437 } 438 439 // Return negative, zero, or positive, if LHS is less than, equal to, or 440 // greater than RHS, respectively. A three-way result allows recursive 441 // comparisons to be more efficient. 442 int compare(const SCEV *LHS, const SCEV *RHS) const { 443 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 444 if (LHS == RHS) 445 return 0; 446 447 // Primarily, sort the SCEVs by their getSCEVType(). 448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 449 if (LType != RType) 450 return (int)LType - (int)RType; 451 452 // Aside from the getSCEVType() ordering, the particular ordering 453 // isn't very important except that it's beneficial to be consistent, 454 // so that (a + b) and (b + a) don't end up as different expressions. 455 switch (LType) { 456 case scUnknown: { 457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 459 460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 461 // not as complete as it could be. 462 const Value *LV = LU->getValue(), *RV = RU->getValue(); 463 464 // Order pointer values after integer values. This helps SCEVExpander 465 // form GEPs. 466 bool LIsPointer = LV->getType()->isPointerTy(), 467 RIsPointer = RV->getType()->isPointerTy(); 468 if (LIsPointer != RIsPointer) 469 return (int)LIsPointer - (int)RIsPointer; 470 471 // Compare getValueID values. 472 unsigned LID = LV->getValueID(), 473 RID = RV->getValueID(); 474 if (LID != RID) 475 return (int)LID - (int)RID; 476 477 // Sort arguments by their position. 478 if (const Argument *LA = dyn_cast<Argument>(LV)) { 479 const Argument *RA = cast<Argument>(RV); 480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 481 return (int)LArgNo - (int)RArgNo; 482 } 483 484 // For instructions, compare their loop depth, and their operand 485 // count. This is pretty loose. 486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 487 const Instruction *RInst = cast<Instruction>(RV); 488 489 // Compare loop depths. 490 const BasicBlock *LParent = LInst->getParent(), 491 *RParent = RInst->getParent(); 492 if (LParent != RParent) { 493 unsigned LDepth = LI->getLoopDepth(LParent), 494 RDepth = LI->getLoopDepth(RParent); 495 if (LDepth != RDepth) 496 return (int)LDepth - (int)RDepth; 497 } 498 499 // Compare the number of operands. 500 unsigned LNumOps = LInst->getNumOperands(), 501 RNumOps = RInst->getNumOperands(); 502 return (int)LNumOps - (int)RNumOps; 503 } 504 505 return 0; 506 } 507 508 case scConstant: { 509 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 510 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 511 512 // Compare constant values. 513 const APInt &LA = LC->getValue()->getValue(); 514 const APInt &RA = RC->getValue()->getValue(); 515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 516 if (LBitWidth != RBitWidth) 517 return (int)LBitWidth - (int)RBitWidth; 518 return LA.ult(RA) ? -1 : 1; 519 } 520 521 case scAddRecExpr: { 522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 524 525 // Compare addrec loop depths. 526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 527 if (LLoop != RLoop) { 528 unsigned LDepth = LLoop->getLoopDepth(), 529 RDepth = RLoop->getLoopDepth(); 530 if (LDepth != RDepth) 531 return (int)LDepth - (int)RDepth; 532 } 533 534 // Addrec complexity grows with operand count. 535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 536 if (LNumOps != RNumOps) 537 return (int)LNumOps - (int)RNumOps; 538 539 // Lexicographically compare. 540 for (unsigned i = 0; i != LNumOps; ++i) { 541 long X = compare(LA->getOperand(i), RA->getOperand(i)); 542 if (X != 0) 543 return X; 544 } 545 546 return 0; 547 } 548 549 case scAddExpr: 550 case scMulExpr: 551 case scSMaxExpr: 552 case scUMaxExpr: { 553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 555 556 // Lexicographically compare n-ary expressions. 557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 558 for (unsigned i = 0; i != LNumOps; ++i) { 559 if (i >= RNumOps) 560 return 1; 561 long X = compare(LC->getOperand(i), RC->getOperand(i)); 562 if (X != 0) 563 return X; 564 } 565 return (int)LNumOps - (int)RNumOps; 566 } 567 568 case scUDivExpr: { 569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 571 572 // Lexicographically compare udiv expressions. 573 long X = compare(LC->getLHS(), RC->getLHS()); 574 if (X != 0) 575 return X; 576 return compare(LC->getRHS(), RC->getRHS()); 577 } 578 579 case scTruncate: 580 case scZeroExtend: 581 case scSignExtend: { 582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 584 585 // Compare cast expressions by operand. 586 return compare(LC->getOperand(), RC->getOperand()); 587 } 588 589 default: 590 break; 591 } 592 593 llvm_unreachable("Unknown SCEV kind!"); 594 return 0; 595 } 596 }; 597} 598 599/// GroupByComplexity - Given a list of SCEV objects, order them by their 600/// complexity, and group objects of the same complexity together by value. 601/// When this routine is finished, we know that any duplicates in the vector are 602/// consecutive and that complexity is monotonically increasing. 603/// 604/// Note that we go take special precautions to ensure that we get deterministic 605/// results from this routine. In other words, we don't want the results of 606/// this to depend on where the addresses of various SCEV objects happened to 607/// land in memory. 608/// 609static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 610 LoopInfo *LI) { 611 if (Ops.size() < 2) return; // Noop 612 if (Ops.size() == 2) { 613 // This is the common case, which also happens to be trivially simple. 614 // Special case it. 615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 616 if (SCEVComplexityCompare(LI)(RHS, LHS)) 617 std::swap(LHS, RHS); 618 return; 619 } 620 621 // Do the rough sort by complexity. 622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 623 624 // Now that we are sorted by complexity, group elements of the same 625 // complexity. Note that this is, at worst, N^2, but the vector is likely to 626 // be extremely short in practice. Note that we take this approach because we 627 // do not want to depend on the addresses of the objects we are grouping. 628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 629 const SCEV *S = Ops[i]; 630 unsigned Complexity = S->getSCEVType(); 631 632 // If there are any objects of the same complexity and same value as this 633 // one, group them. 634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 635 if (Ops[j] == S) { // Found a duplicate. 636 // Move it to immediately after i'th element. 637 std::swap(Ops[i+1], Ops[j]); 638 ++i; // no need to rescan it. 639 if (i == e-2) return; // Done! 640 } 641 } 642 } 643} 644 645 646 647//===----------------------------------------------------------------------===// 648// Simple SCEV method implementations 649//===----------------------------------------------------------------------===// 650 651/// BinomialCoefficient - Compute BC(It, K). The result has width W. 652/// Assume, K > 0. 653static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 654 ScalarEvolution &SE, 655 const Type* ResultTy) { 656 // Handle the simplest case efficiently. 657 if (K == 1) 658 return SE.getTruncateOrZeroExtend(It, ResultTy); 659 660 // We are using the following formula for BC(It, K): 661 // 662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 663 // 664 // Suppose, W is the bitwidth of the return value. We must be prepared for 665 // overflow. Hence, we must assure that the result of our computation is 666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 667 // safe in modular arithmetic. 668 // 669 // However, this code doesn't use exactly that formula; the formula it uses 670 // is something like the following, where T is the number of factors of 2 in 671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 672 // exponentiation: 673 // 674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 675 // 676 // This formula is trivially equivalent to the previous formula. However, 677 // this formula can be implemented much more efficiently. The trick is that 678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 679 // arithmetic. To do exact division in modular arithmetic, all we have 680 // to do is multiply by the inverse. Therefore, this step can be done at 681 // width W. 682 // 683 // The next issue is how to safely do the division by 2^T. The way this 684 // is done is by doing the multiplication step at a width of at least W + T 685 // bits. This way, the bottom W+T bits of the product are accurate. Then, 686 // when we perform the division by 2^T (which is equivalent to a right shift 687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 688 // truncated out after the division by 2^T. 689 // 690 // In comparison to just directly using the first formula, this technique 691 // is much more efficient; using the first formula requires W * K bits, 692 // but this formula less than W + K bits. Also, the first formula requires 693 // a division step, whereas this formula only requires multiplies and shifts. 694 // 695 // It doesn't matter whether the subtraction step is done in the calculation 696 // width or the input iteration count's width; if the subtraction overflows, 697 // the result must be zero anyway. We prefer here to do it in the width of 698 // the induction variable because it helps a lot for certain cases; CodeGen 699 // isn't smart enough to ignore the overflow, which leads to much less 700 // efficient code if the width of the subtraction is wider than the native 701 // register width. 702 // 703 // (It's possible to not widen at all by pulling out factors of 2 before 704 // the multiplication; for example, K=2 can be calculated as 705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 706 // extra arithmetic, so it's not an obvious win, and it gets 707 // much more complicated for K > 3.) 708 709 // Protection from insane SCEVs; this bound is conservative, 710 // but it probably doesn't matter. 711 if (K > 1000) 712 return SE.getCouldNotCompute(); 713 714 unsigned W = SE.getTypeSizeInBits(ResultTy); 715 716 // Calculate K! / 2^T and T; we divide out the factors of two before 717 // multiplying for calculating K! / 2^T to avoid overflow. 718 // Other overflow doesn't matter because we only care about the bottom 719 // W bits of the result. 720 APInt OddFactorial(W, 1); 721 unsigned T = 1; 722 for (unsigned i = 3; i <= K; ++i) { 723 APInt Mult(W, i); 724 unsigned TwoFactors = Mult.countTrailingZeros(); 725 T += TwoFactors; 726 Mult = Mult.lshr(TwoFactors); 727 OddFactorial *= Mult; 728 } 729 730 // We need at least W + T bits for the multiplication step 731 unsigned CalculationBits = W + T; 732 733 // Calculate 2^T, at width T+W. 734 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 735 736 // Calculate the multiplicative inverse of K! / 2^T; 737 // this multiplication factor will perform the exact division by 738 // K! / 2^T. 739 APInt Mod = APInt::getSignedMinValue(W+1); 740 APInt MultiplyFactor = OddFactorial.zext(W+1); 741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 742 MultiplyFactor = MultiplyFactor.trunc(W); 743 744 // Calculate the product, at width T+W 745 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 746 CalculationBits); 747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 748 for (unsigned i = 1; i != K; ++i) { 749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 750 Dividend = SE.getMulExpr(Dividend, 751 SE.getTruncateOrZeroExtend(S, CalculationTy)); 752 } 753 754 // Divide by 2^T 755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 756 757 // Truncate the result, and divide by K! / 2^T. 758 759 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 760 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 761} 762 763/// evaluateAtIteration - Return the value of this chain of recurrences at 764/// the specified iteration number. We can evaluate this recurrence by 765/// multiplying each element in the chain by the binomial coefficient 766/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 767/// 768/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 769/// 770/// where BC(It, k) stands for binomial coefficient. 771/// 772const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 773 ScalarEvolution &SE) const { 774 const SCEV *Result = getStart(); 775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 776 // The computation is correct in the face of overflow provided that the 777 // multiplication is performed _after_ the evaluation of the binomial 778 // coefficient. 779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 780 if (isa<SCEVCouldNotCompute>(Coeff)) 781 return Coeff; 782 783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 784 } 785 return Result; 786} 787 788//===----------------------------------------------------------------------===// 789// SCEV Expression folder implementations 790//===----------------------------------------------------------------------===// 791 792const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 793 const Type *Ty) { 794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 795 "This is not a truncating conversion!"); 796 assert(isSCEVable(Ty) && 797 "This is not a conversion to a SCEVable type!"); 798 Ty = getEffectiveSCEVType(Ty); 799 800 FoldingSetNodeID ID; 801 ID.AddInteger(scTruncate); 802 ID.AddPointer(Op); 803 ID.AddPointer(Ty); 804 void *IP = 0; 805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 806 807 // Fold if the operand is constant. 808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 809 return getConstant( 810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 811 getEffectiveSCEVType(Ty)))); 812 813 // trunc(trunc(x)) --> trunc(x) 814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 815 return getTruncateExpr(ST->getOperand(), Ty); 816 817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 819 return getTruncateOrSignExtend(SS->getOperand(), Ty); 820 821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 824 825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 826 // eliminate all the truncates. 827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 828 SmallVector<const SCEV *, 4> Operands; 829 bool hasTrunc = false; 830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 832 hasTrunc = isa<SCEVTruncateExpr>(S); 833 Operands.push_back(S); 834 } 835 if (!hasTrunc) 836 return getAddExpr(Operands); 837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 838 } 839 840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 841 // eliminate all the truncates. 842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 843 SmallVector<const SCEV *, 4> Operands; 844 bool hasTrunc = false; 845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 847 hasTrunc = isa<SCEVTruncateExpr>(S); 848 Operands.push_back(S); 849 } 850 if (!hasTrunc) 851 return getMulExpr(Operands); 852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 853 } 854 855 // If the input value is a chrec scev, truncate the chrec's operands. 856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 857 SmallVector<const SCEV *, 4> Operands; 858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 861 } 862 863 // As a special case, fold trunc(undef) to undef. We don't want to 864 // know too much about SCEVUnknowns, but this special case is handy 865 // and harmless. 866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 867 if (isa<UndefValue>(U->getValue())) 868 return getSCEV(UndefValue::get(Ty)); 869 870 // The cast wasn't folded; create an explicit cast node. We can reuse 871 // the existing insert position since if we get here, we won't have 872 // made any changes which would invalidate it. 873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 874 Op, Ty); 875 UniqueSCEVs.InsertNode(S, IP); 876 return S; 877} 878 879const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 880 const Type *Ty) { 881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 882 "This is not an extending conversion!"); 883 assert(isSCEVable(Ty) && 884 "This is not a conversion to a SCEVable type!"); 885 Ty = getEffectiveSCEVType(Ty); 886 887 // Fold if the operand is constant. 888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 889 return getConstant( 890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 891 getEffectiveSCEVType(Ty)))); 892 893 // zext(zext(x)) --> zext(x) 894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 895 return getZeroExtendExpr(SZ->getOperand(), Ty); 896 897 // Before doing any expensive analysis, check to see if we've already 898 // computed a SCEV for this Op and Ty. 899 FoldingSetNodeID ID; 900 ID.AddInteger(scZeroExtend); 901 ID.AddPointer(Op); 902 ID.AddPointer(Ty); 903 void *IP = 0; 904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 905 906 // zext(trunc(x)) --> zext(x) or x or trunc(x) 907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 908 // It's possible the bits taken off by the truncate were all zero bits. If 909 // so, we should be able to simplify this further. 910 const SCEV *X = ST->getOperand(); 911 ConstantRange CR = getUnsignedRange(X); 912 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 913 unsigned NewBits = getTypeSizeInBits(Ty); 914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 915 CR.zextOrTrunc(NewBits))) 916 return getTruncateOrZeroExtend(X, Ty); 917 } 918 919 // If the input value is a chrec scev, and we can prove that the value 920 // did not overflow the old, smaller, value, we can zero extend all of the 921 // operands (often constants). This allows analysis of something like 922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 924 if (AR->isAffine()) { 925 const SCEV *Start = AR->getStart(); 926 const SCEV *Step = AR->getStepRecurrence(*this); 927 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 928 const Loop *L = AR->getLoop(); 929 930 // If we have special knowledge that this addrec won't overflow, 931 // we don't need to do any further analysis. 932 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 933 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 934 getZeroExtendExpr(Step, Ty), 935 L, AR->getNoWrapFlags()); 936 937 // Check whether the backedge-taken count is SCEVCouldNotCompute. 938 // Note that this serves two purposes: It filters out loops that are 939 // simply not analyzable, and it covers the case where this code is 940 // being called from within backedge-taken count analysis, such that 941 // attempting to ask for the backedge-taken count would likely result 942 // in infinite recursion. In the later case, the analysis code will 943 // cope with a conservative value, and it will take care to purge 944 // that value once it has finished. 945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 947 // Manually compute the final value for AR, checking for 948 // overflow. 949 950 // Check whether the backedge-taken count can be losslessly casted to 951 // the addrec's type. The count is always unsigned. 952 const SCEV *CastedMaxBECount = 953 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 954 const SCEV *RecastedMaxBECount = 955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 956 if (MaxBECount == RecastedMaxBECount) { 957 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 958 // Check whether Start+Step*MaxBECount has no unsigned overflow. 959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 960 const SCEV *Add = getAddExpr(Start, ZMul); 961 const SCEV *OperandExtendedAdd = 962 getAddExpr(getZeroExtendExpr(Start, WideTy), 963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 964 getZeroExtendExpr(Step, WideTy))); 965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 966 // Cache knowledge of AR NUW, which is propagated to this AddRec. 967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 968 // Return the expression with the addrec on the outside. 969 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 970 getZeroExtendExpr(Step, Ty), 971 L, AR->getNoWrapFlags()); 972 } 973 // Similar to above, only this time treat the step value as signed. 974 // This covers loops that count down. 975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 976 Add = getAddExpr(Start, SMul); 977 OperandExtendedAdd = 978 getAddExpr(getZeroExtendExpr(Start, WideTy), 979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 980 getSignExtendExpr(Step, WideTy))); 981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 982 // Cache knowledge of AR NW, which is propagated to this AddRec. 983 // Negative step causes unsigned wrap, but it still can't self-wrap. 984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 985 // Return the expression with the addrec on the outside. 986 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 987 getSignExtendExpr(Step, Ty), 988 L, AR->getNoWrapFlags()); 989 } 990 } 991 992 // If the backedge is guarded by a comparison with the pre-inc value 993 // the addrec is safe. Also, if the entry is guarded by a comparison 994 // with the start value and the backedge is guarded by a comparison 995 // with the post-inc value, the addrec is safe. 996 if (isKnownPositive(Step)) { 997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 998 getUnsignedRange(Step).getUnsignedMax()); 999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1002 AR->getPostIncExpr(*this), N))) { 1003 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1005 // Return the expression with the addrec on the outside. 1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1007 getZeroExtendExpr(Step, Ty), 1008 L, AR->getNoWrapFlags()); 1009 } 1010 } else if (isKnownNegative(Step)) { 1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1012 getSignedRange(Step).getSignedMin()); 1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1016 AR->getPostIncExpr(*this), N))) { 1017 // Cache knowledge of AR NW, which is propagated to this AddRec. 1018 // Negative step causes unsigned wrap, but it still can't self-wrap. 1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1020 // Return the expression with the addrec on the outside. 1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1022 getSignExtendExpr(Step, Ty), 1023 L, AR->getNoWrapFlags()); 1024 } 1025 } 1026 } 1027 } 1028 1029 // The cast wasn't folded; create an explicit cast node. 1030 // Recompute the insert position, as it may have been invalidated. 1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1033 Op, Ty); 1034 UniqueSCEVs.InsertNode(S, IP); 1035 return S; 1036} 1037 1038const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1039 const Type *Ty) { 1040 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1041 "This is not an extending conversion!"); 1042 assert(isSCEVable(Ty) && 1043 "This is not a conversion to a SCEVable type!"); 1044 Ty = getEffectiveSCEVType(Ty); 1045 1046 // Fold if the operand is constant. 1047 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1048 return getConstant( 1049 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1050 getEffectiveSCEVType(Ty)))); 1051 1052 // sext(sext(x)) --> sext(x) 1053 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1054 return getSignExtendExpr(SS->getOperand(), Ty); 1055 1056 // sext(zext(x)) --> zext(x) 1057 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1058 return getZeroExtendExpr(SZ->getOperand(), Ty); 1059 1060 // Before doing any expensive analysis, check to see if we've already 1061 // computed a SCEV for this Op and Ty. 1062 FoldingSetNodeID ID; 1063 ID.AddInteger(scSignExtend); 1064 ID.AddPointer(Op); 1065 ID.AddPointer(Ty); 1066 void *IP = 0; 1067 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1068 1069 // If the input value is provably positive, build a zext instead. 1070 if (isKnownNonNegative(Op)) 1071 return getZeroExtendExpr(Op, Ty); 1072 1073 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1074 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1075 // It's possible the bits taken off by the truncate were all sign bits. If 1076 // so, we should be able to simplify this further. 1077 const SCEV *X = ST->getOperand(); 1078 ConstantRange CR = getSignedRange(X); 1079 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1080 unsigned NewBits = getTypeSizeInBits(Ty); 1081 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1082 CR.sextOrTrunc(NewBits))) 1083 return getTruncateOrSignExtend(X, Ty); 1084 } 1085 1086 // If the input value is a chrec scev, and we can prove that the value 1087 // did not overflow the old, smaller, value, we can sign extend all of the 1088 // operands (often constants). This allows analysis of something like 1089 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1090 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1091 if (AR->isAffine()) { 1092 const SCEV *Start = AR->getStart(); 1093 const SCEV *Step = AR->getStepRecurrence(*this); 1094 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1095 const Loop *L = AR->getLoop(); 1096 1097 // If we have special knowledge that this addrec won't overflow, 1098 // we don't need to do any further analysis. 1099 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1100 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1101 getSignExtendExpr(Step, Ty), 1102 L, SCEV::FlagNSW); 1103 1104 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1105 // Note that this serves two purposes: It filters out loops that are 1106 // simply not analyzable, and it covers the case where this code is 1107 // being called from within backedge-taken count analysis, such that 1108 // attempting to ask for the backedge-taken count would likely result 1109 // in infinite recursion. In the later case, the analysis code will 1110 // cope with a conservative value, and it will take care to purge 1111 // that value once it has finished. 1112 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1113 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1114 // Manually compute the final value for AR, checking for 1115 // overflow. 1116 1117 // Check whether the backedge-taken count can be losslessly casted to 1118 // the addrec's type. The count is always unsigned. 1119 const SCEV *CastedMaxBECount = 1120 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1121 const SCEV *RecastedMaxBECount = 1122 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1123 if (MaxBECount == RecastedMaxBECount) { 1124 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1125 // Check whether Start+Step*MaxBECount has no signed overflow. 1126 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1127 const SCEV *Add = getAddExpr(Start, SMul); 1128 const SCEV *OperandExtendedAdd = 1129 getAddExpr(getSignExtendExpr(Start, WideTy), 1130 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1131 getSignExtendExpr(Step, WideTy))); 1132 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1133 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1134 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1135 // Return the expression with the addrec on the outside. 1136 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1137 getSignExtendExpr(Step, Ty), 1138 L, AR->getNoWrapFlags()); 1139 } 1140 // Similar to above, only this time treat the step value as unsigned. 1141 // This covers loops that count up with an unsigned step. 1142 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1143 Add = getAddExpr(Start, UMul); 1144 OperandExtendedAdd = 1145 getAddExpr(getSignExtendExpr(Start, WideTy), 1146 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1147 getZeroExtendExpr(Step, WideTy))); 1148 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1149 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1150 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1151 // Return the expression with the addrec on the outside. 1152 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1153 getZeroExtendExpr(Step, Ty), 1154 L, AR->getNoWrapFlags()); 1155 } 1156 } 1157 1158 // If the backedge is guarded by a comparison with the pre-inc value 1159 // the addrec is safe. Also, if the entry is guarded by a comparison 1160 // with the start value and the backedge is guarded by a comparison 1161 // with the post-inc value, the addrec is safe. 1162 if (isKnownPositive(Step)) { 1163 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1164 getSignedRange(Step).getSignedMax()); 1165 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1166 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1167 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1168 AR->getPostIncExpr(*this), N))) { 1169 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1170 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1171 // Return the expression with the addrec on the outside. 1172 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1173 getSignExtendExpr(Step, Ty), 1174 L, AR->getNoWrapFlags()); 1175 } 1176 } else if (isKnownNegative(Step)) { 1177 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1178 getSignedRange(Step).getSignedMin()); 1179 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1180 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1181 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1182 AR->getPostIncExpr(*this), N))) { 1183 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1184 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1185 // Return the expression with the addrec on the outside. 1186 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1187 getSignExtendExpr(Step, Ty), 1188 L, AR->getNoWrapFlags()); 1189 } 1190 } 1191 } 1192 } 1193 1194 // The cast wasn't folded; create an explicit cast node. 1195 // Recompute the insert position, as it may have been invalidated. 1196 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1197 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1198 Op, Ty); 1199 UniqueSCEVs.InsertNode(S, IP); 1200 return S; 1201} 1202 1203/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1204/// unspecified bits out to the given type. 1205/// 1206const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1207 const Type *Ty) { 1208 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1209 "This is not an extending conversion!"); 1210 assert(isSCEVable(Ty) && 1211 "This is not a conversion to a SCEVable type!"); 1212 Ty = getEffectiveSCEVType(Ty); 1213 1214 // Sign-extend negative constants. 1215 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1216 if (SC->getValue()->getValue().isNegative()) 1217 return getSignExtendExpr(Op, Ty); 1218 1219 // Peel off a truncate cast. 1220 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1221 const SCEV *NewOp = T->getOperand(); 1222 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1223 return getAnyExtendExpr(NewOp, Ty); 1224 return getTruncateOrNoop(NewOp, Ty); 1225 } 1226 1227 // Next try a zext cast. If the cast is folded, use it. 1228 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1229 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1230 return ZExt; 1231 1232 // Next try a sext cast. If the cast is folded, use it. 1233 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1234 if (!isa<SCEVSignExtendExpr>(SExt)) 1235 return SExt; 1236 1237 // Force the cast to be folded into the operands of an addrec. 1238 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1239 SmallVector<const SCEV *, 4> Ops; 1240 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1241 I != E; ++I) 1242 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1243 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1244 } 1245 1246 // As a special case, fold anyext(undef) to undef. We don't want to 1247 // know too much about SCEVUnknowns, but this special case is handy 1248 // and harmless. 1249 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1250 if (isa<UndefValue>(U->getValue())) 1251 return getSCEV(UndefValue::get(Ty)); 1252 1253 // If the expression is obviously signed, use the sext cast value. 1254 if (isa<SCEVSMaxExpr>(Op)) 1255 return SExt; 1256 1257 // Absent any other information, use the zext cast value. 1258 return ZExt; 1259} 1260 1261/// CollectAddOperandsWithScales - Process the given Ops list, which is 1262/// a list of operands to be added under the given scale, update the given 1263/// map. This is a helper function for getAddRecExpr. As an example of 1264/// what it does, given a sequence of operands that would form an add 1265/// expression like this: 1266/// 1267/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1268/// 1269/// where A and B are constants, update the map with these values: 1270/// 1271/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1272/// 1273/// and add 13 + A*B*29 to AccumulatedConstant. 1274/// This will allow getAddRecExpr to produce this: 1275/// 1276/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1277/// 1278/// This form often exposes folding opportunities that are hidden in 1279/// the original operand list. 1280/// 1281/// Return true iff it appears that any interesting folding opportunities 1282/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1283/// the common case where no interesting opportunities are present, and 1284/// is also used as a check to avoid infinite recursion. 1285/// 1286static bool 1287CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1288 SmallVector<const SCEV *, 8> &NewOps, 1289 APInt &AccumulatedConstant, 1290 const SCEV *const *Ops, size_t NumOperands, 1291 const APInt &Scale, 1292 ScalarEvolution &SE) { 1293 bool Interesting = false; 1294 1295 // Iterate over the add operands. They are sorted, with constants first. 1296 unsigned i = 0; 1297 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1298 ++i; 1299 // Pull a buried constant out to the outside. 1300 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1301 Interesting = true; 1302 AccumulatedConstant += Scale * C->getValue()->getValue(); 1303 } 1304 1305 // Next comes everything else. We're especially interested in multiplies 1306 // here, but they're in the middle, so just visit the rest with one loop. 1307 for (; i != NumOperands; ++i) { 1308 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1309 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1310 APInt NewScale = 1311 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1312 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1313 // A multiplication of a constant with another add; recurse. 1314 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1315 Interesting |= 1316 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1317 Add->op_begin(), Add->getNumOperands(), 1318 NewScale, SE); 1319 } else { 1320 // A multiplication of a constant with some other value. Update 1321 // the map. 1322 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1323 const SCEV *Key = SE.getMulExpr(MulOps); 1324 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1325 M.insert(std::make_pair(Key, NewScale)); 1326 if (Pair.second) { 1327 NewOps.push_back(Pair.first->first); 1328 } else { 1329 Pair.first->second += NewScale; 1330 // The map already had an entry for this value, which may indicate 1331 // a folding opportunity. 1332 Interesting = true; 1333 } 1334 } 1335 } else { 1336 // An ordinary operand. Update the map. 1337 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1338 M.insert(std::make_pair(Ops[i], Scale)); 1339 if (Pair.second) { 1340 NewOps.push_back(Pair.first->first); 1341 } else { 1342 Pair.first->second += Scale; 1343 // The map already had an entry for this value, which may indicate 1344 // a folding opportunity. 1345 Interesting = true; 1346 } 1347 } 1348 } 1349 1350 return Interesting; 1351} 1352 1353namespace { 1354 struct APIntCompare { 1355 bool operator()(const APInt &LHS, const APInt &RHS) const { 1356 return LHS.ult(RHS); 1357 } 1358 }; 1359} 1360 1361/// getAddExpr - Get a canonical add expression, or something simpler if 1362/// possible. 1363const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1364 SCEV::NoWrapFlags Flags) { 1365 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1366 "only nuw or nsw allowed"); 1367 assert(!Ops.empty() && "Cannot get empty add!"); 1368 if (Ops.size() == 1) return Ops[0]; 1369#ifndef NDEBUG 1370 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1371 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1372 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1373 "SCEVAddExpr operand types don't match!"); 1374#endif 1375 1376 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1377 // And vice-versa. 1378 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1379 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1380 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1381 bool All = true; 1382 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1383 E = Ops.end(); I != E; ++I) 1384 if (!isKnownNonNegative(*I)) { 1385 All = false; 1386 break; 1387 } 1388 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1389 } 1390 1391 // Sort by complexity, this groups all similar expression types together. 1392 GroupByComplexity(Ops, LI); 1393 1394 // If there are any constants, fold them together. 1395 unsigned Idx = 0; 1396 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1397 ++Idx; 1398 assert(Idx < Ops.size()); 1399 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1400 // We found two constants, fold them together! 1401 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1402 RHSC->getValue()->getValue()); 1403 if (Ops.size() == 2) return Ops[0]; 1404 Ops.erase(Ops.begin()+1); // Erase the folded element 1405 LHSC = cast<SCEVConstant>(Ops[0]); 1406 } 1407 1408 // If we are left with a constant zero being added, strip it off. 1409 if (LHSC->getValue()->isZero()) { 1410 Ops.erase(Ops.begin()); 1411 --Idx; 1412 } 1413 1414 if (Ops.size() == 1) return Ops[0]; 1415 } 1416 1417 // Okay, check to see if the same value occurs in the operand list more than 1418 // once. If so, merge them together into an multiply expression. Since we 1419 // sorted the list, these values are required to be adjacent. 1420 const Type *Ty = Ops[0]->getType(); 1421 bool FoundMatch = false; 1422 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1423 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1424 // Scan ahead to count how many equal operands there are. 1425 unsigned Count = 2; 1426 while (i+Count != e && Ops[i+Count] == Ops[i]) 1427 ++Count; 1428 // Merge the values into a multiply. 1429 const SCEV *Scale = getConstant(Ty, Count); 1430 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1431 if (Ops.size() == Count) 1432 return Mul; 1433 Ops[i] = Mul; 1434 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1435 --i; e -= Count - 1; 1436 FoundMatch = true; 1437 } 1438 if (FoundMatch) 1439 return getAddExpr(Ops, Flags); 1440 1441 // Check for truncates. If all the operands are truncated from the same 1442 // type, see if factoring out the truncate would permit the result to be 1443 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1444 // if the contents of the resulting outer trunc fold to something simple. 1445 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1446 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1447 const Type *DstType = Trunc->getType(); 1448 const Type *SrcType = Trunc->getOperand()->getType(); 1449 SmallVector<const SCEV *, 8> LargeOps; 1450 bool Ok = true; 1451 // Check all the operands to see if they can be represented in the 1452 // source type of the truncate. 1453 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1454 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1455 if (T->getOperand()->getType() != SrcType) { 1456 Ok = false; 1457 break; 1458 } 1459 LargeOps.push_back(T->getOperand()); 1460 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1461 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1462 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1463 SmallVector<const SCEV *, 8> LargeMulOps; 1464 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1465 if (const SCEVTruncateExpr *T = 1466 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1467 if (T->getOperand()->getType() != SrcType) { 1468 Ok = false; 1469 break; 1470 } 1471 LargeMulOps.push_back(T->getOperand()); 1472 } else if (const SCEVConstant *C = 1473 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1474 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1475 } else { 1476 Ok = false; 1477 break; 1478 } 1479 } 1480 if (Ok) 1481 LargeOps.push_back(getMulExpr(LargeMulOps)); 1482 } else { 1483 Ok = false; 1484 break; 1485 } 1486 } 1487 if (Ok) { 1488 // Evaluate the expression in the larger type. 1489 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1490 // If it folds to something simple, use it. Otherwise, don't. 1491 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1492 return getTruncateExpr(Fold, DstType); 1493 } 1494 } 1495 1496 // Skip past any other cast SCEVs. 1497 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1498 ++Idx; 1499 1500 // If there are add operands they would be next. 1501 if (Idx < Ops.size()) { 1502 bool DeletedAdd = false; 1503 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1504 // If we have an add, expand the add operands onto the end of the operands 1505 // list. 1506 Ops.erase(Ops.begin()+Idx); 1507 Ops.append(Add->op_begin(), Add->op_end()); 1508 DeletedAdd = true; 1509 } 1510 1511 // If we deleted at least one add, we added operands to the end of the list, 1512 // and they are not necessarily sorted. Recurse to resort and resimplify 1513 // any operands we just acquired. 1514 if (DeletedAdd) 1515 return getAddExpr(Ops); 1516 } 1517 1518 // Skip over the add expression until we get to a multiply. 1519 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1520 ++Idx; 1521 1522 // Check to see if there are any folding opportunities present with 1523 // operands multiplied by constant values. 1524 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1525 uint64_t BitWidth = getTypeSizeInBits(Ty); 1526 DenseMap<const SCEV *, APInt> M; 1527 SmallVector<const SCEV *, 8> NewOps; 1528 APInt AccumulatedConstant(BitWidth, 0); 1529 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1530 Ops.data(), Ops.size(), 1531 APInt(BitWidth, 1), *this)) { 1532 // Some interesting folding opportunity is present, so its worthwhile to 1533 // re-generate the operands list. Group the operands by constant scale, 1534 // to avoid multiplying by the same constant scale multiple times. 1535 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1536 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1537 E = NewOps.end(); I != E; ++I) 1538 MulOpLists[M.find(*I)->second].push_back(*I); 1539 // Re-generate the operands list. 1540 Ops.clear(); 1541 if (AccumulatedConstant != 0) 1542 Ops.push_back(getConstant(AccumulatedConstant)); 1543 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1544 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1545 if (I->first != 0) 1546 Ops.push_back(getMulExpr(getConstant(I->first), 1547 getAddExpr(I->second))); 1548 if (Ops.empty()) 1549 return getConstant(Ty, 0); 1550 if (Ops.size() == 1) 1551 return Ops[0]; 1552 return getAddExpr(Ops); 1553 } 1554 } 1555 1556 // If we are adding something to a multiply expression, make sure the 1557 // something is not already an operand of the multiply. If so, merge it into 1558 // the multiply. 1559 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1560 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1561 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1562 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1563 if (isa<SCEVConstant>(MulOpSCEV)) 1564 continue; 1565 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1566 if (MulOpSCEV == Ops[AddOp]) { 1567 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1568 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1569 if (Mul->getNumOperands() != 2) { 1570 // If the multiply has more than two operands, we must get the 1571 // Y*Z term. 1572 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1573 Mul->op_begin()+MulOp); 1574 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1575 InnerMul = getMulExpr(MulOps); 1576 } 1577 const SCEV *One = getConstant(Ty, 1); 1578 const SCEV *AddOne = getAddExpr(One, InnerMul); 1579 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1580 if (Ops.size() == 2) return OuterMul; 1581 if (AddOp < Idx) { 1582 Ops.erase(Ops.begin()+AddOp); 1583 Ops.erase(Ops.begin()+Idx-1); 1584 } else { 1585 Ops.erase(Ops.begin()+Idx); 1586 Ops.erase(Ops.begin()+AddOp-1); 1587 } 1588 Ops.push_back(OuterMul); 1589 return getAddExpr(Ops); 1590 } 1591 1592 // Check this multiply against other multiplies being added together. 1593 for (unsigned OtherMulIdx = Idx+1; 1594 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1595 ++OtherMulIdx) { 1596 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1597 // If MulOp occurs in OtherMul, we can fold the two multiplies 1598 // together. 1599 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1600 OMulOp != e; ++OMulOp) 1601 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1602 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1603 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1604 if (Mul->getNumOperands() != 2) { 1605 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1606 Mul->op_begin()+MulOp); 1607 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1608 InnerMul1 = getMulExpr(MulOps); 1609 } 1610 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1611 if (OtherMul->getNumOperands() != 2) { 1612 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1613 OtherMul->op_begin()+OMulOp); 1614 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1615 InnerMul2 = getMulExpr(MulOps); 1616 } 1617 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1618 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1619 if (Ops.size() == 2) return OuterMul; 1620 Ops.erase(Ops.begin()+Idx); 1621 Ops.erase(Ops.begin()+OtherMulIdx-1); 1622 Ops.push_back(OuterMul); 1623 return getAddExpr(Ops); 1624 } 1625 } 1626 } 1627 } 1628 1629 // If there are any add recurrences in the operands list, see if any other 1630 // added values are loop invariant. If so, we can fold them into the 1631 // recurrence. 1632 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1633 ++Idx; 1634 1635 // Scan over all recurrences, trying to fold loop invariants into them. 1636 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1637 // Scan all of the other operands to this add and add them to the vector if 1638 // they are loop invariant w.r.t. the recurrence. 1639 SmallVector<const SCEV *, 8> LIOps; 1640 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1641 const Loop *AddRecLoop = AddRec->getLoop(); 1642 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1643 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1644 LIOps.push_back(Ops[i]); 1645 Ops.erase(Ops.begin()+i); 1646 --i; --e; 1647 } 1648 1649 // If we found some loop invariants, fold them into the recurrence. 1650 if (!LIOps.empty()) { 1651 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1652 LIOps.push_back(AddRec->getStart()); 1653 1654 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1655 AddRec->op_end()); 1656 AddRecOps[0] = getAddExpr(LIOps); 1657 1658 // Build the new addrec. Propagate the NUW and NSW flags if both the 1659 // outer add and the inner addrec are guaranteed to have no overflow. 1660 // Always propagate NW. 1661 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1662 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1663 1664 // If all of the other operands were loop invariant, we are done. 1665 if (Ops.size() == 1) return NewRec; 1666 1667 // Otherwise, add the folded AddRec by the non-liv parts. 1668 for (unsigned i = 0;; ++i) 1669 if (Ops[i] == AddRec) { 1670 Ops[i] = NewRec; 1671 break; 1672 } 1673 return getAddExpr(Ops); 1674 } 1675 1676 // Okay, if there weren't any loop invariants to be folded, check to see if 1677 // there are multiple AddRec's with the same loop induction variable being 1678 // added together. If so, we can fold them. 1679 for (unsigned OtherIdx = Idx+1; 1680 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1681 ++OtherIdx) 1682 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1683 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1684 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1685 AddRec->op_end()); 1686 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1687 ++OtherIdx) 1688 if (const SCEVAddRecExpr *OtherAddRec = 1689 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1690 if (OtherAddRec->getLoop() == AddRecLoop) { 1691 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1692 i != e; ++i) { 1693 if (i >= AddRecOps.size()) { 1694 AddRecOps.append(OtherAddRec->op_begin()+i, 1695 OtherAddRec->op_end()); 1696 break; 1697 } 1698 AddRecOps[i] = getAddExpr(AddRecOps[i], 1699 OtherAddRec->getOperand(i)); 1700 } 1701 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1702 } 1703 // Step size has changed, so we cannot guarantee no self-wraparound. 1704 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1705 return getAddExpr(Ops); 1706 } 1707 1708 // Otherwise couldn't fold anything into this recurrence. Move onto the 1709 // next one. 1710 } 1711 1712 // Okay, it looks like we really DO need an add expr. Check to see if we 1713 // already have one, otherwise create a new one. 1714 FoldingSetNodeID ID; 1715 ID.AddInteger(scAddExpr); 1716 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1717 ID.AddPointer(Ops[i]); 1718 void *IP = 0; 1719 SCEVAddExpr *S = 1720 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1721 if (!S) { 1722 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1723 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1724 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1725 O, Ops.size()); 1726 UniqueSCEVs.InsertNode(S, IP); 1727 } 1728 S->setNoWrapFlags(Flags); 1729 return S; 1730} 1731 1732/// getMulExpr - Get a canonical multiply expression, or something simpler if 1733/// possible. 1734const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1735 SCEV::NoWrapFlags Flags) { 1736 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1737 "only nuw or nsw allowed"); 1738 assert(!Ops.empty() && "Cannot get empty mul!"); 1739 if (Ops.size() == 1) return Ops[0]; 1740#ifndef NDEBUG 1741 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1742 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1743 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1744 "SCEVMulExpr operand types don't match!"); 1745#endif 1746 1747 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1748 // And vice-versa. 1749 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1750 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1751 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1752 bool All = true; 1753 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1754 E = Ops.end(); I != E; ++I) 1755 if (!isKnownNonNegative(*I)) { 1756 All = false; 1757 break; 1758 } 1759 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1760 } 1761 1762 // Sort by complexity, this groups all similar expression types together. 1763 GroupByComplexity(Ops, LI); 1764 1765 // If there are any constants, fold them together. 1766 unsigned Idx = 0; 1767 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1768 1769 // C1*(C2+V) -> C1*C2 + C1*V 1770 if (Ops.size() == 2) 1771 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1772 if (Add->getNumOperands() == 2 && 1773 isa<SCEVConstant>(Add->getOperand(0))) 1774 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1775 getMulExpr(LHSC, Add->getOperand(1))); 1776 1777 ++Idx; 1778 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1779 // We found two constants, fold them together! 1780 ConstantInt *Fold = ConstantInt::get(getContext(), 1781 LHSC->getValue()->getValue() * 1782 RHSC->getValue()->getValue()); 1783 Ops[0] = getConstant(Fold); 1784 Ops.erase(Ops.begin()+1); // Erase the folded element 1785 if (Ops.size() == 1) return Ops[0]; 1786 LHSC = cast<SCEVConstant>(Ops[0]); 1787 } 1788 1789 // If we are left with a constant one being multiplied, strip it off. 1790 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1791 Ops.erase(Ops.begin()); 1792 --Idx; 1793 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1794 // If we have a multiply of zero, it will always be zero. 1795 return Ops[0]; 1796 } else if (Ops[0]->isAllOnesValue()) { 1797 // If we have a mul by -1 of an add, try distributing the -1 among the 1798 // add operands. 1799 if (Ops.size() == 2) { 1800 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1801 SmallVector<const SCEV *, 4> NewOps; 1802 bool AnyFolded = false; 1803 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1804 E = Add->op_end(); I != E; ++I) { 1805 const SCEV *Mul = getMulExpr(Ops[0], *I); 1806 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1807 NewOps.push_back(Mul); 1808 } 1809 if (AnyFolded) 1810 return getAddExpr(NewOps); 1811 } 1812 else if (const SCEVAddRecExpr * 1813 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1814 // Negation preserves a recurrence's no self-wrap property. 1815 SmallVector<const SCEV *, 4> Operands; 1816 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1817 E = AddRec->op_end(); I != E; ++I) { 1818 Operands.push_back(getMulExpr(Ops[0], *I)); 1819 } 1820 return getAddRecExpr(Operands, AddRec->getLoop(), 1821 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1822 } 1823 } 1824 } 1825 1826 if (Ops.size() == 1) 1827 return Ops[0]; 1828 } 1829 1830 // Skip over the add expression until we get to a multiply. 1831 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1832 ++Idx; 1833 1834 // If there are mul operands inline them all into this expression. 1835 if (Idx < Ops.size()) { 1836 bool DeletedMul = false; 1837 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1838 // If we have an mul, expand the mul operands onto the end of the operands 1839 // list. 1840 Ops.erase(Ops.begin()+Idx); 1841 Ops.append(Mul->op_begin(), Mul->op_end()); 1842 DeletedMul = true; 1843 } 1844 1845 // If we deleted at least one mul, we added operands to the end of the list, 1846 // and they are not necessarily sorted. Recurse to resort and resimplify 1847 // any operands we just acquired. 1848 if (DeletedMul) 1849 return getMulExpr(Ops); 1850 } 1851 1852 // If there are any add recurrences in the operands list, see if any other 1853 // added values are loop invariant. If so, we can fold them into the 1854 // recurrence. 1855 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1856 ++Idx; 1857 1858 // Scan over all recurrences, trying to fold loop invariants into them. 1859 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1860 // Scan all of the other operands to this mul and add them to the vector if 1861 // they are loop invariant w.r.t. the recurrence. 1862 SmallVector<const SCEV *, 8> LIOps; 1863 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1864 const Loop *AddRecLoop = AddRec->getLoop(); 1865 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1866 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1867 LIOps.push_back(Ops[i]); 1868 Ops.erase(Ops.begin()+i); 1869 --i; --e; 1870 } 1871 1872 // If we found some loop invariants, fold them into the recurrence. 1873 if (!LIOps.empty()) { 1874 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1875 SmallVector<const SCEV *, 4> NewOps; 1876 NewOps.reserve(AddRec->getNumOperands()); 1877 const SCEV *Scale = getMulExpr(LIOps); 1878 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1879 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1880 1881 // Build the new addrec. Propagate the NUW and NSW flags if both the 1882 // outer mul and the inner addrec are guaranteed to have no overflow. 1883 // 1884 // No self-wrap cannot be guaranteed after changing the step size, but 1885 // will be inferred if either NUW or NSW is true. 1886 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 1887 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 1888 1889 // If all of the other operands were loop invariant, we are done. 1890 if (Ops.size() == 1) return NewRec; 1891 1892 // Otherwise, multiply the folded AddRec by the non-liv parts. 1893 for (unsigned i = 0;; ++i) 1894 if (Ops[i] == AddRec) { 1895 Ops[i] = NewRec; 1896 break; 1897 } 1898 return getMulExpr(Ops); 1899 } 1900 1901 // Okay, if there weren't any loop invariants to be folded, check to see if 1902 // there are multiple AddRec's with the same loop induction variable being 1903 // multiplied together. If so, we can fold them. 1904 for (unsigned OtherIdx = Idx+1; 1905 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1906 ++OtherIdx) 1907 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1908 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1909 // {A*C,+,F*D + G*B + B*D}<L> 1910 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1911 ++OtherIdx) 1912 if (const SCEVAddRecExpr *OtherAddRec = 1913 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1914 if (OtherAddRec->getLoop() == AddRecLoop) { 1915 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1916 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1917 const SCEV *B = F->getStepRecurrence(*this); 1918 const SCEV *D = G->getStepRecurrence(*this); 1919 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1920 getMulExpr(G, B), 1921 getMulExpr(B, D)); 1922 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1923 F->getLoop(), 1924 SCEV::FlagAnyWrap); 1925 if (Ops.size() == 2) return NewAddRec; 1926 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1927 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1928 } 1929 return getMulExpr(Ops); 1930 } 1931 1932 // Otherwise couldn't fold anything into this recurrence. Move onto the 1933 // next one. 1934 } 1935 1936 // Okay, it looks like we really DO need an mul expr. Check to see if we 1937 // already have one, otherwise create a new one. 1938 FoldingSetNodeID ID; 1939 ID.AddInteger(scMulExpr); 1940 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1941 ID.AddPointer(Ops[i]); 1942 void *IP = 0; 1943 SCEVMulExpr *S = 1944 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1945 if (!S) { 1946 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1947 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1948 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1949 O, Ops.size()); 1950 UniqueSCEVs.InsertNode(S, IP); 1951 } 1952 S->setNoWrapFlags(Flags); 1953 return S; 1954} 1955 1956/// getUDivExpr - Get a canonical unsigned division expression, or something 1957/// simpler if possible. 1958const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1959 const SCEV *RHS) { 1960 assert(getEffectiveSCEVType(LHS->getType()) == 1961 getEffectiveSCEVType(RHS->getType()) && 1962 "SCEVUDivExpr operand types don't match!"); 1963 1964 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1965 if (RHSC->getValue()->equalsInt(1)) 1966 return LHS; // X udiv 1 --> x 1967 // If the denominator is zero, the result of the udiv is undefined. Don't 1968 // try to analyze it, because the resolution chosen here may differ from 1969 // the resolution chosen in other parts of the compiler. 1970 if (!RHSC->getValue()->isZero()) { 1971 // Determine if the division can be folded into the operands of 1972 // its operands. 1973 // TODO: Generalize this to non-constants by using known-bits information. 1974 const Type *Ty = LHS->getType(); 1975 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1976 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1977 // For non-power-of-two values, effectively round the value up to the 1978 // nearest power of two. 1979 if (!RHSC->getValue()->getValue().isPowerOf2()) 1980 ++MaxShiftAmt; 1981 const IntegerType *ExtTy = 1982 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1983 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1984 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1985 if (const SCEVConstant *Step = 1986 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1987 if (!Step->getValue()->getValue() 1988 .urem(RHSC->getValue()->getValue()) && 1989 getZeroExtendExpr(AR, ExtTy) == 1990 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1991 getZeroExtendExpr(Step, ExtTy), 1992 AR->getLoop(), SCEV::FlagAnyWrap)) { 1993 SmallVector<const SCEV *, 4> Operands; 1994 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1995 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1996 return getAddRecExpr(Operands, AR->getLoop(), 1997 SCEV::FlagNW); 1998 } 1999 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2000 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2001 SmallVector<const SCEV *, 4> Operands; 2002 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2003 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2004 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2005 // Find an operand that's safely divisible. 2006 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2007 const SCEV *Op = M->getOperand(i); 2008 const SCEV *Div = getUDivExpr(Op, RHSC); 2009 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2010 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2011 M->op_end()); 2012 Operands[i] = Div; 2013 return getMulExpr(Operands); 2014 } 2015 } 2016 } 2017 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2018 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 2019 SmallVector<const SCEV *, 4> Operands; 2020 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2021 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2022 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2023 Operands.clear(); 2024 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2025 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2026 if (isa<SCEVUDivExpr>(Op) || 2027 getMulExpr(Op, RHS) != A->getOperand(i)) 2028 break; 2029 Operands.push_back(Op); 2030 } 2031 if (Operands.size() == A->getNumOperands()) 2032 return getAddExpr(Operands); 2033 } 2034 } 2035 2036 // Fold if both operands are constant. 2037 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2038 Constant *LHSCV = LHSC->getValue(); 2039 Constant *RHSCV = RHSC->getValue(); 2040 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2041 RHSCV))); 2042 } 2043 } 2044 } 2045 2046 FoldingSetNodeID ID; 2047 ID.AddInteger(scUDivExpr); 2048 ID.AddPointer(LHS); 2049 ID.AddPointer(RHS); 2050 void *IP = 0; 2051 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2052 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2053 LHS, RHS); 2054 UniqueSCEVs.InsertNode(S, IP); 2055 return S; 2056} 2057 2058 2059/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2060/// Simplify the expression as much as possible. 2061const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2062 const Loop *L, 2063 SCEV::NoWrapFlags Flags) { 2064 SmallVector<const SCEV *, 4> Operands; 2065 Operands.push_back(Start); 2066 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2067 if (StepChrec->getLoop() == L) { 2068 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2069 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2070 } 2071 2072 Operands.push_back(Step); 2073 return getAddRecExpr(Operands, L, Flags); 2074} 2075 2076/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2077/// Simplify the expression as much as possible. 2078const SCEV * 2079ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2080 const Loop *L, SCEV::NoWrapFlags Flags) { 2081 if (Operands.size() == 1) return Operands[0]; 2082#ifndef NDEBUG 2083 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2084 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2085 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2086 "SCEVAddRecExpr operand types don't match!"); 2087 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2088 assert(isLoopInvariant(Operands[i], L) && 2089 "SCEVAddRecExpr operand is not loop-invariant!"); 2090#endif 2091 2092 if (Operands.back()->isZero()) { 2093 Operands.pop_back(); 2094 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2095 } 2096 2097 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2098 // use that information to infer NUW and NSW flags. However, computing a 2099 // BE count requires calling getAddRecExpr, so we may not yet have a 2100 // meaningful BE count at this point (and if we don't, we'd be stuck 2101 // with a SCEVCouldNotCompute as the cached BE count). 2102 2103 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2104 // And vice-versa. 2105 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2106 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2107 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2108 bool All = true; 2109 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2110 E = Operands.end(); I != E; ++I) 2111 if (!isKnownNonNegative(*I)) { 2112 All = false; 2113 break; 2114 } 2115 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2116 } 2117 2118 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2119 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2120 const Loop *NestedLoop = NestedAR->getLoop(); 2121 if (L->contains(NestedLoop) ? 2122 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2123 (!NestedLoop->contains(L) && 2124 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2125 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2126 NestedAR->op_end()); 2127 Operands[0] = NestedAR->getStart(); 2128 // AddRecs require their operands be loop-invariant with respect to their 2129 // loops. Don't perform this transformation if it would break this 2130 // requirement. 2131 bool AllInvariant = true; 2132 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2133 if (!isLoopInvariant(Operands[i], L)) { 2134 AllInvariant = false; 2135 break; 2136 } 2137 if (AllInvariant) { 2138 // Create a recurrence for the outer loop with the same step size. 2139 // 2140 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2141 // inner recurrence has the same property. 2142 SCEV::NoWrapFlags OuterFlags = 2143 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2144 2145 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2146 AllInvariant = true; 2147 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2148 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2149 AllInvariant = false; 2150 break; 2151 } 2152 if (AllInvariant) { 2153 // Ok, both add recurrences are valid after the transformation. 2154 // 2155 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2156 // the outer recurrence has the same property. 2157 SCEV::NoWrapFlags InnerFlags = 2158 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2159 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2160 } 2161 } 2162 // Reset Operands to its original state. 2163 Operands[0] = NestedAR; 2164 } 2165 } 2166 2167 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2168 // already have one, otherwise create a new one. 2169 FoldingSetNodeID ID; 2170 ID.AddInteger(scAddRecExpr); 2171 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2172 ID.AddPointer(Operands[i]); 2173 ID.AddPointer(L); 2174 void *IP = 0; 2175 SCEVAddRecExpr *S = 2176 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2177 if (!S) { 2178 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2179 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2180 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2181 O, Operands.size(), L); 2182 UniqueSCEVs.InsertNode(S, IP); 2183 } 2184 S->setNoWrapFlags(Flags); 2185 return S; 2186} 2187 2188const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2189 const SCEV *RHS) { 2190 SmallVector<const SCEV *, 2> Ops; 2191 Ops.push_back(LHS); 2192 Ops.push_back(RHS); 2193 return getSMaxExpr(Ops); 2194} 2195 2196const SCEV * 2197ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2198 assert(!Ops.empty() && "Cannot get empty smax!"); 2199 if (Ops.size() == 1) return Ops[0]; 2200#ifndef NDEBUG 2201 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2202 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2203 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2204 "SCEVSMaxExpr operand types don't match!"); 2205#endif 2206 2207 // Sort by complexity, this groups all similar expression types together. 2208 GroupByComplexity(Ops, LI); 2209 2210 // If there are any constants, fold them together. 2211 unsigned Idx = 0; 2212 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2213 ++Idx; 2214 assert(Idx < Ops.size()); 2215 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2216 // We found two constants, fold them together! 2217 ConstantInt *Fold = ConstantInt::get(getContext(), 2218 APIntOps::smax(LHSC->getValue()->getValue(), 2219 RHSC->getValue()->getValue())); 2220 Ops[0] = getConstant(Fold); 2221 Ops.erase(Ops.begin()+1); // Erase the folded element 2222 if (Ops.size() == 1) return Ops[0]; 2223 LHSC = cast<SCEVConstant>(Ops[0]); 2224 } 2225 2226 // If we are left with a constant minimum-int, strip it off. 2227 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2228 Ops.erase(Ops.begin()); 2229 --Idx; 2230 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2231 // If we have an smax with a constant maximum-int, it will always be 2232 // maximum-int. 2233 return Ops[0]; 2234 } 2235 2236 if (Ops.size() == 1) return Ops[0]; 2237 } 2238 2239 // Find the first SMax 2240 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2241 ++Idx; 2242 2243 // Check to see if one of the operands is an SMax. If so, expand its operands 2244 // onto our operand list, and recurse to simplify. 2245 if (Idx < Ops.size()) { 2246 bool DeletedSMax = false; 2247 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2248 Ops.erase(Ops.begin()+Idx); 2249 Ops.append(SMax->op_begin(), SMax->op_end()); 2250 DeletedSMax = true; 2251 } 2252 2253 if (DeletedSMax) 2254 return getSMaxExpr(Ops); 2255 } 2256 2257 // Okay, check to see if the same value occurs in the operand list twice. If 2258 // so, delete one. Since we sorted the list, these values are required to 2259 // be adjacent. 2260 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2261 // X smax Y smax Y --> X smax Y 2262 // X smax Y --> X, if X is always greater than Y 2263 if (Ops[i] == Ops[i+1] || 2264 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2265 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2266 --i; --e; 2267 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2268 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2269 --i; --e; 2270 } 2271 2272 if (Ops.size() == 1) return Ops[0]; 2273 2274 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2275 2276 // Okay, it looks like we really DO need an smax expr. Check to see if we 2277 // already have one, otherwise create a new one. 2278 FoldingSetNodeID ID; 2279 ID.AddInteger(scSMaxExpr); 2280 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2281 ID.AddPointer(Ops[i]); 2282 void *IP = 0; 2283 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2284 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2285 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2286 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2287 O, Ops.size()); 2288 UniqueSCEVs.InsertNode(S, IP); 2289 return S; 2290} 2291 2292const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2293 const SCEV *RHS) { 2294 SmallVector<const SCEV *, 2> Ops; 2295 Ops.push_back(LHS); 2296 Ops.push_back(RHS); 2297 return getUMaxExpr(Ops); 2298} 2299 2300const SCEV * 2301ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2302 assert(!Ops.empty() && "Cannot get empty umax!"); 2303 if (Ops.size() == 1) return Ops[0]; 2304#ifndef NDEBUG 2305 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2306 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2307 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2308 "SCEVUMaxExpr operand types don't match!"); 2309#endif 2310 2311 // Sort by complexity, this groups all similar expression types together. 2312 GroupByComplexity(Ops, LI); 2313 2314 // If there are any constants, fold them together. 2315 unsigned Idx = 0; 2316 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2317 ++Idx; 2318 assert(Idx < Ops.size()); 2319 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2320 // We found two constants, fold them together! 2321 ConstantInt *Fold = ConstantInt::get(getContext(), 2322 APIntOps::umax(LHSC->getValue()->getValue(), 2323 RHSC->getValue()->getValue())); 2324 Ops[0] = getConstant(Fold); 2325 Ops.erase(Ops.begin()+1); // Erase the folded element 2326 if (Ops.size() == 1) return Ops[0]; 2327 LHSC = cast<SCEVConstant>(Ops[0]); 2328 } 2329 2330 // If we are left with a constant minimum-int, strip it off. 2331 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2332 Ops.erase(Ops.begin()); 2333 --Idx; 2334 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2335 // If we have an umax with a constant maximum-int, it will always be 2336 // maximum-int. 2337 return Ops[0]; 2338 } 2339 2340 if (Ops.size() == 1) return Ops[0]; 2341 } 2342 2343 // Find the first UMax 2344 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2345 ++Idx; 2346 2347 // Check to see if one of the operands is a UMax. If so, expand its operands 2348 // onto our operand list, and recurse to simplify. 2349 if (Idx < Ops.size()) { 2350 bool DeletedUMax = false; 2351 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2352 Ops.erase(Ops.begin()+Idx); 2353 Ops.append(UMax->op_begin(), UMax->op_end()); 2354 DeletedUMax = true; 2355 } 2356 2357 if (DeletedUMax) 2358 return getUMaxExpr(Ops); 2359 } 2360 2361 // Okay, check to see if the same value occurs in the operand list twice. If 2362 // so, delete one. Since we sorted the list, these values are required to 2363 // be adjacent. 2364 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2365 // X umax Y umax Y --> X umax Y 2366 // X umax Y --> X, if X is always greater than Y 2367 if (Ops[i] == Ops[i+1] || 2368 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2369 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2370 --i; --e; 2371 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2372 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2373 --i; --e; 2374 } 2375 2376 if (Ops.size() == 1) return Ops[0]; 2377 2378 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2379 2380 // Okay, it looks like we really DO need a umax expr. Check to see if we 2381 // already have one, otherwise create a new one. 2382 FoldingSetNodeID ID; 2383 ID.AddInteger(scUMaxExpr); 2384 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2385 ID.AddPointer(Ops[i]); 2386 void *IP = 0; 2387 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2388 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2389 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2390 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2391 O, Ops.size()); 2392 UniqueSCEVs.InsertNode(S, IP); 2393 return S; 2394} 2395 2396const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2397 const SCEV *RHS) { 2398 // ~smax(~x, ~y) == smin(x, y). 2399 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2400} 2401 2402const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2403 const SCEV *RHS) { 2404 // ~umax(~x, ~y) == umin(x, y) 2405 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2406} 2407 2408const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2409 // If we have TargetData, we can bypass creating a target-independent 2410 // constant expression and then folding it back into a ConstantInt. 2411 // This is just a compile-time optimization. 2412 if (TD) 2413 return getConstant(TD->getIntPtrType(getContext()), 2414 TD->getTypeAllocSize(AllocTy)); 2415 2416 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2417 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2418 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2419 C = Folded; 2420 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2421 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2422} 2423 2424const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2425 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2426 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2427 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2428 C = Folded; 2429 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2430 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2431} 2432 2433const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2434 unsigned FieldNo) { 2435 // If we have TargetData, we can bypass creating a target-independent 2436 // constant expression and then folding it back into a ConstantInt. 2437 // This is just a compile-time optimization. 2438 if (TD) 2439 return getConstant(TD->getIntPtrType(getContext()), 2440 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2441 2442 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2443 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2444 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2445 C = Folded; 2446 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2447 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2448} 2449 2450const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2451 Constant *FieldNo) { 2452 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2453 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2454 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2455 C = Folded; 2456 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2457 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2458} 2459 2460const SCEV *ScalarEvolution::getUnknown(Value *V) { 2461 // Don't attempt to do anything other than create a SCEVUnknown object 2462 // here. createSCEV only calls getUnknown after checking for all other 2463 // interesting possibilities, and any other code that calls getUnknown 2464 // is doing so in order to hide a value from SCEV canonicalization. 2465 2466 FoldingSetNodeID ID; 2467 ID.AddInteger(scUnknown); 2468 ID.AddPointer(V); 2469 void *IP = 0; 2470 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2471 assert(cast<SCEVUnknown>(S)->getValue() == V && 2472 "Stale SCEVUnknown in uniquing map!"); 2473 return S; 2474 } 2475 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2476 FirstUnknown); 2477 FirstUnknown = cast<SCEVUnknown>(S); 2478 UniqueSCEVs.InsertNode(S, IP); 2479 return S; 2480} 2481 2482//===----------------------------------------------------------------------===// 2483// Basic SCEV Analysis and PHI Idiom Recognition Code 2484// 2485 2486/// isSCEVable - Test if values of the given type are analyzable within 2487/// the SCEV framework. This primarily includes integer types, and it 2488/// can optionally include pointer types if the ScalarEvolution class 2489/// has access to target-specific information. 2490bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2491 // Integers and pointers are always SCEVable. 2492 return Ty->isIntegerTy() || Ty->isPointerTy(); 2493} 2494 2495/// getTypeSizeInBits - Return the size in bits of the specified type, 2496/// for which isSCEVable must return true. 2497uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2498 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2499 2500 // If we have a TargetData, use it! 2501 if (TD) 2502 return TD->getTypeSizeInBits(Ty); 2503 2504 // Integer types have fixed sizes. 2505 if (Ty->isIntegerTy()) 2506 return Ty->getPrimitiveSizeInBits(); 2507 2508 // The only other support type is pointer. Without TargetData, conservatively 2509 // assume pointers are 64-bit. 2510 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2511 return 64; 2512} 2513 2514/// getEffectiveSCEVType - Return a type with the same bitwidth as 2515/// the given type and which represents how SCEV will treat the given 2516/// type, for which isSCEVable must return true. For pointer types, 2517/// this is the pointer-sized integer type. 2518const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2519 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2520 2521 if (Ty->isIntegerTy()) 2522 return Ty; 2523 2524 // The only other support type is pointer. 2525 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2526 if (TD) return TD->getIntPtrType(getContext()); 2527 2528 // Without TargetData, conservatively assume pointers are 64-bit. 2529 return Type::getInt64Ty(getContext()); 2530} 2531 2532const SCEV *ScalarEvolution::getCouldNotCompute() { 2533 return &CouldNotCompute; 2534} 2535 2536/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2537/// expression and create a new one. 2538const SCEV *ScalarEvolution::getSCEV(Value *V) { 2539 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2540 2541 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2542 if (I != ValueExprMap.end()) return I->second; 2543 const SCEV *S = createSCEV(V); 2544 2545 // The process of creating a SCEV for V may have caused other SCEVs 2546 // to have been created, so it's necessary to insert the new entry 2547 // from scratch, rather than trying to remember the insert position 2548 // above. 2549 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2550 return S; 2551} 2552 2553/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2554/// 2555const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2556 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2557 return getConstant( 2558 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2559 2560 const Type *Ty = V->getType(); 2561 Ty = getEffectiveSCEVType(Ty); 2562 return getMulExpr(V, 2563 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2564} 2565 2566/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2567const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2568 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2569 return getConstant( 2570 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2571 2572 const Type *Ty = V->getType(); 2573 Ty = getEffectiveSCEVType(Ty); 2574 const SCEV *AllOnes = 2575 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2576 return getMinusSCEV(AllOnes, V); 2577} 2578 2579/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2580const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2581 SCEV::NoWrapFlags Flags) { 2582 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2583 2584 // Fast path: X - X --> 0. 2585 if (LHS == RHS) 2586 return getConstant(LHS->getType(), 0); 2587 2588 // X - Y --> X + -Y 2589 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2590} 2591 2592/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2593/// input value to the specified type. If the type must be extended, it is zero 2594/// extended. 2595const SCEV * 2596ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) { 2597 const Type *SrcTy = V->getType(); 2598 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2599 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2600 "Cannot truncate or zero extend with non-integer arguments!"); 2601 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2602 return V; // No conversion 2603 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2604 return getTruncateExpr(V, Ty); 2605 return getZeroExtendExpr(V, Ty); 2606} 2607 2608/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2609/// input value to the specified type. If the type must be extended, it is sign 2610/// extended. 2611const SCEV * 2612ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2613 const Type *Ty) { 2614 const Type *SrcTy = V->getType(); 2615 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2616 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2617 "Cannot truncate or zero extend with non-integer arguments!"); 2618 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2619 return V; // No conversion 2620 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2621 return getTruncateExpr(V, Ty); 2622 return getSignExtendExpr(V, Ty); 2623} 2624 2625/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2626/// input value to the specified type. If the type must be extended, it is zero 2627/// extended. The conversion must not be narrowing. 2628const SCEV * 2629ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2630 const Type *SrcTy = V->getType(); 2631 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2632 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2633 "Cannot noop or zero extend with non-integer arguments!"); 2634 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2635 "getNoopOrZeroExtend cannot truncate!"); 2636 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2637 return V; // No conversion 2638 return getZeroExtendExpr(V, Ty); 2639} 2640 2641/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2642/// input value to the specified type. If the type must be extended, it is sign 2643/// extended. The conversion must not be narrowing. 2644const SCEV * 2645ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2646 const Type *SrcTy = V->getType(); 2647 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2648 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2649 "Cannot noop or sign extend with non-integer arguments!"); 2650 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2651 "getNoopOrSignExtend cannot truncate!"); 2652 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2653 return V; // No conversion 2654 return getSignExtendExpr(V, Ty); 2655} 2656 2657/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2658/// the input value to the specified type. If the type must be extended, 2659/// it is extended with unspecified bits. The conversion must not be 2660/// narrowing. 2661const SCEV * 2662ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2663 const Type *SrcTy = V->getType(); 2664 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2665 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2666 "Cannot noop or any extend with non-integer arguments!"); 2667 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2668 "getNoopOrAnyExtend cannot truncate!"); 2669 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2670 return V; // No conversion 2671 return getAnyExtendExpr(V, Ty); 2672} 2673 2674/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2675/// input value to the specified type. The conversion must not be widening. 2676const SCEV * 2677ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2678 const Type *SrcTy = V->getType(); 2679 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2680 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2681 "Cannot truncate or noop with non-integer arguments!"); 2682 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2683 "getTruncateOrNoop cannot extend!"); 2684 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2685 return V; // No conversion 2686 return getTruncateExpr(V, Ty); 2687} 2688 2689/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2690/// the types using zero-extension, and then perform a umax operation 2691/// with them. 2692const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2693 const SCEV *RHS) { 2694 const SCEV *PromotedLHS = LHS; 2695 const SCEV *PromotedRHS = RHS; 2696 2697 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2698 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2699 else 2700 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2701 2702 return getUMaxExpr(PromotedLHS, PromotedRHS); 2703} 2704 2705/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2706/// the types using zero-extension, and then perform a umin operation 2707/// with them. 2708const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2709 const SCEV *RHS) { 2710 const SCEV *PromotedLHS = LHS; 2711 const SCEV *PromotedRHS = RHS; 2712 2713 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2714 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2715 else 2716 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2717 2718 return getUMinExpr(PromotedLHS, PromotedRHS); 2719} 2720 2721/// getPointerBase - Transitively follow the chain of pointer-type operands 2722/// until reaching a SCEV that does not have a single pointer operand. This 2723/// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2724/// but corner cases do exist. 2725const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2726 // A pointer operand may evaluate to a nonpointer expression, such as null. 2727 if (!V->getType()->isPointerTy()) 2728 return V; 2729 2730 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2731 return getPointerBase(Cast->getOperand()); 2732 } 2733 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2734 const SCEV *PtrOp = 0; 2735 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2736 I != E; ++I) { 2737 if ((*I)->getType()->isPointerTy()) { 2738 // Cannot find the base of an expression with multiple pointer operands. 2739 if (PtrOp) 2740 return V; 2741 PtrOp = *I; 2742 } 2743 } 2744 if (!PtrOp) 2745 return V; 2746 return getPointerBase(PtrOp); 2747 } 2748 return V; 2749} 2750 2751/// PushDefUseChildren - Push users of the given Instruction 2752/// onto the given Worklist. 2753static void 2754PushDefUseChildren(Instruction *I, 2755 SmallVectorImpl<Instruction *> &Worklist) { 2756 // Push the def-use children onto the Worklist stack. 2757 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2758 UI != UE; ++UI) 2759 Worklist.push_back(cast<Instruction>(*UI)); 2760} 2761 2762/// ForgetSymbolicValue - This looks up computed SCEV values for all 2763/// instructions that depend on the given instruction and removes them from 2764/// the ValueExprMapType map if they reference SymName. This is used during PHI 2765/// resolution. 2766void 2767ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2768 SmallVector<Instruction *, 16> Worklist; 2769 PushDefUseChildren(PN, Worklist); 2770 2771 SmallPtrSet<Instruction *, 8> Visited; 2772 Visited.insert(PN); 2773 while (!Worklist.empty()) { 2774 Instruction *I = Worklist.pop_back_val(); 2775 if (!Visited.insert(I)) continue; 2776 2777 ValueExprMapType::iterator It = 2778 ValueExprMap.find(static_cast<Value *>(I)); 2779 if (It != ValueExprMap.end()) { 2780 const SCEV *Old = It->second; 2781 2782 // Short-circuit the def-use traversal if the symbolic name 2783 // ceases to appear in expressions. 2784 if (Old != SymName && !hasOperand(Old, SymName)) 2785 continue; 2786 2787 // SCEVUnknown for a PHI either means that it has an unrecognized 2788 // structure, it's a PHI that's in the progress of being computed 2789 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2790 // additional loop trip count information isn't going to change anything. 2791 // In the second case, createNodeForPHI will perform the necessary 2792 // updates on its own when it gets to that point. In the third, we do 2793 // want to forget the SCEVUnknown. 2794 if (!isa<PHINode>(I) || 2795 !isa<SCEVUnknown>(Old) || 2796 (I != PN && Old == SymName)) { 2797 forgetMemoizedResults(Old); 2798 ValueExprMap.erase(It); 2799 } 2800 } 2801 2802 PushDefUseChildren(I, Worklist); 2803 } 2804} 2805 2806/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2807/// a loop header, making it a potential recurrence, or it doesn't. 2808/// 2809const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2810 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2811 if (L->getHeader() == PN->getParent()) { 2812 // The loop may have multiple entrances or multiple exits; we can analyze 2813 // this phi as an addrec if it has a unique entry value and a unique 2814 // backedge value. 2815 Value *BEValueV = 0, *StartValueV = 0; 2816 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2817 Value *V = PN->getIncomingValue(i); 2818 if (L->contains(PN->getIncomingBlock(i))) { 2819 if (!BEValueV) { 2820 BEValueV = V; 2821 } else if (BEValueV != V) { 2822 BEValueV = 0; 2823 break; 2824 } 2825 } else if (!StartValueV) { 2826 StartValueV = V; 2827 } else if (StartValueV != V) { 2828 StartValueV = 0; 2829 break; 2830 } 2831 } 2832 if (BEValueV && StartValueV) { 2833 // While we are analyzing this PHI node, handle its value symbolically. 2834 const SCEV *SymbolicName = getUnknown(PN); 2835 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2836 "PHI node already processed?"); 2837 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2838 2839 // Using this symbolic name for the PHI, analyze the value coming around 2840 // the back-edge. 2841 const SCEV *BEValue = getSCEV(BEValueV); 2842 2843 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2844 // has a special value for the first iteration of the loop. 2845 2846 // If the value coming around the backedge is an add with the symbolic 2847 // value we just inserted, then we found a simple induction variable! 2848 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2849 // If there is a single occurrence of the symbolic value, replace it 2850 // with a recurrence. 2851 unsigned FoundIndex = Add->getNumOperands(); 2852 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2853 if (Add->getOperand(i) == SymbolicName) 2854 if (FoundIndex == e) { 2855 FoundIndex = i; 2856 break; 2857 } 2858 2859 if (FoundIndex != Add->getNumOperands()) { 2860 // Create an add with everything but the specified operand. 2861 SmallVector<const SCEV *, 8> Ops; 2862 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2863 if (i != FoundIndex) 2864 Ops.push_back(Add->getOperand(i)); 2865 const SCEV *Accum = getAddExpr(Ops); 2866 2867 // This is not a valid addrec if the step amount is varying each 2868 // loop iteration, but is not itself an addrec in this loop. 2869 if (isLoopInvariant(Accum, L) || 2870 (isa<SCEVAddRecExpr>(Accum) && 2871 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2872 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 2873 2874 // If the increment doesn't overflow, then neither the addrec nor 2875 // the post-increment will overflow. 2876 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2877 if (OBO->hasNoUnsignedWrap()) 2878 Flags = setFlags(Flags, SCEV::FlagNUW); 2879 if (OBO->hasNoSignedWrap()) 2880 Flags = setFlags(Flags, SCEV::FlagNSW); 2881 } else if (const GEPOperator *GEP = 2882 dyn_cast<GEPOperator>(BEValueV)) { 2883 // If the increment is an inbounds GEP, then we know the address 2884 // space cannot be wrapped around. We cannot make any guarantee 2885 // about signed or unsigned overflow because pointers are 2886 // unsigned but we may have a negative index from the base 2887 // pointer. 2888 if (GEP->isInBounds()) 2889 Flags = setFlags(Flags, SCEV::FlagNW); 2890 } 2891 2892 const SCEV *StartVal = getSCEV(StartValueV); 2893 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 2894 2895 // Since the no-wrap flags are on the increment, they apply to the 2896 // post-incremented value as well. 2897 if (isLoopInvariant(Accum, L)) 2898 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2899 Accum, L, Flags); 2900 2901 // Okay, for the entire analysis of this edge we assumed the PHI 2902 // to be symbolic. We now need to go back and purge all of the 2903 // entries for the scalars that use the symbolic expression. 2904 ForgetSymbolicName(PN, SymbolicName); 2905 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2906 return PHISCEV; 2907 } 2908 } 2909 } else if (const SCEVAddRecExpr *AddRec = 2910 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2911 // Otherwise, this could be a loop like this: 2912 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2913 // In this case, j = {1,+,1} and BEValue is j. 2914 // Because the other in-value of i (0) fits the evolution of BEValue 2915 // i really is an addrec evolution. 2916 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2917 const SCEV *StartVal = getSCEV(StartValueV); 2918 2919 // If StartVal = j.start - j.stride, we can use StartVal as the 2920 // initial step of the addrec evolution. 2921 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2922 AddRec->getOperand(1))) { 2923 // FIXME: For constant StartVal, we should be able to infer 2924 // no-wrap flags. 2925 const SCEV *PHISCEV = 2926 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 2927 SCEV::FlagAnyWrap); 2928 2929 // Okay, for the entire analysis of this edge we assumed the PHI 2930 // to be symbolic. We now need to go back and purge all of the 2931 // entries for the scalars that use the symbolic expression. 2932 ForgetSymbolicName(PN, SymbolicName); 2933 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2934 return PHISCEV; 2935 } 2936 } 2937 } 2938 } 2939 } 2940 2941 // If the PHI has a single incoming value, follow that value, unless the 2942 // PHI's incoming blocks are in a different loop, in which case doing so 2943 // risks breaking LCSSA form. Instcombine would normally zap these, but 2944 // it doesn't have DominatorTree information, so it may miss cases. 2945 if (Value *V = SimplifyInstruction(PN, TD, DT)) 2946 if (LI->replacementPreservesLCSSAForm(PN, V)) 2947 return getSCEV(V); 2948 2949 // If it's not a loop phi, we can't handle it yet. 2950 return getUnknown(PN); 2951} 2952 2953/// createNodeForGEP - Expand GEP instructions into add and multiply 2954/// operations. This allows them to be analyzed by regular SCEV code. 2955/// 2956const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2957 2958 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2959 // Add expression, because the Instruction may be guarded by control flow 2960 // and the no-overflow bits may not be valid for the expression in any 2961 // context. 2962 bool isInBounds = GEP->isInBounds(); 2963 2964 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2965 Value *Base = GEP->getOperand(0); 2966 // Don't attempt to analyze GEPs over unsized objects. 2967 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2968 return getUnknown(GEP); 2969 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2970 gep_type_iterator GTI = gep_type_begin(GEP); 2971 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2972 E = GEP->op_end(); 2973 I != E; ++I) { 2974 Value *Index = *I; 2975 // Compute the (potentially symbolic) offset in bytes for this index. 2976 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2977 // For a struct, add the member offset. 2978 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2979 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2980 2981 // Add the field offset to the running total offset. 2982 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2983 } else { 2984 // For an array, add the element offset, explicitly scaled. 2985 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2986 const SCEV *IndexS = getSCEV(Index); 2987 // Getelementptr indices are signed. 2988 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2989 2990 // Multiply the index by the element size to compute the element offset. 2991 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 2992 isInBounds ? SCEV::FlagNSW : 2993 SCEV::FlagAnyWrap); 2994 2995 // Add the element offset to the running total offset. 2996 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2997 } 2998 } 2999 3000 // Get the SCEV for the GEP base. 3001 const SCEV *BaseS = getSCEV(Base); 3002 3003 // Add the total offset from all the GEP indices to the base. 3004 return getAddExpr(BaseS, TotalOffset, 3005 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3006} 3007 3008/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3009/// guaranteed to end in (at every loop iteration). It is, at the same time, 3010/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3011/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3012uint32_t 3013ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3014 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3015 return C->getValue()->getValue().countTrailingZeros(); 3016 3017 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3018 return std::min(GetMinTrailingZeros(T->getOperand()), 3019 (uint32_t)getTypeSizeInBits(T->getType())); 3020 3021 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3022 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3023 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3024 getTypeSizeInBits(E->getType()) : OpRes; 3025 } 3026 3027 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3028 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3029 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3030 getTypeSizeInBits(E->getType()) : OpRes; 3031 } 3032 3033 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3034 // The result is the min of all operands results. 3035 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3036 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3037 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3038 return MinOpRes; 3039 } 3040 3041 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3042 // The result is the sum of all operands results. 3043 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3044 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3045 for (unsigned i = 1, e = M->getNumOperands(); 3046 SumOpRes != BitWidth && i != e; ++i) 3047 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3048 BitWidth); 3049 return SumOpRes; 3050 } 3051 3052 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3053 // The result is the min of all operands results. 3054 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3055 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3056 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3057 return MinOpRes; 3058 } 3059 3060 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3061 // The result is the min of all operands results. 3062 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3063 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3064 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3065 return MinOpRes; 3066 } 3067 3068 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3069 // The result is the min of all operands results. 3070 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3071 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3072 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3073 return MinOpRes; 3074 } 3075 3076 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3077 // For a SCEVUnknown, ask ValueTracking. 3078 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3079 APInt Mask = APInt::getAllOnesValue(BitWidth); 3080 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3081 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3082 return Zeros.countTrailingOnes(); 3083 } 3084 3085 // SCEVUDivExpr 3086 return 0; 3087} 3088 3089/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3090/// 3091ConstantRange 3092ScalarEvolution::getUnsignedRange(const SCEV *S) { 3093 // See if we've computed this range already. 3094 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3095 if (I != UnsignedRanges.end()) 3096 return I->second; 3097 3098 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3099 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3100 3101 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3102 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3103 3104 // If the value has known zeros, the maximum unsigned value will have those 3105 // known zeros as well. 3106 uint32_t TZ = GetMinTrailingZeros(S); 3107 if (TZ != 0) 3108 ConservativeResult = 3109 ConstantRange(APInt::getMinValue(BitWidth), 3110 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3111 3112 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3113 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3114 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3115 X = X.add(getUnsignedRange(Add->getOperand(i))); 3116 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3117 } 3118 3119 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3120 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3121 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3122 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3123 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3124 } 3125 3126 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3127 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3128 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3129 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3130 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3131 } 3132 3133 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3134 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3135 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3136 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3137 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3138 } 3139 3140 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3141 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3142 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3143 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3144 } 3145 3146 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3147 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3148 return setUnsignedRange(ZExt, 3149 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3150 } 3151 3152 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3153 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3154 return setUnsignedRange(SExt, 3155 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3156 } 3157 3158 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3159 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3160 return setUnsignedRange(Trunc, 3161 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3162 } 3163 3164 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3165 // If there's no unsigned wrap, the value will never be less than its 3166 // initial value. 3167 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3168 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3169 if (!C->getValue()->isZero()) 3170 ConservativeResult = 3171 ConservativeResult.intersectWith( 3172 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3173 3174 // TODO: non-affine addrec 3175 if (AddRec->isAffine()) { 3176 const Type *Ty = AddRec->getType(); 3177 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3178 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3179 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3180 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3181 3182 const SCEV *Start = AddRec->getStart(); 3183 const SCEV *Step = AddRec->getStepRecurrence(*this); 3184 3185 ConstantRange StartRange = getUnsignedRange(Start); 3186 ConstantRange StepRange = getSignedRange(Step); 3187 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3188 ConstantRange EndRange = 3189 StartRange.add(MaxBECountRange.multiply(StepRange)); 3190 3191 // Check for overflow. This must be done with ConstantRange arithmetic 3192 // because we could be called from within the ScalarEvolution overflow 3193 // checking code. 3194 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3195 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3196 ConstantRange ExtMaxBECountRange = 3197 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3198 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3199 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3200 ExtEndRange) 3201 return setUnsignedRange(AddRec, ConservativeResult); 3202 3203 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3204 EndRange.getUnsignedMin()); 3205 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3206 EndRange.getUnsignedMax()); 3207 if (Min.isMinValue() && Max.isMaxValue()) 3208 return setUnsignedRange(AddRec, ConservativeResult); 3209 return setUnsignedRange(AddRec, 3210 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3211 } 3212 } 3213 3214 return setUnsignedRange(AddRec, ConservativeResult); 3215 } 3216 3217 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3218 // For a SCEVUnknown, ask ValueTracking. 3219 APInt Mask = APInt::getAllOnesValue(BitWidth); 3220 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3221 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3222 if (Ones == ~Zeros + 1) 3223 return setUnsignedRange(U, ConservativeResult); 3224 return setUnsignedRange(U, 3225 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3226 } 3227 3228 return setUnsignedRange(S, ConservativeResult); 3229} 3230 3231/// getSignedRange - Determine the signed range for a particular SCEV. 3232/// 3233ConstantRange 3234ScalarEvolution::getSignedRange(const SCEV *S) { 3235 // See if we've computed this range already. 3236 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3237 if (I != SignedRanges.end()) 3238 return I->second; 3239 3240 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3241 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3242 3243 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3244 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3245 3246 // If the value has known zeros, the maximum signed value will have those 3247 // known zeros as well. 3248 uint32_t TZ = GetMinTrailingZeros(S); 3249 if (TZ != 0) 3250 ConservativeResult = 3251 ConstantRange(APInt::getSignedMinValue(BitWidth), 3252 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3253 3254 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3255 ConstantRange X = getSignedRange(Add->getOperand(0)); 3256 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3257 X = X.add(getSignedRange(Add->getOperand(i))); 3258 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3259 } 3260 3261 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3262 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3263 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3264 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3265 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3266 } 3267 3268 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3269 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3270 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3271 X = X.smax(getSignedRange(SMax->getOperand(i))); 3272 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3273 } 3274 3275 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3276 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3277 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3278 X = X.umax(getSignedRange(UMax->getOperand(i))); 3279 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3280 } 3281 3282 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3283 ConstantRange X = getSignedRange(UDiv->getLHS()); 3284 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3285 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3286 } 3287 3288 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3289 ConstantRange X = getSignedRange(ZExt->getOperand()); 3290 return setSignedRange(ZExt, 3291 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3292 } 3293 3294 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3295 ConstantRange X = getSignedRange(SExt->getOperand()); 3296 return setSignedRange(SExt, 3297 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3298 } 3299 3300 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3301 ConstantRange X = getSignedRange(Trunc->getOperand()); 3302 return setSignedRange(Trunc, 3303 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3304 } 3305 3306 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3307 // If there's no signed wrap, and all the operands have the same sign or 3308 // zero, the value won't ever change sign. 3309 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3310 bool AllNonNeg = true; 3311 bool AllNonPos = true; 3312 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3313 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3314 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3315 } 3316 if (AllNonNeg) 3317 ConservativeResult = ConservativeResult.intersectWith( 3318 ConstantRange(APInt(BitWidth, 0), 3319 APInt::getSignedMinValue(BitWidth))); 3320 else if (AllNonPos) 3321 ConservativeResult = ConservativeResult.intersectWith( 3322 ConstantRange(APInt::getSignedMinValue(BitWidth), 3323 APInt(BitWidth, 1))); 3324 } 3325 3326 // TODO: non-affine addrec 3327 if (AddRec->isAffine()) { 3328 const Type *Ty = AddRec->getType(); 3329 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3330 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3331 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3332 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3333 3334 const SCEV *Start = AddRec->getStart(); 3335 const SCEV *Step = AddRec->getStepRecurrence(*this); 3336 3337 ConstantRange StartRange = getSignedRange(Start); 3338 ConstantRange StepRange = getSignedRange(Step); 3339 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3340 ConstantRange EndRange = 3341 StartRange.add(MaxBECountRange.multiply(StepRange)); 3342 3343 // Check for overflow. This must be done with ConstantRange arithmetic 3344 // because we could be called from within the ScalarEvolution overflow 3345 // checking code. 3346 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3347 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3348 ConstantRange ExtMaxBECountRange = 3349 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3350 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3351 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3352 ExtEndRange) 3353 return setSignedRange(AddRec, ConservativeResult); 3354 3355 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3356 EndRange.getSignedMin()); 3357 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3358 EndRange.getSignedMax()); 3359 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3360 return setSignedRange(AddRec, ConservativeResult); 3361 return setSignedRange(AddRec, 3362 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3363 } 3364 } 3365 3366 return setSignedRange(AddRec, ConservativeResult); 3367 } 3368 3369 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3370 // For a SCEVUnknown, ask ValueTracking. 3371 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3372 return setSignedRange(U, ConservativeResult); 3373 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3374 if (NS == 1) 3375 return setSignedRange(U, ConservativeResult); 3376 return setSignedRange(U, ConservativeResult.intersectWith( 3377 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3378 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3379 } 3380 3381 return setSignedRange(S, ConservativeResult); 3382} 3383 3384/// createSCEV - We know that there is no SCEV for the specified value. 3385/// Analyze the expression. 3386/// 3387const SCEV *ScalarEvolution::createSCEV(Value *V) { 3388 if (!isSCEVable(V->getType())) 3389 return getUnknown(V); 3390 3391 unsigned Opcode = Instruction::UserOp1; 3392 if (Instruction *I = dyn_cast<Instruction>(V)) { 3393 Opcode = I->getOpcode(); 3394 3395 // Don't attempt to analyze instructions in blocks that aren't 3396 // reachable. Such instructions don't matter, and they aren't required 3397 // to obey basic rules for definitions dominating uses which this 3398 // analysis depends on. 3399 if (!DT->isReachableFromEntry(I->getParent())) 3400 return getUnknown(V); 3401 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3402 Opcode = CE->getOpcode(); 3403 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3404 return getConstant(CI); 3405 else if (isa<ConstantPointerNull>(V)) 3406 return getConstant(V->getType(), 0); 3407 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3408 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3409 else 3410 return getUnknown(V); 3411 3412 Operator *U = cast<Operator>(V); 3413 switch (Opcode) { 3414 case Instruction::Add: { 3415 // The simple thing to do would be to just call getSCEV on both operands 3416 // and call getAddExpr with the result. However if we're looking at a 3417 // bunch of things all added together, this can be quite inefficient, 3418 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3419 // Instead, gather up all the operands and make a single getAddExpr call. 3420 // LLVM IR canonical form means we need only traverse the left operands. 3421 SmallVector<const SCEV *, 4> AddOps; 3422 AddOps.push_back(getSCEV(U->getOperand(1))); 3423 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3424 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3425 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3426 break; 3427 U = cast<Operator>(Op); 3428 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3429 if (Opcode == Instruction::Sub) 3430 AddOps.push_back(getNegativeSCEV(Op1)); 3431 else 3432 AddOps.push_back(Op1); 3433 } 3434 AddOps.push_back(getSCEV(U->getOperand(0))); 3435 return getAddExpr(AddOps); 3436 } 3437 case Instruction::Mul: { 3438 // See the Add code above. 3439 SmallVector<const SCEV *, 4> MulOps; 3440 MulOps.push_back(getSCEV(U->getOperand(1))); 3441 for (Value *Op = U->getOperand(0); 3442 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3443 Op = U->getOperand(0)) { 3444 U = cast<Operator>(Op); 3445 MulOps.push_back(getSCEV(U->getOperand(1))); 3446 } 3447 MulOps.push_back(getSCEV(U->getOperand(0))); 3448 return getMulExpr(MulOps); 3449 } 3450 case Instruction::UDiv: 3451 return getUDivExpr(getSCEV(U->getOperand(0)), 3452 getSCEV(U->getOperand(1))); 3453 case Instruction::Sub: 3454 return getMinusSCEV(getSCEV(U->getOperand(0)), 3455 getSCEV(U->getOperand(1))); 3456 case Instruction::And: 3457 // For an expression like x&255 that merely masks off the high bits, 3458 // use zext(trunc(x)) as the SCEV expression. 3459 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3460 if (CI->isNullValue()) 3461 return getSCEV(U->getOperand(1)); 3462 if (CI->isAllOnesValue()) 3463 return getSCEV(U->getOperand(0)); 3464 const APInt &A = CI->getValue(); 3465 3466 // Instcombine's ShrinkDemandedConstant may strip bits out of 3467 // constants, obscuring what would otherwise be a low-bits mask. 3468 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3469 // knew about to reconstruct a low-bits mask value. 3470 unsigned LZ = A.countLeadingZeros(); 3471 unsigned BitWidth = A.getBitWidth(); 3472 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3473 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3474 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3475 3476 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3477 3478 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3479 return 3480 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3481 IntegerType::get(getContext(), BitWidth - LZ)), 3482 U->getType()); 3483 } 3484 break; 3485 3486 case Instruction::Or: 3487 // If the RHS of the Or is a constant, we may have something like: 3488 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3489 // optimizations will transparently handle this case. 3490 // 3491 // In order for this transformation to be safe, the LHS must be of the 3492 // form X*(2^n) and the Or constant must be less than 2^n. 3493 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3494 const SCEV *LHS = getSCEV(U->getOperand(0)); 3495 const APInt &CIVal = CI->getValue(); 3496 if (GetMinTrailingZeros(LHS) >= 3497 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3498 // Build a plain add SCEV. 3499 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3500 // If the LHS of the add was an addrec and it has no-wrap flags, 3501 // transfer the no-wrap flags, since an or won't introduce a wrap. 3502 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3503 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3504 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3505 OldAR->getNoWrapFlags()); 3506 } 3507 return S; 3508 } 3509 } 3510 break; 3511 case Instruction::Xor: 3512 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3513 // If the RHS of the xor is a signbit, then this is just an add. 3514 // Instcombine turns add of signbit into xor as a strength reduction step. 3515 if (CI->getValue().isSignBit()) 3516 return getAddExpr(getSCEV(U->getOperand(0)), 3517 getSCEV(U->getOperand(1))); 3518 3519 // If the RHS of xor is -1, then this is a not operation. 3520 if (CI->isAllOnesValue()) 3521 return getNotSCEV(getSCEV(U->getOperand(0))); 3522 3523 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3524 // This is a variant of the check for xor with -1, and it handles 3525 // the case where instcombine has trimmed non-demanded bits out 3526 // of an xor with -1. 3527 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3528 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3529 if (BO->getOpcode() == Instruction::And && 3530 LCI->getValue() == CI->getValue()) 3531 if (const SCEVZeroExtendExpr *Z = 3532 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3533 const Type *UTy = U->getType(); 3534 const SCEV *Z0 = Z->getOperand(); 3535 const Type *Z0Ty = Z0->getType(); 3536 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3537 3538 // If C is a low-bits mask, the zero extend is serving to 3539 // mask off the high bits. Complement the operand and 3540 // re-apply the zext. 3541 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3542 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3543 3544 // If C is a single bit, it may be in the sign-bit position 3545 // before the zero-extend. In this case, represent the xor 3546 // using an add, which is equivalent, and re-apply the zext. 3547 APInt Trunc = CI->getValue().trunc(Z0TySize); 3548 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3549 Trunc.isSignBit()) 3550 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3551 UTy); 3552 } 3553 } 3554 break; 3555 3556 case Instruction::Shl: 3557 // Turn shift left of a constant amount into a multiply. 3558 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3559 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3560 3561 // If the shift count is not less than the bitwidth, the result of 3562 // the shift is undefined. Don't try to analyze it, because the 3563 // resolution chosen here may differ from the resolution chosen in 3564 // other parts of the compiler. 3565 if (SA->getValue().uge(BitWidth)) 3566 break; 3567 3568 Constant *X = ConstantInt::get(getContext(), 3569 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3570 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3571 } 3572 break; 3573 3574 case Instruction::LShr: 3575 // Turn logical shift right of a constant into a unsigned divide. 3576 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3577 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3578 3579 // If the shift count is not less than the bitwidth, the result of 3580 // the shift is undefined. Don't try to analyze it, because the 3581 // resolution chosen here may differ from the resolution chosen in 3582 // other parts of the compiler. 3583 if (SA->getValue().uge(BitWidth)) 3584 break; 3585 3586 Constant *X = ConstantInt::get(getContext(), 3587 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3588 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3589 } 3590 break; 3591 3592 case Instruction::AShr: 3593 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3594 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3595 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3596 if (L->getOpcode() == Instruction::Shl && 3597 L->getOperand(1) == U->getOperand(1)) { 3598 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3599 3600 // If the shift count is not less than the bitwidth, the result of 3601 // the shift is undefined. Don't try to analyze it, because the 3602 // resolution chosen here may differ from the resolution chosen in 3603 // other parts of the compiler. 3604 if (CI->getValue().uge(BitWidth)) 3605 break; 3606 3607 uint64_t Amt = BitWidth - CI->getZExtValue(); 3608 if (Amt == BitWidth) 3609 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3610 return 3611 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3612 IntegerType::get(getContext(), 3613 Amt)), 3614 U->getType()); 3615 } 3616 break; 3617 3618 case Instruction::Trunc: 3619 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3620 3621 case Instruction::ZExt: 3622 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3623 3624 case Instruction::SExt: 3625 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3626 3627 case Instruction::BitCast: 3628 // BitCasts are no-op casts so we just eliminate the cast. 3629 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3630 return getSCEV(U->getOperand(0)); 3631 break; 3632 3633 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3634 // lead to pointer expressions which cannot safely be expanded to GEPs, 3635 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3636 // simplifying integer expressions. 3637 3638 case Instruction::GetElementPtr: 3639 return createNodeForGEP(cast<GEPOperator>(U)); 3640 3641 case Instruction::PHI: 3642 return createNodeForPHI(cast<PHINode>(U)); 3643 3644 case Instruction::Select: 3645 // This could be a smax or umax that was lowered earlier. 3646 // Try to recover it. 3647 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3648 Value *LHS = ICI->getOperand(0); 3649 Value *RHS = ICI->getOperand(1); 3650 switch (ICI->getPredicate()) { 3651 case ICmpInst::ICMP_SLT: 3652 case ICmpInst::ICMP_SLE: 3653 std::swap(LHS, RHS); 3654 // fall through 3655 case ICmpInst::ICMP_SGT: 3656 case ICmpInst::ICMP_SGE: 3657 // a >s b ? a+x : b+x -> smax(a, b)+x 3658 // a >s b ? b+x : a+x -> smin(a, b)+x 3659 if (LHS->getType() == U->getType()) { 3660 const SCEV *LS = getSCEV(LHS); 3661 const SCEV *RS = getSCEV(RHS); 3662 const SCEV *LA = getSCEV(U->getOperand(1)); 3663 const SCEV *RA = getSCEV(U->getOperand(2)); 3664 const SCEV *LDiff = getMinusSCEV(LA, LS); 3665 const SCEV *RDiff = getMinusSCEV(RA, RS); 3666 if (LDiff == RDiff) 3667 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3668 LDiff = getMinusSCEV(LA, RS); 3669 RDiff = getMinusSCEV(RA, LS); 3670 if (LDiff == RDiff) 3671 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3672 } 3673 break; 3674 case ICmpInst::ICMP_ULT: 3675 case ICmpInst::ICMP_ULE: 3676 std::swap(LHS, RHS); 3677 // fall through 3678 case ICmpInst::ICMP_UGT: 3679 case ICmpInst::ICMP_UGE: 3680 // a >u b ? a+x : b+x -> umax(a, b)+x 3681 // a >u b ? b+x : a+x -> umin(a, b)+x 3682 if (LHS->getType() == U->getType()) { 3683 const SCEV *LS = getSCEV(LHS); 3684 const SCEV *RS = getSCEV(RHS); 3685 const SCEV *LA = getSCEV(U->getOperand(1)); 3686 const SCEV *RA = getSCEV(U->getOperand(2)); 3687 const SCEV *LDiff = getMinusSCEV(LA, LS); 3688 const SCEV *RDiff = getMinusSCEV(RA, RS); 3689 if (LDiff == RDiff) 3690 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3691 LDiff = getMinusSCEV(LA, RS); 3692 RDiff = getMinusSCEV(RA, LS); 3693 if (LDiff == RDiff) 3694 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3695 } 3696 break; 3697 case ICmpInst::ICMP_NE: 3698 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3699 if (LHS->getType() == U->getType() && 3700 isa<ConstantInt>(RHS) && 3701 cast<ConstantInt>(RHS)->isZero()) { 3702 const SCEV *One = getConstant(LHS->getType(), 1); 3703 const SCEV *LS = getSCEV(LHS); 3704 const SCEV *LA = getSCEV(U->getOperand(1)); 3705 const SCEV *RA = getSCEV(U->getOperand(2)); 3706 const SCEV *LDiff = getMinusSCEV(LA, LS); 3707 const SCEV *RDiff = getMinusSCEV(RA, One); 3708 if (LDiff == RDiff) 3709 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3710 } 3711 break; 3712 case ICmpInst::ICMP_EQ: 3713 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3714 if (LHS->getType() == U->getType() && 3715 isa<ConstantInt>(RHS) && 3716 cast<ConstantInt>(RHS)->isZero()) { 3717 const SCEV *One = getConstant(LHS->getType(), 1); 3718 const SCEV *LS = getSCEV(LHS); 3719 const SCEV *LA = getSCEV(U->getOperand(1)); 3720 const SCEV *RA = getSCEV(U->getOperand(2)); 3721 const SCEV *LDiff = getMinusSCEV(LA, One); 3722 const SCEV *RDiff = getMinusSCEV(RA, LS); 3723 if (LDiff == RDiff) 3724 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3725 } 3726 break; 3727 default: 3728 break; 3729 } 3730 } 3731 3732 default: // We cannot analyze this expression. 3733 break; 3734 } 3735 3736 return getUnknown(V); 3737} 3738 3739 3740 3741//===----------------------------------------------------------------------===// 3742// Iteration Count Computation Code 3743// 3744 3745/// getBackedgeTakenCount - If the specified loop has a predictable 3746/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3747/// object. The backedge-taken count is the number of times the loop header 3748/// will be branched to from within the loop. This is one less than the 3749/// trip count of the loop, since it doesn't count the first iteration, 3750/// when the header is branched to from outside the loop. 3751/// 3752/// Note that it is not valid to call this method on a loop without a 3753/// loop-invariant backedge-taken count (see 3754/// hasLoopInvariantBackedgeTakenCount). 3755/// 3756const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3757 return getBackedgeTakenInfo(L).Exact; 3758} 3759 3760/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3761/// return the least SCEV value that is known never to be less than the 3762/// actual backedge taken count. 3763const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3764 return getBackedgeTakenInfo(L).Max; 3765} 3766 3767/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3768/// onto the given Worklist. 3769static void 3770PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3771 BasicBlock *Header = L->getHeader(); 3772 3773 // Push all Loop-header PHIs onto the Worklist stack. 3774 for (BasicBlock::iterator I = Header->begin(); 3775 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3776 Worklist.push_back(PN); 3777} 3778 3779const ScalarEvolution::BackedgeTakenInfo & 3780ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3781 // Initially insert a CouldNotCompute for this loop. If the insertion 3782 // succeeds, proceed to actually compute a backedge-taken count and 3783 // update the value. The temporary CouldNotCompute value tells SCEV 3784 // code elsewhere that it shouldn't attempt to request a new 3785 // backedge-taken count, which could result in infinite recursion. 3786 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3787 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3788 if (!Pair.second) 3789 return Pair.first->second; 3790 3791 BackedgeTakenInfo Result = getCouldNotCompute(); 3792 BackedgeTakenInfo Computed = ComputeBackedgeTakenCount(L); 3793 if (Computed.Exact != getCouldNotCompute()) { 3794 assert(isLoopInvariant(Computed.Exact, L) && 3795 isLoopInvariant(Computed.Max, L) && 3796 "Computed backedge-taken count isn't loop invariant for loop!"); 3797 ++NumTripCountsComputed; 3798 3799 // Update the value in the map. 3800 Result = Computed; 3801 } else { 3802 if (Computed.Max != getCouldNotCompute()) 3803 // Update the value in the map. 3804 Result = Computed; 3805 if (isa<PHINode>(L->getHeader()->begin())) 3806 // Only count loops that have phi nodes as not being computable. 3807 ++NumTripCountsNotComputed; 3808 } 3809 3810 // Now that we know more about the trip count for this loop, forget any 3811 // existing SCEV values for PHI nodes in this loop since they are only 3812 // conservative estimates made without the benefit of trip count 3813 // information. This is similar to the code in forgetLoop, except that 3814 // it handles SCEVUnknown PHI nodes specially. 3815 if (Computed.hasAnyInfo()) { 3816 SmallVector<Instruction *, 16> Worklist; 3817 PushLoopPHIs(L, Worklist); 3818 3819 SmallPtrSet<Instruction *, 8> Visited; 3820 while (!Worklist.empty()) { 3821 Instruction *I = Worklist.pop_back_val(); 3822 if (!Visited.insert(I)) continue; 3823 3824 ValueExprMapType::iterator It = 3825 ValueExprMap.find(static_cast<Value *>(I)); 3826 if (It != ValueExprMap.end()) { 3827 const SCEV *Old = It->second; 3828 3829 // SCEVUnknown for a PHI either means that it has an unrecognized 3830 // structure, or it's a PHI that's in the progress of being computed 3831 // by createNodeForPHI. In the former case, additional loop trip 3832 // count information isn't going to change anything. In the later 3833 // case, createNodeForPHI will perform the necessary updates on its 3834 // own when it gets to that point. 3835 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3836 forgetMemoizedResults(Old); 3837 ValueExprMap.erase(It); 3838 } 3839 if (PHINode *PN = dyn_cast<PHINode>(I)) 3840 ConstantEvolutionLoopExitValue.erase(PN); 3841 } 3842 3843 PushDefUseChildren(I, Worklist); 3844 } 3845 } 3846 3847 // Re-lookup the insert position, since the call to 3848 // ComputeBackedgeTakenCount above could result in a 3849 // recusive call to getBackedgeTakenInfo (on a different 3850 // loop), which would invalidate the iterator computed 3851 // earlier. 3852 return BackedgeTakenCounts.find(L)->second = Result; 3853} 3854 3855/// forgetLoop - This method should be called by the client when it has 3856/// changed a loop in a way that may effect ScalarEvolution's ability to 3857/// compute a trip count, or if the loop is deleted. 3858void ScalarEvolution::forgetLoop(const Loop *L) { 3859 // Drop any stored trip count value. 3860 BackedgeTakenCounts.erase(L); 3861 3862 // Drop information about expressions based on loop-header PHIs. 3863 SmallVector<Instruction *, 16> Worklist; 3864 PushLoopPHIs(L, Worklist); 3865 3866 SmallPtrSet<Instruction *, 8> Visited; 3867 while (!Worklist.empty()) { 3868 Instruction *I = Worklist.pop_back_val(); 3869 if (!Visited.insert(I)) continue; 3870 3871 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3872 if (It != ValueExprMap.end()) { 3873 forgetMemoizedResults(It->second); 3874 ValueExprMap.erase(It); 3875 if (PHINode *PN = dyn_cast<PHINode>(I)) 3876 ConstantEvolutionLoopExitValue.erase(PN); 3877 } 3878 3879 PushDefUseChildren(I, Worklist); 3880 } 3881 3882 // Forget all contained loops too, to avoid dangling entries in the 3883 // ValuesAtScopes map. 3884 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3885 forgetLoop(*I); 3886} 3887 3888/// forgetValue - This method should be called by the client when it has 3889/// changed a value in a way that may effect its value, or which may 3890/// disconnect it from a def-use chain linking it to a loop. 3891void ScalarEvolution::forgetValue(Value *V) { 3892 Instruction *I = dyn_cast<Instruction>(V); 3893 if (!I) return; 3894 3895 // Drop information about expressions based on loop-header PHIs. 3896 SmallVector<Instruction *, 16> Worklist; 3897 Worklist.push_back(I); 3898 3899 SmallPtrSet<Instruction *, 8> Visited; 3900 while (!Worklist.empty()) { 3901 I = Worklist.pop_back_val(); 3902 if (!Visited.insert(I)) continue; 3903 3904 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3905 if (It != ValueExprMap.end()) { 3906 forgetMemoizedResults(It->second); 3907 ValueExprMap.erase(It); 3908 if (PHINode *PN = dyn_cast<PHINode>(I)) 3909 ConstantEvolutionLoopExitValue.erase(PN); 3910 } 3911 3912 PushDefUseChildren(I, Worklist); 3913 } 3914} 3915 3916/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3917/// of the specified loop will execute. 3918ScalarEvolution::BackedgeTakenInfo 3919ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3920 SmallVector<BasicBlock *, 8> ExitingBlocks; 3921 L->getExitingBlocks(ExitingBlocks); 3922 3923 // Examine all exits and pick the most conservative values. 3924 const SCEV *BECount = getCouldNotCompute(); 3925 const SCEV *MaxBECount = getCouldNotCompute(); 3926 bool CouldNotComputeBECount = false; 3927 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3928 BackedgeTakenInfo NewBTI = 3929 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3930 3931 if (NewBTI.Exact == getCouldNotCompute()) { 3932 // We couldn't compute an exact value for this exit, so 3933 // we won't be able to compute an exact value for the loop. 3934 CouldNotComputeBECount = true; 3935 BECount = getCouldNotCompute(); 3936 } else if (!CouldNotComputeBECount) { 3937 if (BECount == getCouldNotCompute()) 3938 BECount = NewBTI.Exact; 3939 else 3940 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3941 } 3942 if (MaxBECount == getCouldNotCompute()) 3943 MaxBECount = NewBTI.Max; 3944 else if (NewBTI.Max != getCouldNotCompute()) 3945 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3946 } 3947 3948 return BackedgeTakenInfo(BECount, MaxBECount); 3949} 3950 3951/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3952/// of the specified loop will execute if it exits via the specified block. 3953ScalarEvolution::BackedgeTakenInfo 3954ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3955 BasicBlock *ExitingBlock) { 3956 3957 // Okay, we've chosen an exiting block. See what condition causes us to 3958 // exit at this block. 3959 // 3960 // FIXME: we should be able to handle switch instructions (with a single exit) 3961 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3962 if (ExitBr == 0) return getCouldNotCompute(); 3963 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3964 3965 // At this point, we know we have a conditional branch that determines whether 3966 // the loop is exited. However, we don't know if the branch is executed each 3967 // time through the loop. If not, then the execution count of the branch will 3968 // not be equal to the trip count of the loop. 3969 // 3970 // Currently we check for this by checking to see if the Exit branch goes to 3971 // the loop header. If so, we know it will always execute the same number of 3972 // times as the loop. We also handle the case where the exit block *is* the 3973 // loop header. This is common for un-rotated loops. 3974 // 3975 // If both of those tests fail, walk up the unique predecessor chain to the 3976 // header, stopping if there is an edge that doesn't exit the loop. If the 3977 // header is reached, the execution count of the branch will be equal to the 3978 // trip count of the loop. 3979 // 3980 // More extensive analysis could be done to handle more cases here. 3981 // 3982 if (ExitBr->getSuccessor(0) != L->getHeader() && 3983 ExitBr->getSuccessor(1) != L->getHeader() && 3984 ExitBr->getParent() != L->getHeader()) { 3985 // The simple checks failed, try climbing the unique predecessor chain 3986 // up to the header. 3987 bool Ok = false; 3988 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3989 BasicBlock *Pred = BB->getUniquePredecessor(); 3990 if (!Pred) 3991 return getCouldNotCompute(); 3992 TerminatorInst *PredTerm = Pred->getTerminator(); 3993 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3994 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3995 if (PredSucc == BB) 3996 continue; 3997 // If the predecessor has a successor that isn't BB and isn't 3998 // outside the loop, assume the worst. 3999 if (L->contains(PredSucc)) 4000 return getCouldNotCompute(); 4001 } 4002 if (Pred == L->getHeader()) { 4003 Ok = true; 4004 break; 4005 } 4006 BB = Pred; 4007 } 4008 if (!Ok) 4009 return getCouldNotCompute(); 4010 } 4011 4012 // Proceed to the next level to examine the exit condition expression. 4013 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 4014 ExitBr->getSuccessor(0), 4015 ExitBr->getSuccessor(1)); 4016} 4017 4018/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 4019/// backedge of the specified loop will execute if its exit condition 4020/// were a conditional branch of ExitCond, TBB, and FBB. 4021ScalarEvolution::BackedgeTakenInfo 4022ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 4023 Value *ExitCond, 4024 BasicBlock *TBB, 4025 BasicBlock *FBB) { 4026 // Check if the controlling expression for this loop is an And or Or. 4027 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4028 if (BO->getOpcode() == Instruction::And) { 4029 // Recurse on the operands of the and. 4030 BackedgeTakenInfo BTI0 = 4031 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 4032 BackedgeTakenInfo BTI1 = 4033 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 4034 const SCEV *BECount = getCouldNotCompute(); 4035 const SCEV *MaxBECount = getCouldNotCompute(); 4036 if (L->contains(TBB)) { 4037 // Both conditions must be true for the loop to continue executing. 4038 // Choose the less conservative count. 4039 if (BTI0.Exact == getCouldNotCompute() || 4040 BTI1.Exact == getCouldNotCompute()) 4041 BECount = getCouldNotCompute(); 4042 else 4043 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 4044 if (BTI0.Max == getCouldNotCompute()) 4045 MaxBECount = BTI1.Max; 4046 else if (BTI1.Max == getCouldNotCompute()) 4047 MaxBECount = BTI0.Max; 4048 else 4049 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 4050 } else { 4051 // Both conditions must be true at the same time for the loop to exit. 4052 // For now, be conservative. 4053 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4054 if (BTI0.Max == BTI1.Max) 4055 MaxBECount = BTI0.Max; 4056 if (BTI0.Exact == BTI1.Exact) 4057 BECount = BTI0.Exact; 4058 } 4059 4060 return BackedgeTakenInfo(BECount, MaxBECount); 4061 } 4062 if (BO->getOpcode() == Instruction::Or) { 4063 // Recurse on the operands of the or. 4064 BackedgeTakenInfo BTI0 = 4065 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 4066 BackedgeTakenInfo BTI1 = 4067 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 4068 const SCEV *BECount = getCouldNotCompute(); 4069 const SCEV *MaxBECount = getCouldNotCompute(); 4070 if (L->contains(FBB)) { 4071 // Both conditions must be false for the loop to continue executing. 4072 // Choose the less conservative count. 4073 if (BTI0.Exact == getCouldNotCompute() || 4074 BTI1.Exact == getCouldNotCompute()) 4075 BECount = getCouldNotCompute(); 4076 else 4077 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 4078 if (BTI0.Max == getCouldNotCompute()) 4079 MaxBECount = BTI1.Max; 4080 else if (BTI1.Max == getCouldNotCompute()) 4081 MaxBECount = BTI0.Max; 4082 else 4083 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 4084 } else { 4085 // Both conditions must be false at the same time for the loop to exit. 4086 // For now, be conservative. 4087 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4088 if (BTI0.Max == BTI1.Max) 4089 MaxBECount = BTI0.Max; 4090 if (BTI0.Exact == BTI1.Exact) 4091 BECount = BTI0.Exact; 4092 } 4093 4094 return BackedgeTakenInfo(BECount, MaxBECount); 4095 } 4096 } 4097 4098 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4099 // Proceed to the next level to examine the icmp. 4100 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4101 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 4102 4103 // Check for a constant condition. These are normally stripped out by 4104 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4105 // preserve the CFG and is temporarily leaving constant conditions 4106 // in place. 4107 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4108 if (L->contains(FBB) == !CI->getZExtValue()) 4109 // The backedge is always taken. 4110 return getCouldNotCompute(); 4111 else 4112 // The backedge is never taken. 4113 return getConstant(CI->getType(), 0); 4114 } 4115 4116 // If it's not an integer or pointer comparison then compute it the hard way. 4117 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4118} 4119 4120/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4121/// backedge of the specified loop will execute if its exit condition 4122/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4123ScalarEvolution::BackedgeTakenInfo 4124ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4125 ICmpInst *ExitCond, 4126 BasicBlock *TBB, 4127 BasicBlock *FBB) { 4128 4129 // If the condition was exit on true, convert the condition to exit on false 4130 ICmpInst::Predicate Cond; 4131 if (!L->contains(FBB)) 4132 Cond = ExitCond->getPredicate(); 4133 else 4134 Cond = ExitCond->getInversePredicate(); 4135 4136 // Handle common loops like: for (X = "string"; *X; ++X) 4137 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4138 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4139 BackedgeTakenInfo ItCnt = 4140 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4141 if (ItCnt.hasAnyInfo()) 4142 return ItCnt; 4143 } 4144 4145 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4146 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4147 4148 // Try to evaluate any dependencies out of the loop. 4149 LHS = getSCEVAtScope(LHS, L); 4150 RHS = getSCEVAtScope(RHS, L); 4151 4152 // At this point, we would like to compute how many iterations of the 4153 // loop the predicate will return true for these inputs. 4154 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4155 // If there is a loop-invariant, force it into the RHS. 4156 std::swap(LHS, RHS); 4157 Cond = ICmpInst::getSwappedPredicate(Cond); 4158 } 4159 4160 // Simplify the operands before analyzing them. 4161 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4162 4163 // If we have a comparison of a chrec against a constant, try to use value 4164 // ranges to answer this query. 4165 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4166 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4167 if (AddRec->getLoop() == L) { 4168 // Form the constant range. 4169 ConstantRange CompRange( 4170 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4171 4172 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4173 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4174 } 4175 4176 switch (Cond) { 4177 case ICmpInst::ICMP_NE: { // while (X != Y) 4178 // Convert to: while (X-Y != 0) 4179 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4180 if (BTI.hasAnyInfo()) return BTI; 4181 break; 4182 } 4183 case ICmpInst::ICMP_EQ: { // while (X == Y) 4184 // Convert to: while (X-Y == 0) 4185 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4186 if (BTI.hasAnyInfo()) return BTI; 4187 break; 4188 } 4189 case ICmpInst::ICMP_SLT: { 4190 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4191 if (BTI.hasAnyInfo()) return BTI; 4192 break; 4193 } 4194 case ICmpInst::ICMP_SGT: { 4195 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4196 getNotSCEV(RHS), L, true); 4197 if (BTI.hasAnyInfo()) return BTI; 4198 break; 4199 } 4200 case ICmpInst::ICMP_ULT: { 4201 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4202 if (BTI.hasAnyInfo()) return BTI; 4203 break; 4204 } 4205 case ICmpInst::ICMP_UGT: { 4206 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4207 getNotSCEV(RHS), L, false); 4208 if (BTI.hasAnyInfo()) return BTI; 4209 break; 4210 } 4211 default: 4212#if 0 4213 dbgs() << "ComputeBackedgeTakenCount "; 4214 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4215 dbgs() << "[unsigned] "; 4216 dbgs() << *LHS << " " 4217 << Instruction::getOpcodeName(Instruction::ICmp) 4218 << " " << *RHS << "\n"; 4219#endif 4220 break; 4221 } 4222 return 4223 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4224} 4225 4226static ConstantInt * 4227EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4228 ScalarEvolution &SE) { 4229 const SCEV *InVal = SE.getConstant(C); 4230 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4231 assert(isa<SCEVConstant>(Val) && 4232 "Evaluation of SCEV at constant didn't fold correctly?"); 4233 return cast<SCEVConstant>(Val)->getValue(); 4234} 4235 4236/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4237/// and a GEP expression (missing the pointer index) indexing into it, return 4238/// the addressed element of the initializer or null if the index expression is 4239/// invalid. 4240static Constant * 4241GetAddressedElementFromGlobal(GlobalVariable *GV, 4242 const std::vector<ConstantInt*> &Indices) { 4243 Constant *Init = GV->getInitializer(); 4244 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4245 uint64_t Idx = Indices[i]->getZExtValue(); 4246 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4247 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4248 Init = cast<Constant>(CS->getOperand(Idx)); 4249 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4250 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4251 Init = cast<Constant>(CA->getOperand(Idx)); 4252 } else if (isa<ConstantAggregateZero>(Init)) { 4253 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4254 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4255 Init = Constant::getNullValue(STy->getElementType(Idx)); 4256 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4257 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4258 Init = Constant::getNullValue(ATy->getElementType()); 4259 } else { 4260 llvm_unreachable("Unknown constant aggregate type!"); 4261 } 4262 return 0; 4263 } else { 4264 return 0; // Unknown initializer type 4265 } 4266 } 4267 return Init; 4268} 4269 4270/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4271/// 'icmp op load X, cst', try to see if we can compute the backedge 4272/// execution count. 4273ScalarEvolution::BackedgeTakenInfo 4274ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4275 LoadInst *LI, 4276 Constant *RHS, 4277 const Loop *L, 4278 ICmpInst::Predicate predicate) { 4279 if (LI->isVolatile()) return getCouldNotCompute(); 4280 4281 // Check to see if the loaded pointer is a getelementptr of a global. 4282 // TODO: Use SCEV instead of manually grubbing with GEPs. 4283 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4284 if (!GEP) return getCouldNotCompute(); 4285 4286 // Make sure that it is really a constant global we are gepping, with an 4287 // initializer, and make sure the first IDX is really 0. 4288 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4289 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4290 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4291 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4292 return getCouldNotCompute(); 4293 4294 // Okay, we allow one non-constant index into the GEP instruction. 4295 Value *VarIdx = 0; 4296 std::vector<ConstantInt*> Indexes; 4297 unsigned VarIdxNum = 0; 4298 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4299 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4300 Indexes.push_back(CI); 4301 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4302 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4303 VarIdx = GEP->getOperand(i); 4304 VarIdxNum = i-2; 4305 Indexes.push_back(0); 4306 } 4307 4308 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4309 // Check to see if X is a loop variant variable value now. 4310 const SCEV *Idx = getSCEV(VarIdx); 4311 Idx = getSCEVAtScope(Idx, L); 4312 4313 // We can only recognize very limited forms of loop index expressions, in 4314 // particular, only affine AddRec's like {C1,+,C2}. 4315 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4316 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4317 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4318 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4319 return getCouldNotCompute(); 4320 4321 unsigned MaxSteps = MaxBruteForceIterations; 4322 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4323 ConstantInt *ItCst = ConstantInt::get( 4324 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4325 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4326 4327 // Form the GEP offset. 4328 Indexes[VarIdxNum] = Val; 4329 4330 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4331 if (Result == 0) break; // Cannot compute! 4332 4333 // Evaluate the condition for this iteration. 4334 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4335 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4336 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4337#if 0 4338 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4339 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4340 << "***\n"; 4341#endif 4342 ++NumArrayLenItCounts; 4343 return getConstant(ItCst); // Found terminating iteration! 4344 } 4345 } 4346 return getCouldNotCompute(); 4347} 4348 4349 4350/// CanConstantFold - Return true if we can constant fold an instruction of the 4351/// specified type, assuming that all operands were constants. 4352static bool CanConstantFold(const Instruction *I) { 4353 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4354 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4355 return true; 4356 4357 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4358 if (const Function *F = CI->getCalledFunction()) 4359 return canConstantFoldCallTo(F); 4360 return false; 4361} 4362 4363/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4364/// in the loop that V is derived from. We allow arbitrary operations along the 4365/// way, but the operands of an operation must either be constants or a value 4366/// derived from a constant PHI. If this expression does not fit with these 4367/// constraints, return null. 4368static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4369 // If this is not an instruction, or if this is an instruction outside of the 4370 // loop, it can't be derived from a loop PHI. 4371 Instruction *I = dyn_cast<Instruction>(V); 4372 if (I == 0 || !L->contains(I)) return 0; 4373 4374 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4375 if (L->getHeader() == I->getParent()) 4376 return PN; 4377 else 4378 // We don't currently keep track of the control flow needed to evaluate 4379 // PHIs, so we cannot handle PHIs inside of loops. 4380 return 0; 4381 } 4382 4383 // If we won't be able to constant fold this expression even if the operands 4384 // are constants, return early. 4385 if (!CanConstantFold(I)) return 0; 4386 4387 // Otherwise, we can evaluate this instruction if all of its operands are 4388 // constant or derived from a PHI node themselves. 4389 PHINode *PHI = 0; 4390 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4391 if (!isa<Constant>(I->getOperand(Op))) { 4392 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4393 if (P == 0) return 0; // Not evolving from PHI 4394 if (PHI == 0) 4395 PHI = P; 4396 else if (PHI != P) 4397 return 0; // Evolving from multiple different PHIs. 4398 } 4399 4400 // This is a expression evolving from a constant PHI! 4401 return PHI; 4402} 4403 4404/// EvaluateExpression - Given an expression that passes the 4405/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4406/// in the loop has the value PHIVal. If we can't fold this expression for some 4407/// reason, return null. 4408static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4409 const TargetData *TD) { 4410 if (isa<PHINode>(V)) return PHIVal; 4411 if (Constant *C = dyn_cast<Constant>(V)) return C; 4412 Instruction *I = cast<Instruction>(V); 4413 4414 std::vector<Constant*> Operands(I->getNumOperands()); 4415 4416 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4417 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4418 if (Operands[i] == 0) return 0; 4419 } 4420 4421 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4422 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4423 Operands[1], TD); 4424 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4425 &Operands[0], Operands.size(), TD); 4426} 4427 4428/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4429/// in the header of its containing loop, we know the loop executes a 4430/// constant number of times, and the PHI node is just a recurrence 4431/// involving constants, fold it. 4432Constant * 4433ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4434 const APInt &BEs, 4435 const Loop *L) { 4436 std::map<PHINode*, Constant*>::const_iterator I = 4437 ConstantEvolutionLoopExitValue.find(PN); 4438 if (I != ConstantEvolutionLoopExitValue.end()) 4439 return I->second; 4440 4441 if (BEs.ugt(MaxBruteForceIterations)) 4442 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4443 4444 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4445 4446 // Since the loop is canonicalized, the PHI node must have two entries. One 4447 // entry must be a constant (coming in from outside of the loop), and the 4448 // second must be derived from the same PHI. 4449 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4450 Constant *StartCST = 4451 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4452 if (StartCST == 0) 4453 return RetVal = 0; // Must be a constant. 4454 4455 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4456 if (getConstantEvolvingPHI(BEValue, L) != PN && 4457 !isa<Constant>(BEValue)) 4458 return RetVal = 0; // Not derived from same PHI. 4459 4460 // Execute the loop symbolically to determine the exit value. 4461 if (BEs.getActiveBits() >= 32) 4462 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4463 4464 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4465 unsigned IterationNum = 0; 4466 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4467 if (IterationNum == NumIterations) 4468 return RetVal = PHIVal; // Got exit value! 4469 4470 // Compute the value of the PHI node for the next iteration. 4471 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4472 if (NextPHI == PHIVal) 4473 return RetVal = NextPHI; // Stopped evolving! 4474 if (NextPHI == 0) 4475 return 0; // Couldn't evaluate! 4476 PHIVal = NextPHI; 4477 } 4478} 4479 4480/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4481/// constant number of times (the condition evolves only from constants), 4482/// try to evaluate a few iterations of the loop until we get the exit 4483/// condition gets a value of ExitWhen (true or false). If we cannot 4484/// evaluate the trip count of the loop, return getCouldNotCompute(). 4485const SCEV * 4486ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4487 Value *Cond, 4488 bool ExitWhen) { 4489 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4490 if (PN == 0) return getCouldNotCompute(); 4491 4492 // If the loop is canonicalized, the PHI will have exactly two entries. 4493 // That's the only form we support here. 4494 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4495 4496 // One entry must be a constant (coming in from outside of the loop), and the 4497 // second must be derived from the same PHI. 4498 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4499 Constant *StartCST = 4500 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4501 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4502 4503 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4504 if (getConstantEvolvingPHI(BEValue, L) != PN && 4505 !isa<Constant>(BEValue)) 4506 return getCouldNotCompute(); // Not derived from same PHI. 4507 4508 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4509 // the loop symbolically to determine when the condition gets a value of 4510 // "ExitWhen". 4511 unsigned IterationNum = 0; 4512 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4513 for (Constant *PHIVal = StartCST; 4514 IterationNum != MaxIterations; ++IterationNum) { 4515 ConstantInt *CondVal = 4516 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4517 4518 // Couldn't symbolically evaluate. 4519 if (!CondVal) return getCouldNotCompute(); 4520 4521 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4522 ++NumBruteForceTripCountsComputed; 4523 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4524 } 4525 4526 // Compute the value of the PHI node for the next iteration. 4527 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4528 if (NextPHI == 0 || NextPHI == PHIVal) 4529 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4530 PHIVal = NextPHI; 4531 } 4532 4533 // Too many iterations were needed to evaluate. 4534 return getCouldNotCompute(); 4535} 4536 4537/// getSCEVAtScope - Return a SCEV expression for the specified value 4538/// at the specified scope in the program. The L value specifies a loop 4539/// nest to evaluate the expression at, where null is the top-level or a 4540/// specified loop is immediately inside of the loop. 4541/// 4542/// This method can be used to compute the exit value for a variable defined 4543/// in a loop by querying what the value will hold in the parent loop. 4544/// 4545/// In the case that a relevant loop exit value cannot be computed, the 4546/// original value V is returned. 4547const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4548 // Check to see if we've folded this expression at this loop before. 4549 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4550 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4551 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4552 if (!Pair.second) 4553 return Pair.first->second ? Pair.first->second : V; 4554 4555 // Otherwise compute it. 4556 const SCEV *C = computeSCEVAtScope(V, L); 4557 ValuesAtScopes[V][L] = C; 4558 return C; 4559} 4560 4561const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4562 if (isa<SCEVConstant>(V)) return V; 4563 4564 // If this instruction is evolved from a constant-evolving PHI, compute the 4565 // exit value from the loop without using SCEVs. 4566 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4567 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4568 const Loop *LI = (*this->LI)[I->getParent()]; 4569 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4570 if (PHINode *PN = dyn_cast<PHINode>(I)) 4571 if (PN->getParent() == LI->getHeader()) { 4572 // Okay, there is no closed form solution for the PHI node. Check 4573 // to see if the loop that contains it has a known backedge-taken 4574 // count. If so, we may be able to force computation of the exit 4575 // value. 4576 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4577 if (const SCEVConstant *BTCC = 4578 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4579 // Okay, we know how many times the containing loop executes. If 4580 // this is a constant evolving PHI node, get the final value at 4581 // the specified iteration number. 4582 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4583 BTCC->getValue()->getValue(), 4584 LI); 4585 if (RV) return getSCEV(RV); 4586 } 4587 } 4588 4589 // Okay, this is an expression that we cannot symbolically evaluate 4590 // into a SCEV. Check to see if it's possible to symbolically evaluate 4591 // the arguments into constants, and if so, try to constant propagate the 4592 // result. This is particularly useful for computing loop exit values. 4593 if (CanConstantFold(I)) { 4594 SmallVector<Constant *, 4> Operands; 4595 bool MadeImprovement = false; 4596 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4597 Value *Op = I->getOperand(i); 4598 if (Constant *C = dyn_cast<Constant>(Op)) { 4599 Operands.push_back(C); 4600 continue; 4601 } 4602 4603 // If any of the operands is non-constant and if they are 4604 // non-integer and non-pointer, don't even try to analyze them 4605 // with scev techniques. 4606 if (!isSCEVable(Op->getType())) 4607 return V; 4608 4609 const SCEV *OrigV = getSCEV(Op); 4610 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4611 MadeImprovement |= OrigV != OpV; 4612 4613 Constant *C = 0; 4614 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4615 C = SC->getValue(); 4616 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4617 C = dyn_cast<Constant>(SU->getValue()); 4618 if (!C) return V; 4619 if (C->getType() != Op->getType()) 4620 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4621 Op->getType(), 4622 false), 4623 C, Op->getType()); 4624 Operands.push_back(C); 4625 } 4626 4627 // Check to see if getSCEVAtScope actually made an improvement. 4628 if (MadeImprovement) { 4629 Constant *C = 0; 4630 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4631 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4632 Operands[0], Operands[1], TD); 4633 else 4634 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4635 &Operands[0], Operands.size(), TD); 4636 if (!C) return V; 4637 return getSCEV(C); 4638 } 4639 } 4640 } 4641 4642 // This is some other type of SCEVUnknown, just return it. 4643 return V; 4644 } 4645 4646 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4647 // Avoid performing the look-up in the common case where the specified 4648 // expression has no loop-variant portions. 4649 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4650 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4651 if (OpAtScope != Comm->getOperand(i)) { 4652 // Okay, at least one of these operands is loop variant but might be 4653 // foldable. Build a new instance of the folded commutative expression. 4654 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4655 Comm->op_begin()+i); 4656 NewOps.push_back(OpAtScope); 4657 4658 for (++i; i != e; ++i) { 4659 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4660 NewOps.push_back(OpAtScope); 4661 } 4662 if (isa<SCEVAddExpr>(Comm)) 4663 return getAddExpr(NewOps); 4664 if (isa<SCEVMulExpr>(Comm)) 4665 return getMulExpr(NewOps); 4666 if (isa<SCEVSMaxExpr>(Comm)) 4667 return getSMaxExpr(NewOps); 4668 if (isa<SCEVUMaxExpr>(Comm)) 4669 return getUMaxExpr(NewOps); 4670 llvm_unreachable("Unknown commutative SCEV type!"); 4671 } 4672 } 4673 // If we got here, all operands are loop invariant. 4674 return Comm; 4675 } 4676 4677 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4678 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4679 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4680 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4681 return Div; // must be loop invariant 4682 return getUDivExpr(LHS, RHS); 4683 } 4684 4685 // If this is a loop recurrence for a loop that does not contain L, then we 4686 // are dealing with the final value computed by the loop. 4687 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4688 // First, attempt to evaluate each operand. 4689 // Avoid performing the look-up in the common case where the specified 4690 // expression has no loop-variant portions. 4691 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4692 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4693 if (OpAtScope == AddRec->getOperand(i)) 4694 continue; 4695 4696 // Okay, at least one of these operands is loop variant but might be 4697 // foldable. Build a new instance of the folded commutative expression. 4698 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4699 AddRec->op_begin()+i); 4700 NewOps.push_back(OpAtScope); 4701 for (++i; i != e; ++i) 4702 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4703 4704 AddRec = cast<SCEVAddRecExpr>( 4705 getAddRecExpr(NewOps, AddRec->getLoop(), 4706 AddRec->getNoWrapFlags(SCEV::FlagNW))); 4707 break; 4708 } 4709 4710 // If the scope is outside the addrec's loop, evaluate it by using the 4711 // loop exit value of the addrec. 4712 if (!AddRec->getLoop()->contains(L)) { 4713 // To evaluate this recurrence, we need to know how many times the AddRec 4714 // loop iterates. Compute this now. 4715 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4716 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4717 4718 // Then, evaluate the AddRec. 4719 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4720 } 4721 4722 return AddRec; 4723 } 4724 4725 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4726 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4727 if (Op == Cast->getOperand()) 4728 return Cast; // must be loop invariant 4729 return getZeroExtendExpr(Op, Cast->getType()); 4730 } 4731 4732 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4733 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4734 if (Op == Cast->getOperand()) 4735 return Cast; // must be loop invariant 4736 return getSignExtendExpr(Op, Cast->getType()); 4737 } 4738 4739 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4740 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4741 if (Op == Cast->getOperand()) 4742 return Cast; // must be loop invariant 4743 return getTruncateExpr(Op, Cast->getType()); 4744 } 4745 4746 llvm_unreachable("Unknown SCEV type!"); 4747 return 0; 4748} 4749 4750/// getSCEVAtScope - This is a convenience function which does 4751/// getSCEVAtScope(getSCEV(V), L). 4752const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4753 return getSCEVAtScope(getSCEV(V), L); 4754} 4755 4756/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4757/// following equation: 4758/// 4759/// A * X = B (mod N) 4760/// 4761/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4762/// A and B isn't important. 4763/// 4764/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4765static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4766 ScalarEvolution &SE) { 4767 uint32_t BW = A.getBitWidth(); 4768 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4769 assert(A != 0 && "A must be non-zero."); 4770 4771 // 1. D = gcd(A, N) 4772 // 4773 // The gcd of A and N may have only one prime factor: 2. The number of 4774 // trailing zeros in A is its multiplicity 4775 uint32_t Mult2 = A.countTrailingZeros(); 4776 // D = 2^Mult2 4777 4778 // 2. Check if B is divisible by D. 4779 // 4780 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4781 // is not less than multiplicity of this prime factor for D. 4782 if (B.countTrailingZeros() < Mult2) 4783 return SE.getCouldNotCompute(); 4784 4785 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4786 // modulo (N / D). 4787 // 4788 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4789 // bit width during computations. 4790 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4791 APInt Mod(BW + 1, 0); 4792 Mod.setBit(BW - Mult2); // Mod = N / D 4793 APInt I = AD.multiplicativeInverse(Mod); 4794 4795 // 4. Compute the minimum unsigned root of the equation: 4796 // I * (B / D) mod (N / D) 4797 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4798 4799 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4800 // bits. 4801 return SE.getConstant(Result.trunc(BW)); 4802} 4803 4804/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4805/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4806/// might be the same) or two SCEVCouldNotCompute objects. 4807/// 4808static std::pair<const SCEV *,const SCEV *> 4809SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4810 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4811 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4812 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4813 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4814 4815 // We currently can only solve this if the coefficients are constants. 4816 if (!LC || !MC || !NC) { 4817 const SCEV *CNC = SE.getCouldNotCompute(); 4818 return std::make_pair(CNC, CNC); 4819 } 4820 4821 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4822 const APInt &L = LC->getValue()->getValue(); 4823 const APInt &M = MC->getValue()->getValue(); 4824 const APInt &N = NC->getValue()->getValue(); 4825 APInt Two(BitWidth, 2); 4826 APInt Four(BitWidth, 4); 4827 4828 { 4829 using namespace APIntOps; 4830 const APInt& C = L; 4831 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4832 // The B coefficient is M-N/2 4833 APInt B(M); 4834 B -= sdiv(N,Two); 4835 4836 // The A coefficient is N/2 4837 APInt A(N.sdiv(Two)); 4838 4839 // Compute the B^2-4ac term. 4840 APInt SqrtTerm(B); 4841 SqrtTerm *= B; 4842 SqrtTerm -= Four * (A * C); 4843 4844 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4845 // integer value or else APInt::sqrt() will assert. 4846 APInt SqrtVal(SqrtTerm.sqrt()); 4847 4848 // Compute the two solutions for the quadratic formula. 4849 // The divisions must be performed as signed divisions. 4850 APInt NegB(-B); 4851 APInt TwoA( A << 1 ); 4852 if (TwoA.isMinValue()) { 4853 const SCEV *CNC = SE.getCouldNotCompute(); 4854 return std::make_pair(CNC, CNC); 4855 } 4856 4857 LLVMContext &Context = SE.getContext(); 4858 4859 ConstantInt *Solution1 = 4860 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4861 ConstantInt *Solution2 = 4862 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4863 4864 return std::make_pair(SE.getConstant(Solution1), 4865 SE.getConstant(Solution2)); 4866 } // end APIntOps namespace 4867} 4868 4869/// HowFarToZero - Return the number of times a backedge comparing the specified 4870/// value to zero will execute. If not computable, return CouldNotCompute. 4871/// 4872/// This is only used for loops with a "x != y" exit test. The exit condition is 4873/// now expressed as a single expression, V = x-y. So the exit test is 4874/// effectively V != 0. We know and take advantage of the fact that this 4875/// expression only being used in a comparison by zero context. 4876ScalarEvolution::BackedgeTakenInfo 4877ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4878 // If the value is a constant 4879 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4880 // If the value is already zero, the branch will execute zero times. 4881 if (C->getValue()->isZero()) return C; 4882 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4883 } 4884 4885 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4886 if (!AddRec || AddRec->getLoop() != L) 4887 return getCouldNotCompute(); 4888 4889 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4890 // the quadratic equation to solve it. 4891 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4892 std::pair<const SCEV *,const SCEV *> Roots = 4893 SolveQuadraticEquation(AddRec, *this); 4894 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4895 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4896 if (R1 && R2) { 4897#if 0 4898 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4899 << " sol#2: " << *R2 << "\n"; 4900#endif 4901 // Pick the smallest positive root value. 4902 if (ConstantInt *CB = 4903 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 4904 R1->getValue(), 4905 R2->getValue()))) { 4906 if (CB->getZExtValue() == false) 4907 std::swap(R1, R2); // R1 is the minimum root now. 4908 4909 // We can only use this value if the chrec ends up with an exact zero 4910 // value at this index. When solving for "X*X != 5", for example, we 4911 // should not accept a root of 2. 4912 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4913 if (Val->isZero()) 4914 return R1; // We found a quadratic root! 4915 } 4916 } 4917 return getCouldNotCompute(); 4918 } 4919 4920 // Otherwise we can only handle this if it is affine. 4921 if (!AddRec->isAffine()) 4922 return getCouldNotCompute(); 4923 4924 // If this is an affine expression, the execution count of this branch is 4925 // the minimum unsigned root of the following equation: 4926 // 4927 // Start + Step*N = 0 (mod 2^BW) 4928 // 4929 // equivalent to: 4930 // 4931 // Step*N = -Start (mod 2^BW) 4932 // 4933 // where BW is the common bit width of Start and Step. 4934 4935 // Get the initial value for the loop. 4936 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 4937 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 4938 4939 // For now we handle only constant steps. 4940 // 4941 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 4942 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 4943 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 4944 // We have not yet seen any such cases. 4945 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 4946 if (StepC == 0) 4947 return getCouldNotCompute(); 4948 4949 // For positive steps (counting up until unsigned overflow): 4950 // N = -Start/Step (as unsigned) 4951 // For negative steps (counting down to zero): 4952 // N = Start/-Step 4953 // First compute the unsigned distance from zero in the direction of Step. 4954 bool CountDown = StepC->getValue()->getValue().isNegative(); 4955 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 4956 4957 // Handle unitary steps, which cannot wraparound. 4958 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 4959 // N = Distance (as unsigned) 4960 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) 4961 return Distance; 4962 4963 // If the recurrence is known not to wraparound, unsigned divide computes the 4964 // back edge count. We know that the value will either become zero (and thus 4965 // the loop terminates), that the loop will terminate through some other exit 4966 // condition first, or that the loop has undefined behavior. This means 4967 // we can't "miss" the exit value, even with nonunit stride. 4968 // 4969 // FIXME: Prove that loops always exhibits *acceptable* undefined 4970 // behavior. Loops must exhibit defined behavior until a wrapped value is 4971 // actually used. So the trip count computed by udiv could be smaller than the 4972 // number of well-defined iterations. 4973 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) 4974 // FIXME: We really want an "isexact" bit for udiv. 4975 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 4976 4977 // Then, try to solve the above equation provided that Start is constant. 4978 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4979 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4980 -StartC->getValue()->getValue(), 4981 *this); 4982 return getCouldNotCompute(); 4983} 4984 4985/// HowFarToNonZero - Return the number of times a backedge checking the 4986/// specified value for nonzero will execute. If not computable, return 4987/// CouldNotCompute 4988ScalarEvolution::BackedgeTakenInfo 4989ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4990 // Loops that look like: while (X == 0) are very strange indeed. We don't 4991 // handle them yet except for the trivial case. This could be expanded in the 4992 // future as needed. 4993 4994 // If the value is a constant, check to see if it is known to be non-zero 4995 // already. If so, the backedge will execute zero times. 4996 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4997 if (!C->getValue()->isNullValue()) 4998 return getConstant(C->getType(), 0); 4999 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5000 } 5001 5002 // We could implement others, but I really doubt anyone writes loops like 5003 // this, and if they did, they would already be constant folded. 5004 return getCouldNotCompute(); 5005} 5006 5007/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5008/// (which may not be an immediate predecessor) which has exactly one 5009/// successor from which BB is reachable, or null if no such block is 5010/// found. 5011/// 5012std::pair<BasicBlock *, BasicBlock *> 5013ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5014 // If the block has a unique predecessor, then there is no path from the 5015 // predecessor to the block that does not go through the direct edge 5016 // from the predecessor to the block. 5017 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5018 return std::make_pair(Pred, BB); 5019 5020 // A loop's header is defined to be a block that dominates the loop. 5021 // If the header has a unique predecessor outside the loop, it must be 5022 // a block that has exactly one successor that can reach the loop. 5023 if (Loop *L = LI->getLoopFor(BB)) 5024 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5025 5026 return std::pair<BasicBlock *, BasicBlock *>(); 5027} 5028 5029/// HasSameValue - SCEV structural equivalence is usually sufficient for 5030/// testing whether two expressions are equal, however for the purposes of 5031/// looking for a condition guarding a loop, it can be useful to be a little 5032/// more general, since a front-end may have replicated the controlling 5033/// expression. 5034/// 5035static bool HasSameValue(const SCEV *A, const SCEV *B) { 5036 // Quick check to see if they are the same SCEV. 5037 if (A == B) return true; 5038 5039 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5040 // two different instructions with the same value. Check for this case. 5041 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5042 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5043 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5044 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5045 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5046 return true; 5047 5048 // Otherwise assume they may have a different value. 5049 return false; 5050} 5051 5052/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5053/// predicate Pred. Return true iff any changes were made. 5054/// 5055bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5056 const SCEV *&LHS, const SCEV *&RHS) { 5057 bool Changed = false; 5058 5059 // Canonicalize a constant to the right side. 5060 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5061 // Check for both operands constant. 5062 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5063 if (ConstantExpr::getICmp(Pred, 5064 LHSC->getValue(), 5065 RHSC->getValue())->isNullValue()) 5066 goto trivially_false; 5067 else 5068 goto trivially_true; 5069 } 5070 // Otherwise swap the operands to put the constant on the right. 5071 std::swap(LHS, RHS); 5072 Pred = ICmpInst::getSwappedPredicate(Pred); 5073 Changed = true; 5074 } 5075 5076 // If we're comparing an addrec with a value which is loop-invariant in the 5077 // addrec's loop, put the addrec on the left. Also make a dominance check, 5078 // as both operands could be addrecs loop-invariant in each other's loop. 5079 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5080 const Loop *L = AR->getLoop(); 5081 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5082 std::swap(LHS, RHS); 5083 Pred = ICmpInst::getSwappedPredicate(Pred); 5084 Changed = true; 5085 } 5086 } 5087 5088 // If there's a constant operand, canonicalize comparisons with boundary 5089 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5090 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5091 const APInt &RA = RC->getValue()->getValue(); 5092 switch (Pred) { 5093 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5094 case ICmpInst::ICMP_EQ: 5095 case ICmpInst::ICMP_NE: 5096 break; 5097 case ICmpInst::ICMP_UGE: 5098 if ((RA - 1).isMinValue()) { 5099 Pred = ICmpInst::ICMP_NE; 5100 RHS = getConstant(RA - 1); 5101 Changed = true; 5102 break; 5103 } 5104 if (RA.isMaxValue()) { 5105 Pred = ICmpInst::ICMP_EQ; 5106 Changed = true; 5107 break; 5108 } 5109 if (RA.isMinValue()) goto trivially_true; 5110 5111 Pred = ICmpInst::ICMP_UGT; 5112 RHS = getConstant(RA - 1); 5113 Changed = true; 5114 break; 5115 case ICmpInst::ICMP_ULE: 5116 if ((RA + 1).isMaxValue()) { 5117 Pred = ICmpInst::ICMP_NE; 5118 RHS = getConstant(RA + 1); 5119 Changed = true; 5120 break; 5121 } 5122 if (RA.isMinValue()) { 5123 Pred = ICmpInst::ICMP_EQ; 5124 Changed = true; 5125 break; 5126 } 5127 if (RA.isMaxValue()) goto trivially_true; 5128 5129 Pred = ICmpInst::ICMP_ULT; 5130 RHS = getConstant(RA + 1); 5131 Changed = true; 5132 break; 5133 case ICmpInst::ICMP_SGE: 5134 if ((RA - 1).isMinSignedValue()) { 5135 Pred = ICmpInst::ICMP_NE; 5136 RHS = getConstant(RA - 1); 5137 Changed = true; 5138 break; 5139 } 5140 if (RA.isMaxSignedValue()) { 5141 Pred = ICmpInst::ICMP_EQ; 5142 Changed = true; 5143 break; 5144 } 5145 if (RA.isMinSignedValue()) goto trivially_true; 5146 5147 Pred = ICmpInst::ICMP_SGT; 5148 RHS = getConstant(RA - 1); 5149 Changed = true; 5150 break; 5151 case ICmpInst::ICMP_SLE: 5152 if ((RA + 1).isMaxSignedValue()) { 5153 Pred = ICmpInst::ICMP_NE; 5154 RHS = getConstant(RA + 1); 5155 Changed = true; 5156 break; 5157 } 5158 if (RA.isMinSignedValue()) { 5159 Pred = ICmpInst::ICMP_EQ; 5160 Changed = true; 5161 break; 5162 } 5163 if (RA.isMaxSignedValue()) goto trivially_true; 5164 5165 Pred = ICmpInst::ICMP_SLT; 5166 RHS = getConstant(RA + 1); 5167 Changed = true; 5168 break; 5169 case ICmpInst::ICMP_UGT: 5170 if (RA.isMinValue()) { 5171 Pred = ICmpInst::ICMP_NE; 5172 Changed = true; 5173 break; 5174 } 5175 if ((RA + 1).isMaxValue()) { 5176 Pred = ICmpInst::ICMP_EQ; 5177 RHS = getConstant(RA + 1); 5178 Changed = true; 5179 break; 5180 } 5181 if (RA.isMaxValue()) goto trivially_false; 5182 break; 5183 case ICmpInst::ICMP_ULT: 5184 if (RA.isMaxValue()) { 5185 Pred = ICmpInst::ICMP_NE; 5186 Changed = true; 5187 break; 5188 } 5189 if ((RA - 1).isMinValue()) { 5190 Pred = ICmpInst::ICMP_EQ; 5191 RHS = getConstant(RA - 1); 5192 Changed = true; 5193 break; 5194 } 5195 if (RA.isMinValue()) goto trivially_false; 5196 break; 5197 case ICmpInst::ICMP_SGT: 5198 if (RA.isMinSignedValue()) { 5199 Pred = ICmpInst::ICMP_NE; 5200 Changed = true; 5201 break; 5202 } 5203 if ((RA + 1).isMaxSignedValue()) { 5204 Pred = ICmpInst::ICMP_EQ; 5205 RHS = getConstant(RA + 1); 5206 Changed = true; 5207 break; 5208 } 5209 if (RA.isMaxSignedValue()) goto trivially_false; 5210 break; 5211 case ICmpInst::ICMP_SLT: 5212 if (RA.isMaxSignedValue()) { 5213 Pred = ICmpInst::ICMP_NE; 5214 Changed = true; 5215 break; 5216 } 5217 if ((RA - 1).isMinSignedValue()) { 5218 Pred = ICmpInst::ICMP_EQ; 5219 RHS = getConstant(RA - 1); 5220 Changed = true; 5221 break; 5222 } 5223 if (RA.isMinSignedValue()) goto trivially_false; 5224 break; 5225 } 5226 } 5227 5228 // Check for obvious equality. 5229 if (HasSameValue(LHS, RHS)) { 5230 if (ICmpInst::isTrueWhenEqual(Pred)) 5231 goto trivially_true; 5232 if (ICmpInst::isFalseWhenEqual(Pred)) 5233 goto trivially_false; 5234 } 5235 5236 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5237 // adding or subtracting 1 from one of the operands. 5238 switch (Pred) { 5239 case ICmpInst::ICMP_SLE: 5240 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5241 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5242 SCEV::FlagNSW); 5243 Pred = ICmpInst::ICMP_SLT; 5244 Changed = true; 5245 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5246 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5247 SCEV::FlagNSW); 5248 Pred = ICmpInst::ICMP_SLT; 5249 Changed = true; 5250 } 5251 break; 5252 case ICmpInst::ICMP_SGE: 5253 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5254 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5255 SCEV::FlagNSW); 5256 Pred = ICmpInst::ICMP_SGT; 5257 Changed = true; 5258 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5259 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5260 SCEV::FlagNSW); 5261 Pred = ICmpInst::ICMP_SGT; 5262 Changed = true; 5263 } 5264 break; 5265 case ICmpInst::ICMP_ULE: 5266 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5267 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5268 SCEV::FlagNUW); 5269 Pred = ICmpInst::ICMP_ULT; 5270 Changed = true; 5271 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5272 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5273 SCEV::FlagNUW); 5274 Pred = ICmpInst::ICMP_ULT; 5275 Changed = true; 5276 } 5277 break; 5278 case ICmpInst::ICMP_UGE: 5279 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5280 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5281 SCEV::FlagNUW); 5282 Pred = ICmpInst::ICMP_UGT; 5283 Changed = true; 5284 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5285 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5286 SCEV::FlagNUW); 5287 Pred = ICmpInst::ICMP_UGT; 5288 Changed = true; 5289 } 5290 break; 5291 default: 5292 break; 5293 } 5294 5295 // TODO: More simplifications are possible here. 5296 5297 return Changed; 5298 5299trivially_true: 5300 // Return 0 == 0. 5301 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5302 Pred = ICmpInst::ICMP_EQ; 5303 return true; 5304 5305trivially_false: 5306 // Return 0 != 0. 5307 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5308 Pred = ICmpInst::ICMP_NE; 5309 return true; 5310} 5311 5312bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5313 return getSignedRange(S).getSignedMax().isNegative(); 5314} 5315 5316bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5317 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5318} 5319 5320bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5321 return !getSignedRange(S).getSignedMin().isNegative(); 5322} 5323 5324bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5325 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5326} 5327 5328bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5329 return isKnownNegative(S) || isKnownPositive(S); 5330} 5331 5332bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5333 const SCEV *LHS, const SCEV *RHS) { 5334 // Canonicalize the inputs first. 5335 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5336 5337 // If LHS or RHS is an addrec, check to see if the condition is true in 5338 // every iteration of the loop. 5339 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5340 if (isLoopEntryGuardedByCond( 5341 AR->getLoop(), Pred, AR->getStart(), RHS) && 5342 isLoopBackedgeGuardedByCond( 5343 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5344 return true; 5345 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5346 if (isLoopEntryGuardedByCond( 5347 AR->getLoop(), Pred, LHS, AR->getStart()) && 5348 isLoopBackedgeGuardedByCond( 5349 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5350 return true; 5351 5352 // Otherwise see what can be done with known constant ranges. 5353 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5354} 5355 5356bool 5357ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5358 const SCEV *LHS, const SCEV *RHS) { 5359 if (HasSameValue(LHS, RHS)) 5360 return ICmpInst::isTrueWhenEqual(Pred); 5361 5362 // This code is split out from isKnownPredicate because it is called from 5363 // within isLoopEntryGuardedByCond. 5364 switch (Pred) { 5365 default: 5366 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5367 break; 5368 case ICmpInst::ICMP_SGT: 5369 Pred = ICmpInst::ICMP_SLT; 5370 std::swap(LHS, RHS); 5371 case ICmpInst::ICMP_SLT: { 5372 ConstantRange LHSRange = getSignedRange(LHS); 5373 ConstantRange RHSRange = getSignedRange(RHS); 5374 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5375 return true; 5376 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5377 return false; 5378 break; 5379 } 5380 case ICmpInst::ICMP_SGE: 5381 Pred = ICmpInst::ICMP_SLE; 5382 std::swap(LHS, RHS); 5383 case ICmpInst::ICMP_SLE: { 5384 ConstantRange LHSRange = getSignedRange(LHS); 5385 ConstantRange RHSRange = getSignedRange(RHS); 5386 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5387 return true; 5388 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5389 return false; 5390 break; 5391 } 5392 case ICmpInst::ICMP_UGT: 5393 Pred = ICmpInst::ICMP_ULT; 5394 std::swap(LHS, RHS); 5395 case ICmpInst::ICMP_ULT: { 5396 ConstantRange LHSRange = getUnsignedRange(LHS); 5397 ConstantRange RHSRange = getUnsignedRange(RHS); 5398 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5399 return true; 5400 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5401 return false; 5402 break; 5403 } 5404 case ICmpInst::ICMP_UGE: 5405 Pred = ICmpInst::ICMP_ULE; 5406 std::swap(LHS, RHS); 5407 case ICmpInst::ICMP_ULE: { 5408 ConstantRange LHSRange = getUnsignedRange(LHS); 5409 ConstantRange RHSRange = getUnsignedRange(RHS); 5410 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5411 return true; 5412 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5413 return false; 5414 break; 5415 } 5416 case ICmpInst::ICMP_NE: { 5417 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5418 return true; 5419 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5420 return true; 5421 5422 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5423 if (isKnownNonZero(Diff)) 5424 return true; 5425 break; 5426 } 5427 case ICmpInst::ICMP_EQ: 5428 // The check at the top of the function catches the case where 5429 // the values are known to be equal. 5430 break; 5431 } 5432 return false; 5433} 5434 5435/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5436/// protected by a conditional between LHS and RHS. This is used to 5437/// to eliminate casts. 5438bool 5439ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5440 ICmpInst::Predicate Pred, 5441 const SCEV *LHS, const SCEV *RHS) { 5442 // Interpret a null as meaning no loop, where there is obviously no guard 5443 // (interprocedural conditions notwithstanding). 5444 if (!L) return true; 5445 5446 BasicBlock *Latch = L->getLoopLatch(); 5447 if (!Latch) 5448 return false; 5449 5450 BranchInst *LoopContinuePredicate = 5451 dyn_cast<BranchInst>(Latch->getTerminator()); 5452 if (!LoopContinuePredicate || 5453 LoopContinuePredicate->isUnconditional()) 5454 return false; 5455 5456 return isImpliedCond(Pred, LHS, RHS, 5457 LoopContinuePredicate->getCondition(), 5458 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5459} 5460 5461/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5462/// by a conditional between LHS and RHS. This is used to help avoid max 5463/// expressions in loop trip counts, and to eliminate casts. 5464bool 5465ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5466 ICmpInst::Predicate Pred, 5467 const SCEV *LHS, const SCEV *RHS) { 5468 // Interpret a null as meaning no loop, where there is obviously no guard 5469 // (interprocedural conditions notwithstanding). 5470 if (!L) return false; 5471 5472 // Starting at the loop predecessor, climb up the predecessor chain, as long 5473 // as there are predecessors that can be found that have unique successors 5474 // leading to the original header. 5475 for (std::pair<BasicBlock *, BasicBlock *> 5476 Pair(L->getLoopPredecessor(), L->getHeader()); 5477 Pair.first; 5478 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5479 5480 BranchInst *LoopEntryPredicate = 5481 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5482 if (!LoopEntryPredicate || 5483 LoopEntryPredicate->isUnconditional()) 5484 continue; 5485 5486 if (isImpliedCond(Pred, LHS, RHS, 5487 LoopEntryPredicate->getCondition(), 5488 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5489 return true; 5490 } 5491 5492 return false; 5493} 5494 5495/// isImpliedCond - Test whether the condition described by Pred, LHS, 5496/// and RHS is true whenever the given Cond value evaluates to true. 5497bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5498 const SCEV *LHS, const SCEV *RHS, 5499 Value *FoundCondValue, 5500 bool Inverse) { 5501 // Recursively handle And and Or conditions. 5502 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5503 if (BO->getOpcode() == Instruction::And) { 5504 if (!Inverse) 5505 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5506 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5507 } else if (BO->getOpcode() == Instruction::Or) { 5508 if (Inverse) 5509 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5510 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5511 } 5512 } 5513 5514 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5515 if (!ICI) return false; 5516 5517 // Bail if the ICmp's operands' types are wider than the needed type 5518 // before attempting to call getSCEV on them. This avoids infinite 5519 // recursion, since the analysis of widening casts can require loop 5520 // exit condition information for overflow checking, which would 5521 // lead back here. 5522 if (getTypeSizeInBits(LHS->getType()) < 5523 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5524 return false; 5525 5526 // Now that we found a conditional branch that dominates the loop, check to 5527 // see if it is the comparison we are looking for. 5528 ICmpInst::Predicate FoundPred; 5529 if (Inverse) 5530 FoundPred = ICI->getInversePredicate(); 5531 else 5532 FoundPred = ICI->getPredicate(); 5533 5534 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5535 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5536 5537 // Balance the types. The case where FoundLHS' type is wider than 5538 // LHS' type is checked for above. 5539 if (getTypeSizeInBits(LHS->getType()) > 5540 getTypeSizeInBits(FoundLHS->getType())) { 5541 if (CmpInst::isSigned(Pred)) { 5542 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5543 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5544 } else { 5545 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5546 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5547 } 5548 } 5549 5550 // Canonicalize the query to match the way instcombine will have 5551 // canonicalized the comparison. 5552 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5553 if (LHS == RHS) 5554 return CmpInst::isTrueWhenEqual(Pred); 5555 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5556 if (FoundLHS == FoundRHS) 5557 return CmpInst::isFalseWhenEqual(Pred); 5558 5559 // Check to see if we can make the LHS or RHS match. 5560 if (LHS == FoundRHS || RHS == FoundLHS) { 5561 if (isa<SCEVConstant>(RHS)) { 5562 std::swap(FoundLHS, FoundRHS); 5563 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5564 } else { 5565 std::swap(LHS, RHS); 5566 Pred = ICmpInst::getSwappedPredicate(Pred); 5567 } 5568 } 5569 5570 // Check whether the found predicate is the same as the desired predicate. 5571 if (FoundPred == Pred) 5572 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5573 5574 // Check whether swapping the found predicate makes it the same as the 5575 // desired predicate. 5576 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5577 if (isa<SCEVConstant>(RHS)) 5578 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5579 else 5580 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5581 RHS, LHS, FoundLHS, FoundRHS); 5582 } 5583 5584 // Check whether the actual condition is beyond sufficient. 5585 if (FoundPred == ICmpInst::ICMP_EQ) 5586 if (ICmpInst::isTrueWhenEqual(Pred)) 5587 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5588 return true; 5589 if (Pred == ICmpInst::ICMP_NE) 5590 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5591 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5592 return true; 5593 5594 // Otherwise assume the worst. 5595 return false; 5596} 5597 5598/// isImpliedCondOperands - Test whether the condition described by Pred, 5599/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5600/// and FoundRHS is true. 5601bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5602 const SCEV *LHS, const SCEV *RHS, 5603 const SCEV *FoundLHS, 5604 const SCEV *FoundRHS) { 5605 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5606 FoundLHS, FoundRHS) || 5607 // ~x < ~y --> x > y 5608 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5609 getNotSCEV(FoundRHS), 5610 getNotSCEV(FoundLHS)); 5611} 5612 5613/// isImpliedCondOperandsHelper - Test whether the condition described by 5614/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5615/// FoundLHS, and FoundRHS is true. 5616bool 5617ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5618 const SCEV *LHS, const SCEV *RHS, 5619 const SCEV *FoundLHS, 5620 const SCEV *FoundRHS) { 5621 switch (Pred) { 5622 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5623 case ICmpInst::ICMP_EQ: 5624 case ICmpInst::ICMP_NE: 5625 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5626 return true; 5627 break; 5628 case ICmpInst::ICMP_SLT: 5629 case ICmpInst::ICMP_SLE: 5630 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5631 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5632 return true; 5633 break; 5634 case ICmpInst::ICMP_SGT: 5635 case ICmpInst::ICMP_SGE: 5636 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5637 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5638 return true; 5639 break; 5640 case ICmpInst::ICMP_ULT: 5641 case ICmpInst::ICMP_ULE: 5642 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5643 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5644 return true; 5645 break; 5646 case ICmpInst::ICMP_UGT: 5647 case ICmpInst::ICMP_UGE: 5648 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5649 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5650 return true; 5651 break; 5652 } 5653 5654 return false; 5655} 5656 5657/// getBECount - Subtract the end and start values and divide by the step, 5658/// rounding up, to get the number of times the backedge is executed. Return 5659/// CouldNotCompute if an intermediate computation overflows. 5660const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5661 const SCEV *End, 5662 const SCEV *Step, 5663 bool NoWrap) { 5664 assert(!isKnownNegative(Step) && 5665 "This code doesn't handle negative strides yet!"); 5666 5667 const Type *Ty = Start->getType(); 5668 5669 // When Start == End, we have an exact BECount == 0. Short-circuit this case 5670 // here because SCEV may not be able to determine that the unsigned division 5671 // after rounding is zero. 5672 if (Start == End) 5673 return getConstant(Ty, 0); 5674 5675 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5676 const SCEV *Diff = getMinusSCEV(End, Start); 5677 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5678 5679 // Add an adjustment to the difference between End and Start so that 5680 // the division will effectively round up. 5681 const SCEV *Add = getAddExpr(Diff, RoundUp); 5682 5683 if (!NoWrap) { 5684 // Check Add for unsigned overflow. 5685 // TODO: More sophisticated things could be done here. 5686 const Type *WideTy = IntegerType::get(getContext(), 5687 getTypeSizeInBits(Ty) + 1); 5688 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5689 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5690 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5691 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5692 return getCouldNotCompute(); 5693 } 5694 5695 return getUDivExpr(Add, Step); 5696} 5697 5698/// HowManyLessThans - Return the number of times a backedge containing the 5699/// specified less-than comparison will execute. If not computable, return 5700/// CouldNotCompute. 5701ScalarEvolution::BackedgeTakenInfo 5702ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5703 const Loop *L, bool isSigned) { 5704 // Only handle: "ADDREC < LoopInvariant". 5705 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5706 5707 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5708 if (!AddRec || AddRec->getLoop() != L) 5709 return getCouldNotCompute(); 5710 5711 // Check to see if we have a flag which makes analysis easy. 5712 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) : 5713 AddRec->getNoWrapFlags(SCEV::FlagNUW); 5714 5715 if (AddRec->isAffine()) { 5716 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5717 const SCEV *Step = AddRec->getStepRecurrence(*this); 5718 5719 if (Step->isZero()) 5720 return getCouldNotCompute(); 5721 if (Step->isOne()) { 5722 // With unit stride, the iteration never steps past the limit value. 5723 } else if (isKnownPositive(Step)) { 5724 // Test whether a positive iteration can step past the limit 5725 // value and past the maximum value for its type in a single step. 5726 // Note that it's not sufficient to check NoWrap here, because even 5727 // though the value after a wrap is undefined, it's not undefined 5728 // behavior, so if wrap does occur, the loop could either terminate or 5729 // loop infinitely, but in either case, the loop is guaranteed to 5730 // iterate at least until the iteration where the wrapping occurs. 5731 const SCEV *One = getConstant(Step->getType(), 1); 5732 if (isSigned) { 5733 APInt Max = APInt::getSignedMaxValue(BitWidth); 5734 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5735 .slt(getSignedRange(RHS).getSignedMax())) 5736 return getCouldNotCompute(); 5737 } else { 5738 APInt Max = APInt::getMaxValue(BitWidth); 5739 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5740 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5741 return getCouldNotCompute(); 5742 } 5743 } else 5744 // TODO: Handle negative strides here and below. 5745 return getCouldNotCompute(); 5746 5747 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5748 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5749 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5750 // treat m-n as signed nor unsigned due to overflow possibility. 5751 5752 // First, we get the value of the LHS in the first iteration: n 5753 const SCEV *Start = AddRec->getOperand(0); 5754 5755 // Determine the minimum constant start value. 5756 const SCEV *MinStart = getConstant(isSigned ? 5757 getSignedRange(Start).getSignedMin() : 5758 getUnsignedRange(Start).getUnsignedMin()); 5759 5760 // If we know that the condition is true in order to enter the loop, 5761 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5762 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5763 // the division must round up. 5764 const SCEV *End = RHS; 5765 if (!isLoopEntryGuardedByCond(L, 5766 isSigned ? ICmpInst::ICMP_SLT : 5767 ICmpInst::ICMP_ULT, 5768 getMinusSCEV(Start, Step), RHS)) 5769 End = isSigned ? getSMaxExpr(RHS, Start) 5770 : getUMaxExpr(RHS, Start); 5771 5772 // Determine the maximum constant end value. 5773 const SCEV *MaxEnd = getConstant(isSigned ? 5774 getSignedRange(End).getSignedMax() : 5775 getUnsignedRange(End).getUnsignedMax()); 5776 5777 // If MaxEnd is within a step of the maximum integer value in its type, 5778 // adjust it down to the minimum value which would produce the same effect. 5779 // This allows the subsequent ceiling division of (N+(step-1))/step to 5780 // compute the correct value. 5781 const SCEV *StepMinusOne = getMinusSCEV(Step, 5782 getConstant(Step->getType(), 1)); 5783 MaxEnd = isSigned ? 5784 getSMinExpr(MaxEnd, 5785 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5786 StepMinusOne)) : 5787 getUMinExpr(MaxEnd, 5788 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5789 StepMinusOne)); 5790 5791 // Finally, we subtract these two values and divide, rounding up, to get 5792 // the number of times the backedge is executed. 5793 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5794 5795 // The maximum backedge count is similar, except using the minimum start 5796 // value and the maximum end value. 5797 // If we already have an exact constant BECount, use it instead. 5798 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 5799 : getBECount(MinStart, MaxEnd, Step, NoWrap); 5800 5801 // If the stride is nonconstant, and NoWrap == true, then 5802 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 5803 // exact BECount and invalid MaxBECount, which should be avoided to catch 5804 // more optimization opportunities. 5805 if (isa<SCEVCouldNotCompute>(MaxBECount)) 5806 MaxBECount = BECount; 5807 5808 return BackedgeTakenInfo(BECount, MaxBECount); 5809 } 5810 5811 return getCouldNotCompute(); 5812} 5813 5814/// getNumIterationsInRange - Return the number of iterations of this loop that 5815/// produce values in the specified constant range. Another way of looking at 5816/// this is that it returns the first iteration number where the value is not in 5817/// the condition, thus computing the exit count. If the iteration count can't 5818/// be computed, an instance of SCEVCouldNotCompute is returned. 5819const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5820 ScalarEvolution &SE) const { 5821 if (Range.isFullSet()) // Infinite loop. 5822 return SE.getCouldNotCompute(); 5823 5824 // If the start is a non-zero constant, shift the range to simplify things. 5825 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5826 if (!SC->getValue()->isZero()) { 5827 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5828 Operands[0] = SE.getConstant(SC->getType(), 0); 5829 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 5830 getNoWrapFlags(FlagNW)); 5831 if (const SCEVAddRecExpr *ShiftedAddRec = 5832 dyn_cast<SCEVAddRecExpr>(Shifted)) 5833 return ShiftedAddRec->getNumIterationsInRange( 5834 Range.subtract(SC->getValue()->getValue()), SE); 5835 // This is strange and shouldn't happen. 5836 return SE.getCouldNotCompute(); 5837 } 5838 5839 // The only time we can solve this is when we have all constant indices. 5840 // Otherwise, we cannot determine the overflow conditions. 5841 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5842 if (!isa<SCEVConstant>(getOperand(i))) 5843 return SE.getCouldNotCompute(); 5844 5845 5846 // Okay at this point we know that all elements of the chrec are constants and 5847 // that the start element is zero. 5848 5849 // First check to see if the range contains zero. If not, the first 5850 // iteration exits. 5851 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5852 if (!Range.contains(APInt(BitWidth, 0))) 5853 return SE.getConstant(getType(), 0); 5854 5855 if (isAffine()) { 5856 // If this is an affine expression then we have this situation: 5857 // Solve {0,+,A} in Range === Ax in Range 5858 5859 // We know that zero is in the range. If A is positive then we know that 5860 // the upper value of the range must be the first possible exit value. 5861 // If A is negative then the lower of the range is the last possible loop 5862 // value. Also note that we already checked for a full range. 5863 APInt One(BitWidth,1); 5864 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5865 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5866 5867 // The exit value should be (End+A)/A. 5868 APInt ExitVal = (End + A).udiv(A); 5869 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5870 5871 // Evaluate at the exit value. If we really did fall out of the valid 5872 // range, then we computed our trip count, otherwise wrap around or other 5873 // things must have happened. 5874 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5875 if (Range.contains(Val->getValue())) 5876 return SE.getCouldNotCompute(); // Something strange happened 5877 5878 // Ensure that the previous value is in the range. This is a sanity check. 5879 assert(Range.contains( 5880 EvaluateConstantChrecAtConstant(this, 5881 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5882 "Linear scev computation is off in a bad way!"); 5883 return SE.getConstant(ExitValue); 5884 } else if (isQuadratic()) { 5885 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5886 // quadratic equation to solve it. To do this, we must frame our problem in 5887 // terms of figuring out when zero is crossed, instead of when 5888 // Range.getUpper() is crossed. 5889 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5890 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5891 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 5892 // getNoWrapFlags(FlagNW) 5893 FlagAnyWrap); 5894 5895 // Next, solve the constructed addrec 5896 std::pair<const SCEV *,const SCEV *> Roots = 5897 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5898 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5899 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5900 if (R1) { 5901 // Pick the smallest positive root value. 5902 if (ConstantInt *CB = 5903 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5904 R1->getValue(), R2->getValue()))) { 5905 if (CB->getZExtValue() == false) 5906 std::swap(R1, R2); // R1 is the minimum root now. 5907 5908 // Make sure the root is not off by one. The returned iteration should 5909 // not be in the range, but the previous one should be. When solving 5910 // for "X*X < 5", for example, we should not return a root of 2. 5911 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5912 R1->getValue(), 5913 SE); 5914 if (Range.contains(R1Val->getValue())) { 5915 // The next iteration must be out of the range... 5916 ConstantInt *NextVal = 5917 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5918 5919 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5920 if (!Range.contains(R1Val->getValue())) 5921 return SE.getConstant(NextVal); 5922 return SE.getCouldNotCompute(); // Something strange happened 5923 } 5924 5925 // If R1 was not in the range, then it is a good return value. Make 5926 // sure that R1-1 WAS in the range though, just in case. 5927 ConstantInt *NextVal = 5928 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5929 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5930 if (Range.contains(R1Val->getValue())) 5931 return R1; 5932 return SE.getCouldNotCompute(); // Something strange happened 5933 } 5934 } 5935 } 5936 5937 return SE.getCouldNotCompute(); 5938} 5939 5940 5941 5942//===----------------------------------------------------------------------===// 5943// SCEVCallbackVH Class Implementation 5944//===----------------------------------------------------------------------===// 5945 5946void ScalarEvolution::SCEVCallbackVH::deleted() { 5947 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5948 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5949 SE->ConstantEvolutionLoopExitValue.erase(PN); 5950 SE->ValueExprMap.erase(getValPtr()); 5951 // this now dangles! 5952} 5953 5954void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5955 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5956 5957 // Forget all the expressions associated with users of the old value, 5958 // so that future queries will recompute the expressions using the new 5959 // value. 5960 Value *Old = getValPtr(); 5961 SmallVector<User *, 16> Worklist; 5962 SmallPtrSet<User *, 8> Visited; 5963 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5964 UI != UE; ++UI) 5965 Worklist.push_back(*UI); 5966 while (!Worklist.empty()) { 5967 User *U = Worklist.pop_back_val(); 5968 // Deleting the Old value will cause this to dangle. Postpone 5969 // that until everything else is done. 5970 if (U == Old) 5971 continue; 5972 if (!Visited.insert(U)) 5973 continue; 5974 if (PHINode *PN = dyn_cast<PHINode>(U)) 5975 SE->ConstantEvolutionLoopExitValue.erase(PN); 5976 SE->ValueExprMap.erase(U); 5977 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5978 UI != UE; ++UI) 5979 Worklist.push_back(*UI); 5980 } 5981 // Delete the Old value. 5982 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5983 SE->ConstantEvolutionLoopExitValue.erase(PN); 5984 SE->ValueExprMap.erase(Old); 5985 // this now dangles! 5986} 5987 5988ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5989 : CallbackVH(V), SE(se) {} 5990 5991//===----------------------------------------------------------------------===// 5992// ScalarEvolution Class Implementation 5993//===----------------------------------------------------------------------===// 5994 5995ScalarEvolution::ScalarEvolution() 5996 : FunctionPass(ID), FirstUnknown(0) { 5997 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 5998} 5999 6000bool ScalarEvolution::runOnFunction(Function &F) { 6001 this->F = &F; 6002 LI = &getAnalysis<LoopInfo>(); 6003 TD = getAnalysisIfAvailable<TargetData>(); 6004 DT = &getAnalysis<DominatorTree>(); 6005 return false; 6006} 6007 6008void ScalarEvolution::releaseMemory() { 6009 // Iterate through all the SCEVUnknown instances and call their 6010 // destructors, so that they release their references to their values. 6011 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6012 U->~SCEVUnknown(); 6013 FirstUnknown = 0; 6014 6015 ValueExprMap.clear(); 6016 BackedgeTakenCounts.clear(); 6017 ConstantEvolutionLoopExitValue.clear(); 6018 ValuesAtScopes.clear(); 6019 LoopDispositions.clear(); 6020 BlockDispositions.clear(); 6021 UnsignedRanges.clear(); 6022 SignedRanges.clear(); 6023 UniqueSCEVs.clear(); 6024 SCEVAllocator.Reset(); 6025} 6026 6027void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6028 AU.setPreservesAll(); 6029 AU.addRequiredTransitive<LoopInfo>(); 6030 AU.addRequiredTransitive<DominatorTree>(); 6031} 6032 6033bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6034 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6035} 6036 6037static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6038 const Loop *L) { 6039 // Print all inner loops first 6040 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6041 PrintLoopInfo(OS, SE, *I); 6042 6043 OS << "Loop "; 6044 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6045 OS << ": "; 6046 6047 SmallVector<BasicBlock *, 8> ExitBlocks; 6048 L->getExitBlocks(ExitBlocks); 6049 if (ExitBlocks.size() != 1) 6050 OS << "<multiple exits> "; 6051 6052 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6053 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6054 } else { 6055 OS << "Unpredictable backedge-taken count. "; 6056 } 6057 6058 OS << "\n" 6059 "Loop "; 6060 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6061 OS << ": "; 6062 6063 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6064 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6065 } else { 6066 OS << "Unpredictable max backedge-taken count. "; 6067 } 6068 6069 OS << "\n"; 6070} 6071 6072void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6073 // ScalarEvolution's implementation of the print method is to print 6074 // out SCEV values of all instructions that are interesting. Doing 6075 // this potentially causes it to create new SCEV objects though, 6076 // which technically conflicts with the const qualifier. This isn't 6077 // observable from outside the class though, so casting away the 6078 // const isn't dangerous. 6079 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6080 6081 OS << "Classifying expressions for: "; 6082 WriteAsOperand(OS, F, /*PrintType=*/false); 6083 OS << "\n"; 6084 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6085 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6086 OS << *I << '\n'; 6087 OS << " --> "; 6088 const SCEV *SV = SE.getSCEV(&*I); 6089 SV->print(OS); 6090 6091 const Loop *L = LI->getLoopFor((*I).getParent()); 6092 6093 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6094 if (AtUse != SV) { 6095 OS << " --> "; 6096 AtUse->print(OS); 6097 } 6098 6099 if (L) { 6100 OS << "\t\t" "Exits: "; 6101 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6102 if (!SE.isLoopInvariant(ExitValue, L)) { 6103 OS << "<<Unknown>>"; 6104 } else { 6105 OS << *ExitValue; 6106 } 6107 } 6108 6109 OS << "\n"; 6110 } 6111 6112 OS << "Determining loop execution counts for: "; 6113 WriteAsOperand(OS, F, /*PrintType=*/false); 6114 OS << "\n"; 6115 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6116 PrintLoopInfo(OS, &SE, *I); 6117} 6118 6119ScalarEvolution::LoopDisposition 6120ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6121 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6122 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6123 Values.insert(std::make_pair(L, LoopVariant)); 6124 if (!Pair.second) 6125 return Pair.first->second; 6126 6127 LoopDisposition D = computeLoopDisposition(S, L); 6128 return LoopDispositions[S][L] = D; 6129} 6130 6131ScalarEvolution::LoopDisposition 6132ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6133 switch (S->getSCEVType()) { 6134 case scConstant: 6135 return LoopInvariant; 6136 case scTruncate: 6137 case scZeroExtend: 6138 case scSignExtend: 6139 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6140 case scAddRecExpr: { 6141 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6142 6143 // If L is the addrec's loop, it's computable. 6144 if (AR->getLoop() == L) 6145 return LoopComputable; 6146 6147 // Add recurrences are never invariant in the function-body (null loop). 6148 if (!L) 6149 return LoopVariant; 6150 6151 // This recurrence is variant w.r.t. L if L contains AR's loop. 6152 if (L->contains(AR->getLoop())) 6153 return LoopVariant; 6154 6155 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6156 if (AR->getLoop()->contains(L)) 6157 return LoopInvariant; 6158 6159 // This recurrence is variant w.r.t. L if any of its operands 6160 // are variant. 6161 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6162 I != E; ++I) 6163 if (!isLoopInvariant(*I, L)) 6164 return LoopVariant; 6165 6166 // Otherwise it's loop-invariant. 6167 return LoopInvariant; 6168 } 6169 case scAddExpr: 6170 case scMulExpr: 6171 case scUMaxExpr: 6172 case scSMaxExpr: { 6173 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6174 bool HasVarying = false; 6175 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6176 I != E; ++I) { 6177 LoopDisposition D = getLoopDisposition(*I, L); 6178 if (D == LoopVariant) 6179 return LoopVariant; 6180 if (D == LoopComputable) 6181 HasVarying = true; 6182 } 6183 return HasVarying ? LoopComputable : LoopInvariant; 6184 } 6185 case scUDivExpr: { 6186 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6187 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6188 if (LD == LoopVariant) 6189 return LoopVariant; 6190 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6191 if (RD == LoopVariant) 6192 return LoopVariant; 6193 return (LD == LoopInvariant && RD == LoopInvariant) ? 6194 LoopInvariant : LoopComputable; 6195 } 6196 case scUnknown: 6197 // All non-instruction values are loop invariant. All instructions are loop 6198 // invariant if they are not contained in the specified loop. 6199 // Instructions are never considered invariant in the function body 6200 // (null loop) because they are defined within the "loop". 6201 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6202 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6203 return LoopInvariant; 6204 case scCouldNotCompute: 6205 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6206 return LoopVariant; 6207 default: break; 6208 } 6209 llvm_unreachable("Unknown SCEV kind!"); 6210 return LoopVariant; 6211} 6212 6213bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6214 return getLoopDisposition(S, L) == LoopInvariant; 6215} 6216 6217bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6218 return getLoopDisposition(S, L) == LoopComputable; 6219} 6220 6221ScalarEvolution::BlockDisposition 6222ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6223 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6224 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6225 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6226 if (!Pair.second) 6227 return Pair.first->second; 6228 6229 BlockDisposition D = computeBlockDisposition(S, BB); 6230 return BlockDispositions[S][BB] = D; 6231} 6232 6233ScalarEvolution::BlockDisposition 6234ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6235 switch (S->getSCEVType()) { 6236 case scConstant: 6237 return ProperlyDominatesBlock; 6238 case scTruncate: 6239 case scZeroExtend: 6240 case scSignExtend: 6241 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6242 case scAddRecExpr: { 6243 // This uses a "dominates" query instead of "properly dominates" query 6244 // to test for proper dominance too, because the instruction which 6245 // produces the addrec's value is a PHI, and a PHI effectively properly 6246 // dominates its entire containing block. 6247 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6248 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6249 return DoesNotDominateBlock; 6250 } 6251 // FALL THROUGH into SCEVNAryExpr handling. 6252 case scAddExpr: 6253 case scMulExpr: 6254 case scUMaxExpr: 6255 case scSMaxExpr: { 6256 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6257 bool Proper = true; 6258 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6259 I != E; ++I) { 6260 BlockDisposition D = getBlockDisposition(*I, BB); 6261 if (D == DoesNotDominateBlock) 6262 return DoesNotDominateBlock; 6263 if (D == DominatesBlock) 6264 Proper = false; 6265 } 6266 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6267 } 6268 case scUDivExpr: { 6269 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6270 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6271 BlockDisposition LD = getBlockDisposition(LHS, BB); 6272 if (LD == DoesNotDominateBlock) 6273 return DoesNotDominateBlock; 6274 BlockDisposition RD = getBlockDisposition(RHS, BB); 6275 if (RD == DoesNotDominateBlock) 6276 return DoesNotDominateBlock; 6277 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6278 ProperlyDominatesBlock : DominatesBlock; 6279 } 6280 case scUnknown: 6281 if (Instruction *I = 6282 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6283 if (I->getParent() == BB) 6284 return DominatesBlock; 6285 if (DT->properlyDominates(I->getParent(), BB)) 6286 return ProperlyDominatesBlock; 6287 return DoesNotDominateBlock; 6288 } 6289 return ProperlyDominatesBlock; 6290 case scCouldNotCompute: 6291 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6292 return DoesNotDominateBlock; 6293 default: break; 6294 } 6295 llvm_unreachable("Unknown SCEV kind!"); 6296 return DoesNotDominateBlock; 6297} 6298 6299bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6300 return getBlockDisposition(S, BB) >= DominatesBlock; 6301} 6302 6303bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6304 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6305} 6306 6307bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6308 switch (S->getSCEVType()) { 6309 case scConstant: 6310 return false; 6311 case scTruncate: 6312 case scZeroExtend: 6313 case scSignExtend: { 6314 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6315 const SCEV *CastOp = Cast->getOperand(); 6316 return Op == CastOp || hasOperand(CastOp, Op); 6317 } 6318 case scAddRecExpr: 6319 case scAddExpr: 6320 case scMulExpr: 6321 case scUMaxExpr: 6322 case scSMaxExpr: { 6323 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6324 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6325 I != E; ++I) { 6326 const SCEV *NAryOp = *I; 6327 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6328 return true; 6329 } 6330 return false; 6331 } 6332 case scUDivExpr: { 6333 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6334 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6335 return LHS == Op || hasOperand(LHS, Op) || 6336 RHS == Op || hasOperand(RHS, Op); 6337 } 6338 case scUnknown: 6339 return false; 6340 case scCouldNotCompute: 6341 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6342 return false; 6343 default: break; 6344 } 6345 llvm_unreachable("Unknown SCEV kind!"); 6346 return false; 6347} 6348 6349void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6350 ValuesAtScopes.erase(S); 6351 LoopDispositions.erase(S); 6352 BlockDispositions.erase(S); 6353 UnsignedRanges.erase(S); 6354 SignedRanges.erase(S); 6355} 6356