ScalarEvolution.cpp revision 39125d8ef94cbadccd7339d3344e114dedaab12c
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/LoopInfo.h" 73#include "llvm/Analysis/ValueTracking.h" 74#include "llvm/Assembly/Writer.h" 75#include "llvm/Target/TargetData.h" 76#include "llvm/Support/CommandLine.h" 77#include "llvm/Support/ConstantRange.h" 78#include "llvm/Support/Debug.h" 79#include "llvm/Support/ErrorHandling.h" 80#include "llvm/Support/GetElementPtrTypeIterator.h" 81#include "llvm/Support/InstIterator.h" 82#include "llvm/Support/MathExtras.h" 83#include "llvm/Support/raw_ostream.h" 84#include "llvm/ADT/Statistic.h" 85#include "llvm/ADT/STLExtras.h" 86#include "llvm/ADT/SmallPtrSet.h" 87#include <algorithm> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant " 103 "derived loop"), 104 cl::init(100)); 105 106static RegisterPass<ScalarEvolution> 107R("scalar-evolution", "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(dbgs()); 122 dbgs() << '\n'; 123} 124 125bool SCEV::isZero() const { 126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 127 return SC->getValue()->isZero(); 128 return false; 129} 130 131bool SCEV::isOne() const { 132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 133 return SC->getValue()->isOne(); 134 return false; 135} 136 137bool SCEV::isAllOnesValue() const { 138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 139 return SC->getValue()->isAllOnesValue(); 140 return false; 141} 142 143SCEVCouldNotCompute::SCEVCouldNotCompute() : 144 SCEV(FoldingSetNodeID(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 181 new (S) SCEVConstant(ID, V); 182 UniqueSCEVs.InsertNode(S, IP); 183 return S; 184} 185 186const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 187 return getConstant(ConstantInt::get(getContext(), Val)); 188} 189 190const SCEV * 191ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 192 return getConstant( 193 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 194} 195 196const Type *SCEVConstant::getType() const { return V->getType(); } 197 198void SCEVConstant::print(raw_ostream &OS) const { 199 WriteAsOperand(OS, V, false); 200} 201 202SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 203 unsigned SCEVTy, const SCEV *op, const Type *ty) 204 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 205 206bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 207 return Op->dominates(BB, DT); 208} 209 210bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 211 return Op->properlyDominates(BB, DT); 212} 213 214SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 215 const SCEV *op, const Type *ty) 216 : SCEVCastExpr(ID, scTruncate, op, ty) { 217 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 218 (Ty->isInteger() || isa<PointerType>(Ty)) && 219 "Cannot truncate non-integer value!"); 220} 221 222void SCEVTruncateExpr::print(raw_ostream &OS) const { 223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 224} 225 226SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 227 const SCEV *op, const Type *ty) 228 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 229 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 230 (Ty->isInteger() || isa<PointerType>(Ty)) && 231 "Cannot zero extend non-integer value!"); 232} 233 234void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 235 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 236} 237 238SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 239 const SCEV *op, const Type *ty) 240 : SCEVCastExpr(ID, scSignExtend, op, ty) { 241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 242 (Ty->isInteger() || isa<PointerType>(Ty)) && 243 "Cannot sign extend non-integer value!"); 244} 245 246void SCEVSignExtendExpr::print(raw_ostream &OS) const { 247 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 248} 249 250void SCEVCommutativeExpr::print(raw_ostream &OS) const { 251 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 252 const char *OpStr = getOperationStr(); 253 OS << "(" << *Operands[0]; 254 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 255 OS << OpStr << *Operands[i]; 256 OS << ")"; 257} 258 259bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 260 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 261 if (!getOperand(i)->dominates(BB, DT)) 262 return false; 263 } 264 return true; 265} 266 267bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 268 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 269 if (!getOperand(i)->properlyDominates(BB, DT)) 270 return false; 271 } 272 return true; 273} 274 275bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 276 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 277} 278 279bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 280 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 281} 282 283void SCEVUDivExpr::print(raw_ostream &OS) const { 284 OS << "(" << *LHS << " /u " << *RHS << ")"; 285} 286 287const Type *SCEVUDivExpr::getType() const { 288 // In most cases the types of LHS and RHS will be the same, but in some 289 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 290 // depend on the type for correctness, but handling types carefully can 291 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 292 // a pointer type than the RHS, so use the RHS' type here. 293 return RHS->getType(); 294} 295 296bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 297 // Add recurrences are never invariant in the function-body (null loop). 298 if (!QueryLoop) 299 return false; 300 301 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 302 if (QueryLoop->contains(L)) 303 return false; 304 305 // This recurrence is variant w.r.t. QueryLoop if any of its operands 306 // are variant. 307 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 308 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 309 return false; 310 311 // Otherwise it's loop-invariant. 312 return true; 313} 314 315bool 316SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 317 return DT->dominates(L->getHeader(), BB) && 318 SCEVNAryExpr::dominates(BB, DT); 319} 320 321bool 322SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 323 // This uses a "dominates" query instead of "properly dominates" query because 324 // the instruction which produces the addrec's value is a PHI, and a PHI 325 // effectively properly dominates its entire containing block. 326 return DT->dominates(L->getHeader(), BB) && 327 SCEVNAryExpr::properlyDominates(BB, DT); 328} 329 330void SCEVAddRecExpr::print(raw_ostream &OS) const { 331 OS << "{" << *Operands[0]; 332 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 333 OS << ",+," << *Operands[i]; 334 OS << "}<"; 335 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 336 OS << ">"; 337} 338 339bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 340 // All non-instruction values are loop invariant. All instructions are loop 341 // invariant if they are not contained in the specified loop. 342 // Instructions are never considered invariant in the function body 343 // (null loop) because they are defined within the "loop". 344 if (Instruction *I = dyn_cast<Instruction>(V)) 345 return L && !L->contains(I); 346 return true; 347} 348 349bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 350 if (Instruction *I = dyn_cast<Instruction>(getValue())) 351 return DT->dominates(I->getParent(), BB); 352 return true; 353} 354 355bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 356 if (Instruction *I = dyn_cast<Instruction>(getValue())) 357 return DT->properlyDominates(I->getParent(), BB); 358 return true; 359} 360 361const Type *SCEVUnknown::getType() const { 362 return V->getType(); 363} 364 365bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 366 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 367 if (VCE->getOpcode() == Instruction::PtrToInt) 368 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 369 if (CE->getOpcode() == Instruction::GetElementPtr && 370 CE->getOperand(0)->isNullValue() && 371 CE->getNumOperands() == 2) 372 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 373 if (CI->isOne()) { 374 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 375 ->getElementType(); 376 return true; 377 } 378 379 return false; 380} 381 382bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 383 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 384 if (VCE->getOpcode() == Instruction::PtrToInt) 385 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 386 if (CE->getOpcode() == Instruction::GetElementPtr && 387 CE->getOperand(0)->isNullValue()) { 388 const Type *Ty = 389 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 390 if (const StructType *STy = dyn_cast<StructType>(Ty)) 391 if (!STy->isPacked() && 392 CE->getNumOperands() == 3 && 393 CE->getOperand(1)->isNullValue()) { 394 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 395 if (CI->isOne() && 396 STy->getNumElements() == 2 && 397 STy->getElementType(0)->isInteger(1)) { 398 AllocTy = STy->getElementType(1); 399 return true; 400 } 401 } 402 } 403 404 return false; 405} 406 407bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 408 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 409 if (VCE->getOpcode() == Instruction::PtrToInt) 410 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 411 if (CE->getOpcode() == Instruction::GetElementPtr && 412 CE->getNumOperands() == 3 && 413 CE->getOperand(0)->isNullValue() && 414 CE->getOperand(1)->isNullValue()) { 415 const Type *Ty = 416 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 417 // Ignore vector types here so that ScalarEvolutionExpander doesn't 418 // emit getelementptrs that index into vectors. 419 if (isa<StructType>(Ty) || isa<ArrayType>(Ty)) { 420 CTy = Ty; 421 FieldNo = CE->getOperand(2); 422 return true; 423 } 424 } 425 426 return false; 427} 428 429void SCEVUnknown::print(raw_ostream &OS) const { 430 const Type *AllocTy; 431 if (isSizeOf(AllocTy)) { 432 OS << "sizeof(" << *AllocTy << ")"; 433 return; 434 } 435 if (isAlignOf(AllocTy)) { 436 OS << "alignof(" << *AllocTy << ")"; 437 return; 438 } 439 440 const Type *CTy; 441 Constant *FieldNo; 442 if (isOffsetOf(CTy, FieldNo)) { 443 OS << "offsetof(" << *CTy << ", "; 444 WriteAsOperand(OS, FieldNo, false); 445 OS << ")"; 446 return; 447 } 448 449 // Otherwise just print it normally. 450 WriteAsOperand(OS, V, false); 451} 452 453//===----------------------------------------------------------------------===// 454// SCEV Utilities 455//===----------------------------------------------------------------------===// 456 457static bool CompareTypes(const Type *A, const Type *B) { 458 if (A->getTypeID() != B->getTypeID()) 459 return A->getTypeID() < B->getTypeID(); 460 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 461 const IntegerType *BI = cast<IntegerType>(B); 462 return AI->getBitWidth() < BI->getBitWidth(); 463 } 464 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 465 const PointerType *BI = cast<PointerType>(B); 466 return CompareTypes(AI->getElementType(), BI->getElementType()); 467 } 468 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 469 const ArrayType *BI = cast<ArrayType>(B); 470 if (AI->getNumElements() != BI->getNumElements()) 471 return AI->getNumElements() < BI->getNumElements(); 472 return CompareTypes(AI->getElementType(), BI->getElementType()); 473 } 474 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 475 const VectorType *BI = cast<VectorType>(B); 476 if (AI->getNumElements() != BI->getNumElements()) 477 return AI->getNumElements() < BI->getNumElements(); 478 return CompareTypes(AI->getElementType(), BI->getElementType()); 479 } 480 if (const StructType *AI = dyn_cast<StructType>(A)) { 481 const StructType *BI = cast<StructType>(B); 482 if (AI->getNumElements() != BI->getNumElements()) 483 return AI->getNumElements() < BI->getNumElements(); 484 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 485 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 486 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 487 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 488 } 489 return false; 490} 491 492namespace { 493 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 494 /// than the complexity of the RHS. This comparator is used to canonicalize 495 /// expressions. 496 class SCEVComplexityCompare { 497 LoopInfo *LI; 498 public: 499 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 500 501 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 502 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 503 if (LHS == RHS) 504 return false; 505 506 // Primarily, sort the SCEVs by their getSCEVType(). 507 if (LHS->getSCEVType() != RHS->getSCEVType()) 508 return LHS->getSCEVType() < RHS->getSCEVType(); 509 510 // Aside from the getSCEVType() ordering, the particular ordering 511 // isn't very important except that it's beneficial to be consistent, 512 // so that (a + b) and (b + a) don't end up as different expressions. 513 514 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 515 // not as complete as it could be. 516 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 517 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 518 519 // Order pointer values after integer values. This helps SCEVExpander 520 // form GEPs. 521 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 522 return false; 523 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 524 return true; 525 526 // Compare getValueID values. 527 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 528 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 529 530 // Sort arguments by their position. 531 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 532 const Argument *RA = cast<Argument>(RU->getValue()); 533 return LA->getArgNo() < RA->getArgNo(); 534 } 535 536 // For instructions, compare their loop depth, and their opcode. 537 // This is pretty loose. 538 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 539 Instruction *RV = cast<Instruction>(RU->getValue()); 540 541 // Compare loop depths. 542 if (LI->getLoopDepth(LV->getParent()) != 543 LI->getLoopDepth(RV->getParent())) 544 return LI->getLoopDepth(LV->getParent()) < 545 LI->getLoopDepth(RV->getParent()); 546 547 // Compare opcodes. 548 if (LV->getOpcode() != RV->getOpcode()) 549 return LV->getOpcode() < RV->getOpcode(); 550 551 // Compare the number of operands. 552 if (LV->getNumOperands() != RV->getNumOperands()) 553 return LV->getNumOperands() < RV->getNumOperands(); 554 } 555 556 return false; 557 } 558 559 // Compare constant values. 560 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 561 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 562 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 563 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 564 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 565 } 566 567 // Compare addrec loop depths. 568 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 569 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 570 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 571 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 572 } 573 574 // Lexicographically compare n-ary expressions. 575 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 576 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 577 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 578 if (i >= RC->getNumOperands()) 579 return false; 580 if (operator()(LC->getOperand(i), RC->getOperand(i))) 581 return true; 582 if (operator()(RC->getOperand(i), LC->getOperand(i))) 583 return false; 584 } 585 return LC->getNumOperands() < RC->getNumOperands(); 586 } 587 588 // Lexicographically compare udiv expressions. 589 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 590 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 591 if (operator()(LC->getLHS(), RC->getLHS())) 592 return true; 593 if (operator()(RC->getLHS(), LC->getLHS())) 594 return false; 595 if (operator()(LC->getRHS(), RC->getRHS())) 596 return true; 597 if (operator()(RC->getRHS(), LC->getRHS())) 598 return false; 599 return false; 600 } 601 602 // Compare cast expressions by operand. 603 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 604 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 605 return operator()(LC->getOperand(), RC->getOperand()); 606 } 607 608 llvm_unreachable("Unknown SCEV kind!"); 609 return false; 610 } 611 }; 612} 613 614/// GroupByComplexity - Given a list of SCEV objects, order them by their 615/// complexity, and group objects of the same complexity together by value. 616/// When this routine is finished, we know that any duplicates in the vector are 617/// consecutive and that complexity is monotonically increasing. 618/// 619/// Note that we go take special precautions to ensure that we get determinstic 620/// results from this routine. In other words, we don't want the results of 621/// this to depend on where the addresses of various SCEV objects happened to 622/// land in memory. 623/// 624static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 625 LoopInfo *LI) { 626 if (Ops.size() < 2) return; // Noop 627 if (Ops.size() == 2) { 628 // This is the common case, which also happens to be trivially simple. 629 // Special case it. 630 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 631 std::swap(Ops[0], Ops[1]); 632 return; 633 } 634 635 // Do the rough sort by complexity. 636 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 637 638 // Now that we are sorted by complexity, group elements of the same 639 // complexity. Note that this is, at worst, N^2, but the vector is likely to 640 // be extremely short in practice. Note that we take this approach because we 641 // do not want to depend on the addresses of the objects we are grouping. 642 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 643 const SCEV *S = Ops[i]; 644 unsigned Complexity = S->getSCEVType(); 645 646 // If there are any objects of the same complexity and same value as this 647 // one, group them. 648 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 649 if (Ops[j] == S) { // Found a duplicate. 650 // Move it to immediately after i'th element. 651 std::swap(Ops[i+1], Ops[j]); 652 ++i; // no need to rescan it. 653 if (i == e-2) return; // Done! 654 } 655 } 656 } 657} 658 659 660 661//===----------------------------------------------------------------------===// 662// Simple SCEV method implementations 663//===----------------------------------------------------------------------===// 664 665/// BinomialCoefficient - Compute BC(It, K). The result has width W. 666/// Assume, K > 0. 667static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 668 ScalarEvolution &SE, 669 const Type* ResultTy) { 670 // Handle the simplest case efficiently. 671 if (K == 1) 672 return SE.getTruncateOrZeroExtend(It, ResultTy); 673 674 // We are using the following formula for BC(It, K): 675 // 676 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 677 // 678 // Suppose, W is the bitwidth of the return value. We must be prepared for 679 // overflow. Hence, we must assure that the result of our computation is 680 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 681 // safe in modular arithmetic. 682 // 683 // However, this code doesn't use exactly that formula; the formula it uses 684 // is something like the following, where T is the number of factors of 2 in 685 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 686 // exponentiation: 687 // 688 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 689 // 690 // This formula is trivially equivalent to the previous formula. However, 691 // this formula can be implemented much more efficiently. The trick is that 692 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 693 // arithmetic. To do exact division in modular arithmetic, all we have 694 // to do is multiply by the inverse. Therefore, this step can be done at 695 // width W. 696 // 697 // The next issue is how to safely do the division by 2^T. The way this 698 // is done is by doing the multiplication step at a width of at least W + T 699 // bits. This way, the bottom W+T bits of the product are accurate. Then, 700 // when we perform the division by 2^T (which is equivalent to a right shift 701 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 702 // truncated out after the division by 2^T. 703 // 704 // In comparison to just directly using the first formula, this technique 705 // is much more efficient; using the first formula requires W * K bits, 706 // but this formula less than W + K bits. Also, the first formula requires 707 // a division step, whereas this formula only requires multiplies and shifts. 708 // 709 // It doesn't matter whether the subtraction step is done in the calculation 710 // width or the input iteration count's width; if the subtraction overflows, 711 // the result must be zero anyway. We prefer here to do it in the width of 712 // the induction variable because it helps a lot for certain cases; CodeGen 713 // isn't smart enough to ignore the overflow, which leads to much less 714 // efficient code if the width of the subtraction is wider than the native 715 // register width. 716 // 717 // (It's possible to not widen at all by pulling out factors of 2 before 718 // the multiplication; for example, K=2 can be calculated as 719 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 720 // extra arithmetic, so it's not an obvious win, and it gets 721 // much more complicated for K > 3.) 722 723 // Protection from insane SCEVs; this bound is conservative, 724 // but it probably doesn't matter. 725 if (K > 1000) 726 return SE.getCouldNotCompute(); 727 728 unsigned W = SE.getTypeSizeInBits(ResultTy); 729 730 // Calculate K! / 2^T and T; we divide out the factors of two before 731 // multiplying for calculating K! / 2^T to avoid overflow. 732 // Other overflow doesn't matter because we only care about the bottom 733 // W bits of the result. 734 APInt OddFactorial(W, 1); 735 unsigned T = 1; 736 for (unsigned i = 3; i <= K; ++i) { 737 APInt Mult(W, i); 738 unsigned TwoFactors = Mult.countTrailingZeros(); 739 T += TwoFactors; 740 Mult = Mult.lshr(TwoFactors); 741 OddFactorial *= Mult; 742 } 743 744 // We need at least W + T bits for the multiplication step 745 unsigned CalculationBits = W + T; 746 747 // Calcuate 2^T, at width T+W. 748 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 749 750 // Calculate the multiplicative inverse of K! / 2^T; 751 // this multiplication factor will perform the exact division by 752 // K! / 2^T. 753 APInt Mod = APInt::getSignedMinValue(W+1); 754 APInt MultiplyFactor = OddFactorial.zext(W+1); 755 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 756 MultiplyFactor = MultiplyFactor.trunc(W); 757 758 // Calculate the product, at width T+W 759 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 760 CalculationBits); 761 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 762 for (unsigned i = 1; i != K; ++i) { 763 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 764 Dividend = SE.getMulExpr(Dividend, 765 SE.getTruncateOrZeroExtend(S, CalculationTy)); 766 } 767 768 // Divide by 2^T 769 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 770 771 // Truncate the result, and divide by K! / 2^T. 772 773 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 774 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 775} 776 777/// evaluateAtIteration - Return the value of this chain of recurrences at 778/// the specified iteration number. We can evaluate this recurrence by 779/// multiplying each element in the chain by the binomial coefficient 780/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 781/// 782/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 783/// 784/// where BC(It, k) stands for binomial coefficient. 785/// 786const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 787 ScalarEvolution &SE) const { 788 const SCEV *Result = getStart(); 789 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 790 // The computation is correct in the face of overflow provided that the 791 // multiplication is performed _after_ the evaluation of the binomial 792 // coefficient. 793 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 794 if (isa<SCEVCouldNotCompute>(Coeff)) 795 return Coeff; 796 797 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 798 } 799 return Result; 800} 801 802//===----------------------------------------------------------------------===// 803// SCEV Expression folder implementations 804//===----------------------------------------------------------------------===// 805 806const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 807 const Type *Ty) { 808 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 809 "This is not a truncating conversion!"); 810 assert(isSCEVable(Ty) && 811 "This is not a conversion to a SCEVable type!"); 812 Ty = getEffectiveSCEVType(Ty); 813 814 FoldingSetNodeID ID; 815 ID.AddInteger(scTruncate); 816 ID.AddPointer(Op); 817 ID.AddPointer(Ty); 818 void *IP = 0; 819 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 820 821 // Fold if the operand is constant. 822 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 823 return getConstant( 824 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 825 826 // trunc(trunc(x)) --> trunc(x) 827 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 828 return getTruncateExpr(ST->getOperand(), Ty); 829 830 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 831 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 832 return getTruncateOrSignExtend(SS->getOperand(), Ty); 833 834 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 835 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 836 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 837 838 // If the input value is a chrec scev, truncate the chrec's operands. 839 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 840 SmallVector<const SCEV *, 4> Operands; 841 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 842 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 843 return getAddRecExpr(Operands, AddRec->getLoop()); 844 } 845 846 // The cast wasn't folded; create an explicit cast node. 847 // Recompute the insert position, as it may have been invalidated. 848 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 849 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 850 new (S) SCEVTruncateExpr(ID, Op, Ty); 851 UniqueSCEVs.InsertNode(S, IP); 852 return S; 853} 854 855const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 856 const Type *Ty) { 857 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 858 "This is not an extending conversion!"); 859 assert(isSCEVable(Ty) && 860 "This is not a conversion to a SCEVable type!"); 861 Ty = getEffectiveSCEVType(Ty); 862 863 // Fold if the operand is constant. 864 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 865 const Type *IntTy = getEffectiveSCEVType(Ty); 866 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 867 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 868 return getConstant(cast<ConstantInt>(C)); 869 } 870 871 // zext(zext(x)) --> zext(x) 872 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 873 return getZeroExtendExpr(SZ->getOperand(), Ty); 874 875 // Before doing any expensive analysis, check to see if we've already 876 // computed a SCEV for this Op and Ty. 877 FoldingSetNodeID ID; 878 ID.AddInteger(scZeroExtend); 879 ID.AddPointer(Op); 880 ID.AddPointer(Ty); 881 void *IP = 0; 882 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 883 884 // If the input value is a chrec scev, and we can prove that the value 885 // did not overflow the old, smaller, value, we can zero extend all of the 886 // operands (often constants). This allows analysis of something like 887 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 888 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 889 if (AR->isAffine()) { 890 const SCEV *Start = AR->getStart(); 891 const SCEV *Step = AR->getStepRecurrence(*this); 892 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 893 const Loop *L = AR->getLoop(); 894 895 // If we have special knowledge that this addrec won't overflow, 896 // we don't need to do any further analysis. 897 if (AR->hasNoUnsignedWrap()) 898 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 899 getZeroExtendExpr(Step, Ty), 900 L); 901 902 // Check whether the backedge-taken count is SCEVCouldNotCompute. 903 // Note that this serves two purposes: It filters out loops that are 904 // simply not analyzable, and it covers the case where this code is 905 // being called from within backedge-taken count analysis, such that 906 // attempting to ask for the backedge-taken count would likely result 907 // in infinite recursion. In the later case, the analysis code will 908 // cope with a conservative value, and it will take care to purge 909 // that value once it has finished. 910 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 911 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 912 // Manually compute the final value for AR, checking for 913 // overflow. 914 915 // Check whether the backedge-taken count can be losslessly casted to 916 // the addrec's type. The count is always unsigned. 917 const SCEV *CastedMaxBECount = 918 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 919 const SCEV *RecastedMaxBECount = 920 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 921 if (MaxBECount == RecastedMaxBECount) { 922 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 923 // Check whether Start+Step*MaxBECount has no unsigned overflow. 924 const SCEV *ZMul = 925 getMulExpr(CastedMaxBECount, 926 getTruncateOrZeroExtend(Step, Start->getType())); 927 const SCEV *Add = getAddExpr(Start, ZMul); 928 const SCEV *OperandExtendedAdd = 929 getAddExpr(getZeroExtendExpr(Start, WideTy), 930 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 931 getZeroExtendExpr(Step, WideTy))); 932 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 933 // Return the expression with the addrec on the outside. 934 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 935 getZeroExtendExpr(Step, Ty), 936 L); 937 938 // Similar to above, only this time treat the step value as signed. 939 // This covers loops that count down. 940 const SCEV *SMul = 941 getMulExpr(CastedMaxBECount, 942 getTruncateOrSignExtend(Step, Start->getType())); 943 Add = getAddExpr(Start, SMul); 944 OperandExtendedAdd = 945 getAddExpr(getZeroExtendExpr(Start, WideTy), 946 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 947 getSignExtendExpr(Step, WideTy))); 948 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 949 // Return the expression with the addrec on the outside. 950 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 951 getSignExtendExpr(Step, Ty), 952 L); 953 } 954 955 // If the backedge is guarded by a comparison with the pre-inc value 956 // the addrec is safe. Also, if the entry is guarded by a comparison 957 // with the start value and the backedge is guarded by a comparison 958 // with the post-inc value, the addrec is safe. 959 if (isKnownPositive(Step)) { 960 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 961 getUnsignedRange(Step).getUnsignedMax()); 962 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 963 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 964 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 965 AR->getPostIncExpr(*this), N))) 966 // Return the expression with the addrec on the outside. 967 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 968 getZeroExtendExpr(Step, Ty), 969 L); 970 } else if (isKnownNegative(Step)) { 971 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 972 getSignedRange(Step).getSignedMin()); 973 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 974 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 975 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 976 AR->getPostIncExpr(*this), N))) 977 // Return the expression with the addrec on the outside. 978 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 979 getSignExtendExpr(Step, Ty), 980 L); 981 } 982 } 983 } 984 985 // The cast wasn't folded; create an explicit cast node. 986 // Recompute the insert position, as it may have been invalidated. 987 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 988 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 989 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 990 UniqueSCEVs.InsertNode(S, IP); 991 return S; 992} 993 994const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 995 const Type *Ty) { 996 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 997 "This is not an extending conversion!"); 998 assert(isSCEVable(Ty) && 999 "This is not a conversion to a SCEVable type!"); 1000 Ty = getEffectiveSCEVType(Ty); 1001 1002 // Fold if the operand is constant. 1003 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 1004 const Type *IntTy = getEffectiveSCEVType(Ty); 1005 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 1006 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 1007 return getConstant(cast<ConstantInt>(C)); 1008 } 1009 1010 // sext(sext(x)) --> sext(x) 1011 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1012 return getSignExtendExpr(SS->getOperand(), Ty); 1013 1014 // Before doing any expensive analysis, check to see if we've already 1015 // computed a SCEV for this Op and Ty. 1016 FoldingSetNodeID ID; 1017 ID.AddInteger(scSignExtend); 1018 ID.AddPointer(Op); 1019 ID.AddPointer(Ty); 1020 void *IP = 0; 1021 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1022 1023 // If the input value is a chrec scev, and we can prove that the value 1024 // did not overflow the old, smaller, value, we can sign extend all of the 1025 // operands (often constants). This allows analysis of something like 1026 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1027 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1028 if (AR->isAffine()) { 1029 const SCEV *Start = AR->getStart(); 1030 const SCEV *Step = AR->getStepRecurrence(*this); 1031 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1032 const Loop *L = AR->getLoop(); 1033 1034 // If we have special knowledge that this addrec won't overflow, 1035 // we don't need to do any further analysis. 1036 if (AR->hasNoSignedWrap()) 1037 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1038 getSignExtendExpr(Step, Ty), 1039 L); 1040 1041 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1042 // Note that this serves two purposes: It filters out loops that are 1043 // simply not analyzable, and it covers the case where this code is 1044 // being called from within backedge-taken count analysis, such that 1045 // attempting to ask for the backedge-taken count would likely result 1046 // in infinite recursion. In the later case, the analysis code will 1047 // cope with a conservative value, and it will take care to purge 1048 // that value once it has finished. 1049 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1050 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1051 // Manually compute the final value for AR, checking for 1052 // overflow. 1053 1054 // Check whether the backedge-taken count can be losslessly casted to 1055 // the addrec's type. The count is always unsigned. 1056 const SCEV *CastedMaxBECount = 1057 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1058 const SCEV *RecastedMaxBECount = 1059 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1060 if (MaxBECount == RecastedMaxBECount) { 1061 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1062 // Check whether Start+Step*MaxBECount has no signed overflow. 1063 const SCEV *SMul = 1064 getMulExpr(CastedMaxBECount, 1065 getTruncateOrSignExtend(Step, Start->getType())); 1066 const SCEV *Add = getAddExpr(Start, SMul); 1067 const SCEV *OperandExtendedAdd = 1068 getAddExpr(getSignExtendExpr(Start, WideTy), 1069 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1070 getSignExtendExpr(Step, WideTy))); 1071 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1072 // Return the expression with the addrec on the outside. 1073 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1074 getSignExtendExpr(Step, Ty), 1075 L); 1076 1077 // Similar to above, only this time treat the step value as unsigned. 1078 // This covers loops that count up with an unsigned step. 1079 const SCEV *UMul = 1080 getMulExpr(CastedMaxBECount, 1081 getTruncateOrZeroExtend(Step, Start->getType())); 1082 Add = getAddExpr(Start, UMul); 1083 OperandExtendedAdd = 1084 getAddExpr(getSignExtendExpr(Start, WideTy), 1085 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1086 getZeroExtendExpr(Step, WideTy))); 1087 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1088 // Return the expression with the addrec on the outside. 1089 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1090 getZeroExtendExpr(Step, Ty), 1091 L); 1092 } 1093 1094 // If the backedge is guarded by a comparison with the pre-inc value 1095 // the addrec is safe. Also, if the entry is guarded by a comparison 1096 // with the start value and the backedge is guarded by a comparison 1097 // with the post-inc value, the addrec is safe. 1098 if (isKnownPositive(Step)) { 1099 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1100 getSignedRange(Step).getSignedMax()); 1101 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1102 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1103 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1104 AR->getPostIncExpr(*this), N))) 1105 // Return the expression with the addrec on the outside. 1106 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1107 getSignExtendExpr(Step, Ty), 1108 L); 1109 } else if (isKnownNegative(Step)) { 1110 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1111 getSignedRange(Step).getSignedMin()); 1112 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1113 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1114 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1115 AR->getPostIncExpr(*this), N))) 1116 // Return the expression with the addrec on the outside. 1117 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1118 getSignExtendExpr(Step, Ty), 1119 L); 1120 } 1121 } 1122 } 1123 1124 // The cast wasn't folded; create an explicit cast node. 1125 // Recompute the insert position, as it may have been invalidated. 1126 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1127 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 1128 new (S) SCEVSignExtendExpr(ID, Op, Ty); 1129 UniqueSCEVs.InsertNode(S, IP); 1130 return S; 1131} 1132 1133/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1134/// unspecified bits out to the given type. 1135/// 1136const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1137 const Type *Ty) { 1138 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1139 "This is not an extending conversion!"); 1140 assert(isSCEVable(Ty) && 1141 "This is not a conversion to a SCEVable type!"); 1142 Ty = getEffectiveSCEVType(Ty); 1143 1144 // Sign-extend negative constants. 1145 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1146 if (SC->getValue()->getValue().isNegative()) 1147 return getSignExtendExpr(Op, Ty); 1148 1149 // Peel off a truncate cast. 1150 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1151 const SCEV *NewOp = T->getOperand(); 1152 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1153 return getAnyExtendExpr(NewOp, Ty); 1154 return getTruncateOrNoop(NewOp, Ty); 1155 } 1156 1157 // Next try a zext cast. If the cast is folded, use it. 1158 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1159 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1160 return ZExt; 1161 1162 // Next try a sext cast. If the cast is folded, use it. 1163 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1164 if (!isa<SCEVSignExtendExpr>(SExt)) 1165 return SExt; 1166 1167 // Force the cast to be folded into the operands of an addrec. 1168 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1169 SmallVector<const SCEV *, 4> Ops; 1170 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1171 I != E; ++I) 1172 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1173 return getAddRecExpr(Ops, AR->getLoop()); 1174 } 1175 1176 // If the expression is obviously signed, use the sext cast value. 1177 if (isa<SCEVSMaxExpr>(Op)) 1178 return SExt; 1179 1180 // Absent any other information, use the zext cast value. 1181 return ZExt; 1182} 1183 1184/// CollectAddOperandsWithScales - Process the given Ops list, which is 1185/// a list of operands to be added under the given scale, update the given 1186/// map. This is a helper function for getAddRecExpr. As an example of 1187/// what it does, given a sequence of operands that would form an add 1188/// expression like this: 1189/// 1190/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1191/// 1192/// where A and B are constants, update the map with these values: 1193/// 1194/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1195/// 1196/// and add 13 + A*B*29 to AccumulatedConstant. 1197/// This will allow getAddRecExpr to produce this: 1198/// 1199/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1200/// 1201/// This form often exposes folding opportunities that are hidden in 1202/// the original operand list. 1203/// 1204/// Return true iff it appears that any interesting folding opportunities 1205/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1206/// the common case where no interesting opportunities are present, and 1207/// is also used as a check to avoid infinite recursion. 1208/// 1209static bool 1210CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1211 SmallVector<const SCEV *, 8> &NewOps, 1212 APInt &AccumulatedConstant, 1213 const SmallVectorImpl<const SCEV *> &Ops, 1214 const APInt &Scale, 1215 ScalarEvolution &SE) { 1216 bool Interesting = false; 1217 1218 // Iterate over the add operands. 1219 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1220 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1221 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1222 APInt NewScale = 1223 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1224 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1225 // A multiplication of a constant with another add; recurse. 1226 Interesting |= 1227 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1228 cast<SCEVAddExpr>(Mul->getOperand(1)) 1229 ->getOperands(), 1230 NewScale, SE); 1231 } else { 1232 // A multiplication of a constant with some other value. Update 1233 // the map. 1234 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1235 const SCEV *Key = SE.getMulExpr(MulOps); 1236 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1237 M.insert(std::make_pair(Key, NewScale)); 1238 if (Pair.second) { 1239 NewOps.push_back(Pair.first->first); 1240 } else { 1241 Pair.first->second += NewScale; 1242 // The map already had an entry for this value, which may indicate 1243 // a folding opportunity. 1244 Interesting = true; 1245 } 1246 } 1247 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1248 // Pull a buried constant out to the outside. 1249 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1250 Interesting = true; 1251 AccumulatedConstant += Scale * C->getValue()->getValue(); 1252 } else { 1253 // An ordinary operand. Update the map. 1254 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1255 M.insert(std::make_pair(Ops[i], Scale)); 1256 if (Pair.second) { 1257 NewOps.push_back(Pair.first->first); 1258 } else { 1259 Pair.first->second += Scale; 1260 // The map already had an entry for this value, which may indicate 1261 // a folding opportunity. 1262 Interesting = true; 1263 } 1264 } 1265 } 1266 1267 return Interesting; 1268} 1269 1270namespace { 1271 struct APIntCompare { 1272 bool operator()(const APInt &LHS, const APInt &RHS) const { 1273 return LHS.ult(RHS); 1274 } 1275 }; 1276} 1277 1278/// getAddExpr - Get a canonical add expression, or something simpler if 1279/// possible. 1280const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1281 bool HasNUW, bool HasNSW) { 1282 assert(!Ops.empty() && "Cannot get empty add!"); 1283 if (Ops.size() == 1) return Ops[0]; 1284#ifndef NDEBUG 1285 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1286 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1287 getEffectiveSCEVType(Ops[0]->getType()) && 1288 "SCEVAddExpr operand types don't match!"); 1289#endif 1290 1291 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1292 if (!HasNUW && HasNSW) { 1293 bool All = true; 1294 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1295 if (!isKnownNonNegative(Ops[i])) { 1296 All = false; 1297 break; 1298 } 1299 if (All) HasNUW = true; 1300 } 1301 1302 // Sort by complexity, this groups all similar expression types together. 1303 GroupByComplexity(Ops, LI); 1304 1305 // If there are any constants, fold them together. 1306 unsigned Idx = 0; 1307 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1308 ++Idx; 1309 assert(Idx < Ops.size()); 1310 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1311 // We found two constants, fold them together! 1312 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1313 RHSC->getValue()->getValue()); 1314 if (Ops.size() == 2) return Ops[0]; 1315 Ops.erase(Ops.begin()+1); // Erase the folded element 1316 LHSC = cast<SCEVConstant>(Ops[0]); 1317 } 1318 1319 // If we are left with a constant zero being added, strip it off. 1320 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1321 Ops.erase(Ops.begin()); 1322 --Idx; 1323 } 1324 } 1325 1326 if (Ops.size() == 1) return Ops[0]; 1327 1328 // Okay, check to see if the same value occurs in the operand list twice. If 1329 // so, merge them together into an multiply expression. Since we sorted the 1330 // list, these values are required to be adjacent. 1331 const Type *Ty = Ops[0]->getType(); 1332 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1333 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1334 // Found a match, merge the two values into a multiply, and add any 1335 // remaining values to the result. 1336 const SCEV *Two = getIntegerSCEV(2, Ty); 1337 const SCEV *Mul = getMulExpr(Ops[i], Two); 1338 if (Ops.size() == 2) 1339 return Mul; 1340 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1341 Ops.push_back(Mul); 1342 return getAddExpr(Ops, HasNUW, HasNSW); 1343 } 1344 1345 // Check for truncates. If all the operands are truncated from the same 1346 // type, see if factoring out the truncate would permit the result to be 1347 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1348 // if the contents of the resulting outer trunc fold to something simple. 1349 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1350 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1351 const Type *DstType = Trunc->getType(); 1352 const Type *SrcType = Trunc->getOperand()->getType(); 1353 SmallVector<const SCEV *, 8> LargeOps; 1354 bool Ok = true; 1355 // Check all the operands to see if they can be represented in the 1356 // source type of the truncate. 1357 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1358 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1359 if (T->getOperand()->getType() != SrcType) { 1360 Ok = false; 1361 break; 1362 } 1363 LargeOps.push_back(T->getOperand()); 1364 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1365 // This could be either sign or zero extension, but sign extension 1366 // is much more likely to be foldable here. 1367 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1368 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1369 SmallVector<const SCEV *, 8> LargeMulOps; 1370 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1371 if (const SCEVTruncateExpr *T = 1372 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1373 if (T->getOperand()->getType() != SrcType) { 1374 Ok = false; 1375 break; 1376 } 1377 LargeMulOps.push_back(T->getOperand()); 1378 } else if (const SCEVConstant *C = 1379 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1380 // This could be either sign or zero extension, but sign extension 1381 // is much more likely to be foldable here. 1382 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1383 } else { 1384 Ok = false; 1385 break; 1386 } 1387 } 1388 if (Ok) 1389 LargeOps.push_back(getMulExpr(LargeMulOps)); 1390 } else { 1391 Ok = false; 1392 break; 1393 } 1394 } 1395 if (Ok) { 1396 // Evaluate the expression in the larger type. 1397 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1398 // If it folds to something simple, use it. Otherwise, don't. 1399 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1400 return getTruncateExpr(Fold, DstType); 1401 } 1402 } 1403 1404 // Skip past any other cast SCEVs. 1405 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1406 ++Idx; 1407 1408 // If there are add operands they would be next. 1409 if (Idx < Ops.size()) { 1410 bool DeletedAdd = false; 1411 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1412 // If we have an add, expand the add operands onto the end of the operands 1413 // list. 1414 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1415 Ops.erase(Ops.begin()+Idx); 1416 DeletedAdd = true; 1417 } 1418 1419 // If we deleted at least one add, we added operands to the end of the list, 1420 // and they are not necessarily sorted. Recurse to resort and resimplify 1421 // any operands we just aquired. 1422 if (DeletedAdd) 1423 return getAddExpr(Ops); 1424 } 1425 1426 // Skip over the add expression until we get to a multiply. 1427 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1428 ++Idx; 1429 1430 // Check to see if there are any folding opportunities present with 1431 // operands multiplied by constant values. 1432 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1433 uint64_t BitWidth = getTypeSizeInBits(Ty); 1434 DenseMap<const SCEV *, APInt> M; 1435 SmallVector<const SCEV *, 8> NewOps; 1436 APInt AccumulatedConstant(BitWidth, 0); 1437 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1438 Ops, APInt(BitWidth, 1), *this)) { 1439 // Some interesting folding opportunity is present, so its worthwhile to 1440 // re-generate the operands list. Group the operands by constant scale, 1441 // to avoid multiplying by the same constant scale multiple times. 1442 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1443 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1444 E = NewOps.end(); I != E; ++I) 1445 MulOpLists[M.find(*I)->second].push_back(*I); 1446 // Re-generate the operands list. 1447 Ops.clear(); 1448 if (AccumulatedConstant != 0) 1449 Ops.push_back(getConstant(AccumulatedConstant)); 1450 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1451 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1452 if (I->first != 0) 1453 Ops.push_back(getMulExpr(getConstant(I->first), 1454 getAddExpr(I->second))); 1455 if (Ops.empty()) 1456 return getIntegerSCEV(0, Ty); 1457 if (Ops.size() == 1) 1458 return Ops[0]; 1459 return getAddExpr(Ops); 1460 } 1461 } 1462 1463 // If we are adding something to a multiply expression, make sure the 1464 // something is not already an operand of the multiply. If so, merge it into 1465 // the multiply. 1466 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1467 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1468 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1469 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1470 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1471 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1472 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1473 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1474 if (Mul->getNumOperands() != 2) { 1475 // If the multiply has more than two operands, we must get the 1476 // Y*Z term. 1477 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1478 MulOps.erase(MulOps.begin()+MulOp); 1479 InnerMul = getMulExpr(MulOps); 1480 } 1481 const SCEV *One = getIntegerSCEV(1, Ty); 1482 const SCEV *AddOne = getAddExpr(InnerMul, One); 1483 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1484 if (Ops.size() == 2) return OuterMul; 1485 if (AddOp < Idx) { 1486 Ops.erase(Ops.begin()+AddOp); 1487 Ops.erase(Ops.begin()+Idx-1); 1488 } else { 1489 Ops.erase(Ops.begin()+Idx); 1490 Ops.erase(Ops.begin()+AddOp-1); 1491 } 1492 Ops.push_back(OuterMul); 1493 return getAddExpr(Ops); 1494 } 1495 1496 // Check this multiply against other multiplies being added together. 1497 for (unsigned OtherMulIdx = Idx+1; 1498 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1499 ++OtherMulIdx) { 1500 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1501 // If MulOp occurs in OtherMul, we can fold the two multiplies 1502 // together. 1503 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1504 OMulOp != e; ++OMulOp) 1505 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1506 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1507 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1508 if (Mul->getNumOperands() != 2) { 1509 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1510 Mul->op_end()); 1511 MulOps.erase(MulOps.begin()+MulOp); 1512 InnerMul1 = getMulExpr(MulOps); 1513 } 1514 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1515 if (OtherMul->getNumOperands() != 2) { 1516 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1517 OtherMul->op_end()); 1518 MulOps.erase(MulOps.begin()+OMulOp); 1519 InnerMul2 = getMulExpr(MulOps); 1520 } 1521 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1522 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1523 if (Ops.size() == 2) return OuterMul; 1524 Ops.erase(Ops.begin()+Idx); 1525 Ops.erase(Ops.begin()+OtherMulIdx-1); 1526 Ops.push_back(OuterMul); 1527 return getAddExpr(Ops); 1528 } 1529 } 1530 } 1531 } 1532 1533 // If there are any add recurrences in the operands list, see if any other 1534 // added values are loop invariant. If so, we can fold them into the 1535 // recurrence. 1536 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1537 ++Idx; 1538 1539 // Scan over all recurrences, trying to fold loop invariants into them. 1540 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1541 // Scan all of the other operands to this add and add them to the vector if 1542 // they are loop invariant w.r.t. the recurrence. 1543 SmallVector<const SCEV *, 8> LIOps; 1544 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1545 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1546 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1547 LIOps.push_back(Ops[i]); 1548 Ops.erase(Ops.begin()+i); 1549 --i; --e; 1550 } 1551 1552 // If we found some loop invariants, fold them into the recurrence. 1553 if (!LIOps.empty()) { 1554 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1555 LIOps.push_back(AddRec->getStart()); 1556 1557 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1558 AddRec->op_end()); 1559 AddRecOps[0] = getAddExpr(LIOps); 1560 1561 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition 1562 // is not associative so this isn't necessarily safe. 1563 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1564 1565 // If all of the other operands were loop invariant, we are done. 1566 if (Ops.size() == 1) return NewRec; 1567 1568 // Otherwise, add the folded AddRec by the non-liv parts. 1569 for (unsigned i = 0;; ++i) 1570 if (Ops[i] == AddRec) { 1571 Ops[i] = NewRec; 1572 break; 1573 } 1574 return getAddExpr(Ops); 1575 } 1576 1577 // Okay, if there weren't any loop invariants to be folded, check to see if 1578 // there are multiple AddRec's with the same loop induction variable being 1579 // added together. If so, we can fold them. 1580 for (unsigned OtherIdx = Idx+1; 1581 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1582 if (OtherIdx != Idx) { 1583 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1584 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1585 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1586 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1587 AddRec->op_end()); 1588 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1589 if (i >= NewOps.size()) { 1590 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1591 OtherAddRec->op_end()); 1592 break; 1593 } 1594 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1595 } 1596 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1597 1598 if (Ops.size() == 2) return NewAddRec; 1599 1600 Ops.erase(Ops.begin()+Idx); 1601 Ops.erase(Ops.begin()+OtherIdx-1); 1602 Ops.push_back(NewAddRec); 1603 return getAddExpr(Ops); 1604 } 1605 } 1606 1607 // Otherwise couldn't fold anything into this recurrence. Move onto the 1608 // next one. 1609 } 1610 1611 // Okay, it looks like we really DO need an add expr. Check to see if we 1612 // already have one, otherwise create a new one. 1613 FoldingSetNodeID ID; 1614 ID.AddInteger(scAddExpr); 1615 ID.AddInteger(Ops.size()); 1616 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1617 ID.AddPointer(Ops[i]); 1618 void *IP = 0; 1619 SCEVAddExpr *S = 1620 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1621 if (!S) { 1622 S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1623 new (S) SCEVAddExpr(ID, Ops); 1624 UniqueSCEVs.InsertNode(S, IP); 1625 } 1626 if (HasNUW) S->setHasNoUnsignedWrap(true); 1627 if (HasNSW) S->setHasNoSignedWrap(true); 1628 return S; 1629} 1630 1631/// getMulExpr - Get a canonical multiply expression, or something simpler if 1632/// possible. 1633const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1634 bool HasNUW, bool HasNSW) { 1635 assert(!Ops.empty() && "Cannot get empty mul!"); 1636 if (Ops.size() == 1) return Ops[0]; 1637#ifndef NDEBUG 1638 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1639 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1640 getEffectiveSCEVType(Ops[0]->getType()) && 1641 "SCEVMulExpr operand types don't match!"); 1642#endif 1643 1644 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1645 if (!HasNUW && HasNSW) { 1646 bool All = true; 1647 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1648 if (!isKnownNonNegative(Ops[i])) { 1649 All = false; 1650 break; 1651 } 1652 if (All) HasNUW = true; 1653 } 1654 1655 // Sort by complexity, this groups all similar expression types together. 1656 GroupByComplexity(Ops, LI); 1657 1658 // If there are any constants, fold them together. 1659 unsigned Idx = 0; 1660 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1661 1662 // C1*(C2+V) -> C1*C2 + C1*V 1663 if (Ops.size() == 2) 1664 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1665 if (Add->getNumOperands() == 2 && 1666 isa<SCEVConstant>(Add->getOperand(0))) 1667 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1668 getMulExpr(LHSC, Add->getOperand(1))); 1669 1670 ++Idx; 1671 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1672 // We found two constants, fold them together! 1673 ConstantInt *Fold = ConstantInt::get(getContext(), 1674 LHSC->getValue()->getValue() * 1675 RHSC->getValue()->getValue()); 1676 Ops[0] = getConstant(Fold); 1677 Ops.erase(Ops.begin()+1); // Erase the folded element 1678 if (Ops.size() == 1) return Ops[0]; 1679 LHSC = cast<SCEVConstant>(Ops[0]); 1680 } 1681 1682 // If we are left with a constant one being multiplied, strip it off. 1683 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1684 Ops.erase(Ops.begin()); 1685 --Idx; 1686 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1687 // If we have a multiply of zero, it will always be zero. 1688 return Ops[0]; 1689 } else if (Ops[0]->isAllOnesValue()) { 1690 // If we have a mul by -1 of an add, try distributing the -1 among the 1691 // add operands. 1692 if (Ops.size() == 2) 1693 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1694 SmallVector<const SCEV *, 4> NewOps; 1695 bool AnyFolded = false; 1696 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1697 I != E; ++I) { 1698 const SCEV *Mul = getMulExpr(Ops[0], *I); 1699 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1700 NewOps.push_back(Mul); 1701 } 1702 if (AnyFolded) 1703 return getAddExpr(NewOps); 1704 } 1705 } 1706 } 1707 1708 // Skip over the add expression until we get to a multiply. 1709 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1710 ++Idx; 1711 1712 if (Ops.size() == 1) 1713 return Ops[0]; 1714 1715 // If there are mul operands inline them all into this expression. 1716 if (Idx < Ops.size()) { 1717 bool DeletedMul = false; 1718 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1719 // If we have an mul, expand the mul operands onto the end of the operands 1720 // list. 1721 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1722 Ops.erase(Ops.begin()+Idx); 1723 DeletedMul = true; 1724 } 1725 1726 // If we deleted at least one mul, we added operands to the end of the list, 1727 // and they are not necessarily sorted. Recurse to resort and resimplify 1728 // any operands we just aquired. 1729 if (DeletedMul) 1730 return getMulExpr(Ops); 1731 } 1732 1733 // If there are any add recurrences in the operands list, see if any other 1734 // added values are loop invariant. If so, we can fold them into the 1735 // recurrence. 1736 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1737 ++Idx; 1738 1739 // Scan over all recurrences, trying to fold loop invariants into them. 1740 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1741 // Scan all of the other operands to this mul and add them to the vector if 1742 // they are loop invariant w.r.t. the recurrence. 1743 SmallVector<const SCEV *, 8> LIOps; 1744 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1745 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1746 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1747 LIOps.push_back(Ops[i]); 1748 Ops.erase(Ops.begin()+i); 1749 --i; --e; 1750 } 1751 1752 // If we found some loop invariants, fold them into the recurrence. 1753 if (!LIOps.empty()) { 1754 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1755 SmallVector<const SCEV *, 4> NewOps; 1756 NewOps.reserve(AddRec->getNumOperands()); 1757 if (LIOps.size() == 1) { 1758 const SCEV *Scale = LIOps[0]; 1759 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1760 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1761 } else { 1762 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1763 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1764 MulOps.push_back(AddRec->getOperand(i)); 1765 NewOps.push_back(getMulExpr(MulOps)); 1766 } 1767 } 1768 1769 // It's tempting to propagate the NSW flag here, but nsw multiplication 1770 // is not associative so this isn't necessarily safe. 1771 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1772 HasNUW && AddRec->hasNoUnsignedWrap(), 1773 /*HasNSW=*/false); 1774 1775 // If all of the other operands were loop invariant, we are done. 1776 if (Ops.size() == 1) return NewRec; 1777 1778 // Otherwise, multiply the folded AddRec by the non-liv parts. 1779 for (unsigned i = 0;; ++i) 1780 if (Ops[i] == AddRec) { 1781 Ops[i] = NewRec; 1782 break; 1783 } 1784 return getMulExpr(Ops); 1785 } 1786 1787 // Okay, if there weren't any loop invariants to be folded, check to see if 1788 // there are multiple AddRec's with the same loop induction variable being 1789 // multiplied together. If so, we can fold them. 1790 for (unsigned OtherIdx = Idx+1; 1791 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1792 if (OtherIdx != Idx) { 1793 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1794 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1795 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1796 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1797 const SCEV *NewStart = getMulExpr(F->getStart(), 1798 G->getStart()); 1799 const SCEV *B = F->getStepRecurrence(*this); 1800 const SCEV *D = G->getStepRecurrence(*this); 1801 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1802 getMulExpr(G, B), 1803 getMulExpr(B, D)); 1804 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1805 F->getLoop()); 1806 if (Ops.size() == 2) return NewAddRec; 1807 1808 Ops.erase(Ops.begin()+Idx); 1809 Ops.erase(Ops.begin()+OtherIdx-1); 1810 Ops.push_back(NewAddRec); 1811 return getMulExpr(Ops); 1812 } 1813 } 1814 1815 // Otherwise couldn't fold anything into this recurrence. Move onto the 1816 // next one. 1817 } 1818 1819 // Okay, it looks like we really DO need an mul expr. Check to see if we 1820 // already have one, otherwise create a new one. 1821 FoldingSetNodeID ID; 1822 ID.AddInteger(scMulExpr); 1823 ID.AddInteger(Ops.size()); 1824 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1825 ID.AddPointer(Ops[i]); 1826 void *IP = 0; 1827 SCEVMulExpr *S = 1828 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1829 if (!S) { 1830 S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1831 new (S) SCEVMulExpr(ID, Ops); 1832 UniqueSCEVs.InsertNode(S, IP); 1833 } 1834 if (HasNUW) S->setHasNoUnsignedWrap(true); 1835 if (HasNSW) S->setHasNoSignedWrap(true); 1836 return S; 1837} 1838 1839/// getUDivExpr - Get a canonical unsigned division expression, or something 1840/// simpler if possible. 1841const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1842 const SCEV *RHS) { 1843 assert(getEffectiveSCEVType(LHS->getType()) == 1844 getEffectiveSCEVType(RHS->getType()) && 1845 "SCEVUDivExpr operand types don't match!"); 1846 1847 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1848 if (RHSC->getValue()->equalsInt(1)) 1849 return LHS; // X udiv 1 --> x 1850 if (RHSC->isZero()) 1851 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1852 1853 // Determine if the division can be folded into the operands of 1854 // its operands. 1855 // TODO: Generalize this to non-constants by using known-bits information. 1856 const Type *Ty = LHS->getType(); 1857 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1858 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1859 // For non-power-of-two values, effectively round the value up to the 1860 // nearest power of two. 1861 if (!RHSC->getValue()->getValue().isPowerOf2()) 1862 ++MaxShiftAmt; 1863 const IntegerType *ExtTy = 1864 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1865 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1866 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1867 if (const SCEVConstant *Step = 1868 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1869 if (!Step->getValue()->getValue() 1870 .urem(RHSC->getValue()->getValue()) && 1871 getZeroExtendExpr(AR, ExtTy) == 1872 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1873 getZeroExtendExpr(Step, ExtTy), 1874 AR->getLoop())) { 1875 SmallVector<const SCEV *, 4> Operands; 1876 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1877 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1878 return getAddRecExpr(Operands, AR->getLoop()); 1879 } 1880 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1881 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1882 SmallVector<const SCEV *, 4> Operands; 1883 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1884 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1885 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1886 // Find an operand that's safely divisible. 1887 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1888 const SCEV *Op = M->getOperand(i); 1889 const SCEV *Div = getUDivExpr(Op, RHSC); 1890 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1891 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1892 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1893 MOperands.end()); 1894 Operands[i] = Div; 1895 return getMulExpr(Operands); 1896 } 1897 } 1898 } 1899 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1900 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1901 SmallVector<const SCEV *, 4> Operands; 1902 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1903 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1904 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1905 Operands.clear(); 1906 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1907 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1908 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1909 break; 1910 Operands.push_back(Op); 1911 } 1912 if (Operands.size() == A->getNumOperands()) 1913 return getAddExpr(Operands); 1914 } 1915 } 1916 1917 // Fold if both operands are constant. 1918 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1919 Constant *LHSCV = LHSC->getValue(); 1920 Constant *RHSCV = RHSC->getValue(); 1921 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1922 RHSCV))); 1923 } 1924 } 1925 1926 FoldingSetNodeID ID; 1927 ID.AddInteger(scUDivExpr); 1928 ID.AddPointer(LHS); 1929 ID.AddPointer(RHS); 1930 void *IP = 0; 1931 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1932 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1933 new (S) SCEVUDivExpr(ID, LHS, RHS); 1934 UniqueSCEVs.InsertNode(S, IP); 1935 return S; 1936} 1937 1938 1939/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1940/// Simplify the expression as much as possible. 1941const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1942 const SCEV *Step, const Loop *L, 1943 bool HasNUW, bool HasNSW) { 1944 SmallVector<const SCEV *, 4> Operands; 1945 Operands.push_back(Start); 1946 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1947 if (StepChrec->getLoop() == L) { 1948 Operands.insert(Operands.end(), StepChrec->op_begin(), 1949 StepChrec->op_end()); 1950 return getAddRecExpr(Operands, L); 1951 } 1952 1953 Operands.push_back(Step); 1954 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1955} 1956 1957/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1958/// Simplify the expression as much as possible. 1959const SCEV * 1960ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1961 const Loop *L, 1962 bool HasNUW, bool HasNSW) { 1963 if (Operands.size() == 1) return Operands[0]; 1964#ifndef NDEBUG 1965 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1966 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1967 getEffectiveSCEVType(Operands[0]->getType()) && 1968 "SCEVAddRecExpr operand types don't match!"); 1969#endif 1970 1971 if (Operands.back()->isZero()) { 1972 Operands.pop_back(); 1973 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1974 } 1975 1976 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1977 if (!HasNUW && HasNSW) { 1978 bool All = true; 1979 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1980 if (!isKnownNonNegative(Operands[i])) { 1981 All = false; 1982 break; 1983 } 1984 if (All) HasNUW = true; 1985 } 1986 1987 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1988 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1989 const Loop *NestedLoop = NestedAR->getLoop(); 1990 if (L->contains(NestedLoop->getHeader()) ? 1991 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 1992 (!NestedLoop->contains(L->getHeader()) && 1993 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 1994 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1995 NestedAR->op_end()); 1996 Operands[0] = NestedAR->getStart(); 1997 // AddRecs require their operands be loop-invariant with respect to their 1998 // loops. Don't perform this transformation if it would break this 1999 // requirement. 2000 bool AllInvariant = true; 2001 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2002 if (!Operands[i]->isLoopInvariant(L)) { 2003 AllInvariant = false; 2004 break; 2005 } 2006 if (AllInvariant) { 2007 NestedOperands[0] = getAddRecExpr(Operands, L); 2008 AllInvariant = true; 2009 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2010 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2011 AllInvariant = false; 2012 break; 2013 } 2014 if (AllInvariant) 2015 // Ok, both add recurrences are valid after the transformation. 2016 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2017 } 2018 // Reset Operands to its original state. 2019 Operands[0] = NestedAR; 2020 } 2021 } 2022 2023 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2024 // already have one, otherwise create a new one. 2025 FoldingSetNodeID ID; 2026 ID.AddInteger(scAddRecExpr); 2027 ID.AddInteger(Operands.size()); 2028 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2029 ID.AddPointer(Operands[i]); 2030 ID.AddPointer(L); 2031 void *IP = 0; 2032 SCEVAddRecExpr *S = 2033 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2034 if (!S) { 2035 S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 2036 new (S) SCEVAddRecExpr(ID, Operands, L); 2037 UniqueSCEVs.InsertNode(S, IP); 2038 } 2039 if (HasNUW) S->setHasNoUnsignedWrap(true); 2040 if (HasNSW) S->setHasNoSignedWrap(true); 2041 return S; 2042} 2043 2044const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2045 const SCEV *RHS) { 2046 SmallVector<const SCEV *, 2> Ops; 2047 Ops.push_back(LHS); 2048 Ops.push_back(RHS); 2049 return getSMaxExpr(Ops); 2050} 2051 2052const SCEV * 2053ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2054 assert(!Ops.empty() && "Cannot get empty smax!"); 2055 if (Ops.size() == 1) return Ops[0]; 2056#ifndef NDEBUG 2057 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2058 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2059 getEffectiveSCEVType(Ops[0]->getType()) && 2060 "SCEVSMaxExpr operand types don't match!"); 2061#endif 2062 2063 // Sort by complexity, this groups all similar expression types together. 2064 GroupByComplexity(Ops, LI); 2065 2066 // If there are any constants, fold them together. 2067 unsigned Idx = 0; 2068 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2069 ++Idx; 2070 assert(Idx < Ops.size()); 2071 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2072 // We found two constants, fold them together! 2073 ConstantInt *Fold = ConstantInt::get(getContext(), 2074 APIntOps::smax(LHSC->getValue()->getValue(), 2075 RHSC->getValue()->getValue())); 2076 Ops[0] = getConstant(Fold); 2077 Ops.erase(Ops.begin()+1); // Erase the folded element 2078 if (Ops.size() == 1) return Ops[0]; 2079 LHSC = cast<SCEVConstant>(Ops[0]); 2080 } 2081 2082 // If we are left with a constant minimum-int, strip it off. 2083 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2084 Ops.erase(Ops.begin()); 2085 --Idx; 2086 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2087 // If we have an smax with a constant maximum-int, it will always be 2088 // maximum-int. 2089 return Ops[0]; 2090 } 2091 } 2092 2093 if (Ops.size() == 1) return Ops[0]; 2094 2095 // Find the first SMax 2096 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2097 ++Idx; 2098 2099 // Check to see if one of the operands is an SMax. If so, expand its operands 2100 // onto our operand list, and recurse to simplify. 2101 if (Idx < Ops.size()) { 2102 bool DeletedSMax = false; 2103 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2104 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 2105 Ops.erase(Ops.begin()+Idx); 2106 DeletedSMax = true; 2107 } 2108 2109 if (DeletedSMax) 2110 return getSMaxExpr(Ops); 2111 } 2112 2113 // Okay, check to see if the same value occurs in the operand list twice. If 2114 // so, delete one. Since we sorted the list, these values are required to 2115 // be adjacent. 2116 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2117 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 2118 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2119 --i; --e; 2120 } 2121 2122 if (Ops.size() == 1) return Ops[0]; 2123 2124 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2125 2126 // Okay, it looks like we really DO need an smax expr. Check to see if we 2127 // already have one, otherwise create a new one. 2128 FoldingSetNodeID ID; 2129 ID.AddInteger(scSMaxExpr); 2130 ID.AddInteger(Ops.size()); 2131 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2132 ID.AddPointer(Ops[i]); 2133 void *IP = 0; 2134 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2135 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 2136 new (S) SCEVSMaxExpr(ID, Ops); 2137 UniqueSCEVs.InsertNode(S, IP); 2138 return S; 2139} 2140 2141const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2142 const SCEV *RHS) { 2143 SmallVector<const SCEV *, 2> Ops; 2144 Ops.push_back(LHS); 2145 Ops.push_back(RHS); 2146 return getUMaxExpr(Ops); 2147} 2148 2149const SCEV * 2150ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2151 assert(!Ops.empty() && "Cannot get empty umax!"); 2152 if (Ops.size() == 1) return Ops[0]; 2153#ifndef NDEBUG 2154 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2155 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2156 getEffectiveSCEVType(Ops[0]->getType()) && 2157 "SCEVUMaxExpr operand types don't match!"); 2158#endif 2159 2160 // Sort by complexity, this groups all similar expression types together. 2161 GroupByComplexity(Ops, LI); 2162 2163 // If there are any constants, fold them together. 2164 unsigned Idx = 0; 2165 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2166 ++Idx; 2167 assert(Idx < Ops.size()); 2168 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2169 // We found two constants, fold them together! 2170 ConstantInt *Fold = ConstantInt::get(getContext(), 2171 APIntOps::umax(LHSC->getValue()->getValue(), 2172 RHSC->getValue()->getValue())); 2173 Ops[0] = getConstant(Fold); 2174 Ops.erase(Ops.begin()+1); // Erase the folded element 2175 if (Ops.size() == 1) return Ops[0]; 2176 LHSC = cast<SCEVConstant>(Ops[0]); 2177 } 2178 2179 // If we are left with a constant minimum-int, strip it off. 2180 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2181 Ops.erase(Ops.begin()); 2182 --Idx; 2183 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2184 // If we have an umax with a constant maximum-int, it will always be 2185 // maximum-int. 2186 return Ops[0]; 2187 } 2188 } 2189 2190 if (Ops.size() == 1) return Ops[0]; 2191 2192 // Find the first UMax 2193 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2194 ++Idx; 2195 2196 // Check to see if one of the operands is a UMax. If so, expand its operands 2197 // onto our operand list, and recurse to simplify. 2198 if (Idx < Ops.size()) { 2199 bool DeletedUMax = false; 2200 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2201 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2202 Ops.erase(Ops.begin()+Idx); 2203 DeletedUMax = true; 2204 } 2205 2206 if (DeletedUMax) 2207 return getUMaxExpr(Ops); 2208 } 2209 2210 // Okay, check to see if the same value occurs in the operand list twice. If 2211 // so, delete one. Since we sorted the list, these values are required to 2212 // be adjacent. 2213 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2214 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2215 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2216 --i; --e; 2217 } 2218 2219 if (Ops.size() == 1) return Ops[0]; 2220 2221 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2222 2223 // Okay, it looks like we really DO need a umax expr. Check to see if we 2224 // already have one, otherwise create a new one. 2225 FoldingSetNodeID ID; 2226 ID.AddInteger(scUMaxExpr); 2227 ID.AddInteger(Ops.size()); 2228 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2229 ID.AddPointer(Ops[i]); 2230 void *IP = 0; 2231 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2232 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2233 new (S) SCEVUMaxExpr(ID, Ops); 2234 UniqueSCEVs.InsertNode(S, IP); 2235 return S; 2236} 2237 2238const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2239 const SCEV *RHS) { 2240 // ~smax(~x, ~y) == smin(x, y). 2241 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2242} 2243 2244const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2245 const SCEV *RHS) { 2246 // ~umax(~x, ~y) == umin(x, y) 2247 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2248} 2249 2250const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2251 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2252 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2253 C = ConstantFoldConstantExpression(CE, TD); 2254 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2255 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2256} 2257 2258const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2259 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2260 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2261 C = ConstantFoldConstantExpression(CE, TD); 2262 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2263 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2264} 2265 2266const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2267 unsigned FieldNo) { 2268 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2269 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2270 C = ConstantFoldConstantExpression(CE, TD); 2271 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2272 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2273} 2274 2275const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2276 Constant *FieldNo) { 2277 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2278 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2279 C = ConstantFoldConstantExpression(CE, TD); 2280 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2281 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2282} 2283 2284const SCEV *ScalarEvolution::getUnknown(Value *V) { 2285 // Don't attempt to do anything other than create a SCEVUnknown object 2286 // here. createSCEV only calls getUnknown after checking for all other 2287 // interesting possibilities, and any other code that calls getUnknown 2288 // is doing so in order to hide a value from SCEV canonicalization. 2289 2290 FoldingSetNodeID ID; 2291 ID.AddInteger(scUnknown); 2292 ID.AddPointer(V); 2293 void *IP = 0; 2294 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2295 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2296 new (S) SCEVUnknown(ID, V); 2297 UniqueSCEVs.InsertNode(S, IP); 2298 return S; 2299} 2300 2301//===----------------------------------------------------------------------===// 2302// Basic SCEV Analysis and PHI Idiom Recognition Code 2303// 2304 2305/// isSCEVable - Test if values of the given type are analyzable within 2306/// the SCEV framework. This primarily includes integer types, and it 2307/// can optionally include pointer types if the ScalarEvolution class 2308/// has access to target-specific information. 2309bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2310 // Integers and pointers are always SCEVable. 2311 return Ty->isInteger() || isa<PointerType>(Ty); 2312} 2313 2314/// getTypeSizeInBits - Return the size in bits of the specified type, 2315/// for which isSCEVable must return true. 2316uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2317 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2318 2319 // If we have a TargetData, use it! 2320 if (TD) 2321 return TD->getTypeSizeInBits(Ty); 2322 2323 // Integer types have fixed sizes. 2324 if (Ty->isInteger()) 2325 return Ty->getPrimitiveSizeInBits(); 2326 2327 // The only other support type is pointer. Without TargetData, conservatively 2328 // assume pointers are 64-bit. 2329 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!"); 2330 return 64; 2331} 2332 2333/// getEffectiveSCEVType - Return a type with the same bitwidth as 2334/// the given type and which represents how SCEV will treat the given 2335/// type, for which isSCEVable must return true. For pointer types, 2336/// this is the pointer-sized integer type. 2337const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2338 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2339 2340 if (Ty->isInteger()) 2341 return Ty; 2342 2343 // The only other support type is pointer. 2344 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2345 if (TD) return TD->getIntPtrType(getContext()); 2346 2347 // Without TargetData, conservatively assume pointers are 64-bit. 2348 return Type::getInt64Ty(getContext()); 2349} 2350 2351const SCEV *ScalarEvolution::getCouldNotCompute() { 2352 return &CouldNotCompute; 2353} 2354 2355/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2356/// expression and create a new one. 2357const SCEV *ScalarEvolution::getSCEV(Value *V) { 2358 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2359 2360 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2361 if (I != Scalars.end()) return I->second; 2362 const SCEV *S = createSCEV(V); 2363 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2364 return S; 2365} 2366 2367/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2368/// specified signed integer value and return a SCEV for the constant. 2369const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) { 2370 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2371 return getConstant(ConstantInt::get(ITy, Val)); 2372} 2373 2374/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2375/// 2376const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2377 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2378 return getConstant( 2379 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2380 2381 const Type *Ty = V->getType(); 2382 Ty = getEffectiveSCEVType(Ty); 2383 return getMulExpr(V, 2384 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2385} 2386 2387/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2388const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2389 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2390 return getConstant( 2391 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2392 2393 const Type *Ty = V->getType(); 2394 Ty = getEffectiveSCEVType(Ty); 2395 const SCEV *AllOnes = 2396 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2397 return getMinusSCEV(AllOnes, V); 2398} 2399 2400/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2401/// 2402const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2403 const SCEV *RHS) { 2404 // X - Y --> X + -Y 2405 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2406} 2407 2408/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2409/// input value to the specified type. If the type must be extended, it is zero 2410/// extended. 2411const SCEV * 2412ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2413 const Type *Ty) { 2414 const Type *SrcTy = V->getType(); 2415 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2416 (Ty->isInteger() || isa<PointerType>(Ty)) && 2417 "Cannot truncate or zero extend with non-integer arguments!"); 2418 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2419 return V; // No conversion 2420 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2421 return getTruncateExpr(V, Ty); 2422 return getZeroExtendExpr(V, Ty); 2423} 2424 2425/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2426/// input value to the specified type. If the type must be extended, it is sign 2427/// extended. 2428const SCEV * 2429ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2430 const Type *Ty) { 2431 const Type *SrcTy = V->getType(); 2432 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2433 (Ty->isInteger() || isa<PointerType>(Ty)) && 2434 "Cannot truncate or zero extend with non-integer arguments!"); 2435 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2436 return V; // No conversion 2437 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2438 return getTruncateExpr(V, Ty); 2439 return getSignExtendExpr(V, Ty); 2440} 2441 2442/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2443/// input value to the specified type. If the type must be extended, it is zero 2444/// extended. The conversion must not be narrowing. 2445const SCEV * 2446ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2447 const Type *SrcTy = V->getType(); 2448 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2449 (Ty->isInteger() || isa<PointerType>(Ty)) && 2450 "Cannot noop or zero extend with non-integer arguments!"); 2451 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2452 "getNoopOrZeroExtend cannot truncate!"); 2453 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2454 return V; // No conversion 2455 return getZeroExtendExpr(V, Ty); 2456} 2457 2458/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2459/// input value to the specified type. If the type must be extended, it is sign 2460/// extended. The conversion must not be narrowing. 2461const SCEV * 2462ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2463 const Type *SrcTy = V->getType(); 2464 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2465 (Ty->isInteger() || isa<PointerType>(Ty)) && 2466 "Cannot noop or sign extend with non-integer arguments!"); 2467 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2468 "getNoopOrSignExtend cannot truncate!"); 2469 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2470 return V; // No conversion 2471 return getSignExtendExpr(V, Ty); 2472} 2473 2474/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2475/// the input value to the specified type. If the type must be extended, 2476/// it is extended with unspecified bits. The conversion must not be 2477/// narrowing. 2478const SCEV * 2479ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2480 const Type *SrcTy = V->getType(); 2481 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2482 (Ty->isInteger() || isa<PointerType>(Ty)) && 2483 "Cannot noop or any extend with non-integer arguments!"); 2484 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2485 "getNoopOrAnyExtend cannot truncate!"); 2486 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2487 return V; // No conversion 2488 return getAnyExtendExpr(V, Ty); 2489} 2490 2491/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2492/// input value to the specified type. The conversion must not be widening. 2493const SCEV * 2494ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2495 const Type *SrcTy = V->getType(); 2496 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2497 (Ty->isInteger() || isa<PointerType>(Ty)) && 2498 "Cannot truncate or noop with non-integer arguments!"); 2499 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2500 "getTruncateOrNoop cannot extend!"); 2501 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2502 return V; // No conversion 2503 return getTruncateExpr(V, Ty); 2504} 2505 2506/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2507/// the types using zero-extension, and then perform a umax operation 2508/// with them. 2509const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2510 const SCEV *RHS) { 2511 const SCEV *PromotedLHS = LHS; 2512 const SCEV *PromotedRHS = RHS; 2513 2514 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2515 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2516 else 2517 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2518 2519 return getUMaxExpr(PromotedLHS, PromotedRHS); 2520} 2521 2522/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2523/// the types using zero-extension, and then perform a umin operation 2524/// with them. 2525const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2526 const SCEV *RHS) { 2527 const SCEV *PromotedLHS = LHS; 2528 const SCEV *PromotedRHS = RHS; 2529 2530 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2531 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2532 else 2533 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2534 2535 return getUMinExpr(PromotedLHS, PromotedRHS); 2536} 2537 2538/// PushDefUseChildren - Push users of the given Instruction 2539/// onto the given Worklist. 2540static void 2541PushDefUseChildren(Instruction *I, 2542 SmallVectorImpl<Instruction *> &Worklist) { 2543 // Push the def-use children onto the Worklist stack. 2544 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2545 UI != UE; ++UI) 2546 Worklist.push_back(cast<Instruction>(UI)); 2547} 2548 2549/// ForgetSymbolicValue - This looks up computed SCEV values for all 2550/// instructions that depend on the given instruction and removes them from 2551/// the Scalars map if they reference SymName. This is used during PHI 2552/// resolution. 2553void 2554ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) { 2555 SmallVector<Instruction *, 16> Worklist; 2556 PushDefUseChildren(I, Worklist); 2557 2558 SmallPtrSet<Instruction *, 8> Visited; 2559 Visited.insert(I); 2560 while (!Worklist.empty()) { 2561 Instruction *I = Worklist.pop_back_val(); 2562 if (!Visited.insert(I)) continue; 2563 2564 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2565 Scalars.find(static_cast<Value *>(I)); 2566 if (It != Scalars.end()) { 2567 // Short-circuit the def-use traversal if the symbolic name 2568 // ceases to appear in expressions. 2569 if (!It->second->hasOperand(SymName)) 2570 continue; 2571 2572 // SCEVUnknown for a PHI either means that it has an unrecognized 2573 // structure, or it's a PHI that's in the progress of being computed 2574 // by createNodeForPHI. In the former case, additional loop trip 2575 // count information isn't going to change anything. In the later 2576 // case, createNodeForPHI will perform the necessary updates on its 2577 // own when it gets to that point. 2578 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 2579 ValuesAtScopes.erase(It->second); 2580 Scalars.erase(It); 2581 } 2582 } 2583 2584 PushDefUseChildren(I, Worklist); 2585 } 2586} 2587 2588/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2589/// a loop header, making it a potential recurrence, or it doesn't. 2590/// 2591const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2592 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2593 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2594 if (L->getHeader() == PN->getParent()) { 2595 // If it lives in the loop header, it has two incoming values, one 2596 // from outside the loop, and one from inside. 2597 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2598 unsigned BackEdge = IncomingEdge^1; 2599 2600 // While we are analyzing this PHI node, handle its value symbolically. 2601 const SCEV *SymbolicName = getUnknown(PN); 2602 assert(Scalars.find(PN) == Scalars.end() && 2603 "PHI node already processed?"); 2604 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2605 2606 // Using this symbolic name for the PHI, analyze the value coming around 2607 // the back-edge. 2608 Value *BEValueV = PN->getIncomingValue(BackEdge); 2609 const SCEV *BEValue = getSCEV(BEValueV); 2610 2611 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2612 // has a special value for the first iteration of the loop. 2613 2614 // If the value coming around the backedge is an add with the symbolic 2615 // value we just inserted, then we found a simple induction variable! 2616 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2617 // If there is a single occurrence of the symbolic value, replace it 2618 // with a recurrence. 2619 unsigned FoundIndex = Add->getNumOperands(); 2620 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2621 if (Add->getOperand(i) == SymbolicName) 2622 if (FoundIndex == e) { 2623 FoundIndex = i; 2624 break; 2625 } 2626 2627 if (FoundIndex != Add->getNumOperands()) { 2628 // Create an add with everything but the specified operand. 2629 SmallVector<const SCEV *, 8> Ops; 2630 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2631 if (i != FoundIndex) 2632 Ops.push_back(Add->getOperand(i)); 2633 const SCEV *Accum = getAddExpr(Ops); 2634 2635 // This is not a valid addrec if the step amount is varying each 2636 // loop iteration, but is not itself an addrec in this loop. 2637 if (Accum->isLoopInvariant(L) || 2638 (isa<SCEVAddRecExpr>(Accum) && 2639 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2640 bool HasNUW = false; 2641 bool HasNSW = false; 2642 2643 // If the increment doesn't overflow, then neither the addrec nor 2644 // the post-increment will overflow. 2645 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2646 if (OBO->hasNoUnsignedWrap()) 2647 HasNUW = true; 2648 if (OBO->hasNoSignedWrap()) 2649 HasNSW = true; 2650 } 2651 2652 const SCEV *StartVal = 2653 getSCEV(PN->getIncomingValue(IncomingEdge)); 2654 const SCEV *PHISCEV = 2655 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2656 2657 // Since the no-wrap flags are on the increment, they apply to the 2658 // post-incremented value as well. 2659 if (Accum->isLoopInvariant(L)) 2660 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2661 Accum, L, HasNUW, HasNSW); 2662 2663 // Okay, for the entire analysis of this edge we assumed the PHI 2664 // to be symbolic. We now need to go back and purge all of the 2665 // entries for the scalars that use the symbolic expression. 2666 ForgetSymbolicName(PN, SymbolicName); 2667 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2668 return PHISCEV; 2669 } 2670 } 2671 } else if (const SCEVAddRecExpr *AddRec = 2672 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2673 // Otherwise, this could be a loop like this: 2674 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2675 // In this case, j = {1,+,1} and BEValue is j. 2676 // Because the other in-value of i (0) fits the evolution of BEValue 2677 // i really is an addrec evolution. 2678 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2679 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2680 2681 // If StartVal = j.start - j.stride, we can use StartVal as the 2682 // initial step of the addrec evolution. 2683 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2684 AddRec->getOperand(1))) { 2685 const SCEV *PHISCEV = 2686 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2687 2688 // Okay, for the entire analysis of this edge we assumed the PHI 2689 // to be symbolic. We now need to go back and purge all of the 2690 // entries for the scalars that use the symbolic expression. 2691 ForgetSymbolicName(PN, SymbolicName); 2692 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2693 return PHISCEV; 2694 } 2695 } 2696 } 2697 2698 return SymbolicName; 2699 } 2700 2701 // It's tempting to recognize PHIs with a unique incoming value, however 2702 // this leads passes like indvars to break LCSSA form. Fortunately, such 2703 // PHIs are rare, as instcombine zaps them. 2704 2705 // If it's not a loop phi, we can't handle it yet. 2706 return getUnknown(PN); 2707} 2708 2709/// createNodeForGEP - Expand GEP instructions into add and multiply 2710/// operations. This allows them to be analyzed by regular SCEV code. 2711/// 2712const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2713 2714 bool InBounds = GEP->isInBounds(); 2715 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2716 Value *Base = GEP->getOperand(0); 2717 // Don't attempt to analyze GEPs over unsized objects. 2718 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2719 return getUnknown(GEP); 2720 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2721 gep_type_iterator GTI = gep_type_begin(GEP); 2722 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2723 E = GEP->op_end(); 2724 I != E; ++I) { 2725 Value *Index = *I; 2726 // Compute the (potentially symbolic) offset in bytes for this index. 2727 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2728 // For a struct, add the member offset. 2729 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2730 TotalOffset = getAddExpr(TotalOffset, 2731 getOffsetOfExpr(STy, FieldNo), 2732 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2733 } else { 2734 // For an array, add the element offset, explicitly scaled. 2735 const SCEV *LocalOffset = getSCEV(Index); 2736 // Getelementptr indicies are signed. 2737 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2738 // Lower "inbounds" GEPs to NSW arithmetic. 2739 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), 2740 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2741 TotalOffset = getAddExpr(TotalOffset, LocalOffset, 2742 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2743 } 2744 } 2745 return getAddExpr(getSCEV(Base), TotalOffset, 2746 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2747} 2748 2749/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2750/// guaranteed to end in (at every loop iteration). It is, at the same time, 2751/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2752/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2753uint32_t 2754ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2755 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2756 return C->getValue()->getValue().countTrailingZeros(); 2757 2758 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2759 return std::min(GetMinTrailingZeros(T->getOperand()), 2760 (uint32_t)getTypeSizeInBits(T->getType())); 2761 2762 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2763 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2764 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2765 getTypeSizeInBits(E->getType()) : OpRes; 2766 } 2767 2768 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2769 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2770 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2771 getTypeSizeInBits(E->getType()) : OpRes; 2772 } 2773 2774 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2775 // The result is the min of all operands results. 2776 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2777 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2778 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2779 return MinOpRes; 2780 } 2781 2782 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2783 // The result is the sum of all operands results. 2784 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2785 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2786 for (unsigned i = 1, e = M->getNumOperands(); 2787 SumOpRes != BitWidth && i != e; ++i) 2788 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2789 BitWidth); 2790 return SumOpRes; 2791 } 2792 2793 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2794 // The result is the min of all operands results. 2795 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2796 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2797 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2798 return MinOpRes; 2799 } 2800 2801 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2802 // The result is the min of all operands results. 2803 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2804 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2805 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2806 return MinOpRes; 2807 } 2808 2809 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2810 // The result is the min of all operands results. 2811 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2812 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2813 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2814 return MinOpRes; 2815 } 2816 2817 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2818 // For a SCEVUnknown, ask ValueTracking. 2819 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2820 APInt Mask = APInt::getAllOnesValue(BitWidth); 2821 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2822 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2823 return Zeros.countTrailingOnes(); 2824 } 2825 2826 // SCEVUDivExpr 2827 return 0; 2828} 2829 2830/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2831/// 2832ConstantRange 2833ScalarEvolution::getUnsignedRange(const SCEV *S) { 2834 2835 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2836 return ConstantRange(C->getValue()->getValue()); 2837 2838 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2839 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2840 2841 // If the value has known zeros, the maximum unsigned value will have those 2842 // known zeros as well. 2843 uint32_t TZ = GetMinTrailingZeros(S); 2844 if (TZ != 0) 2845 ConservativeResult = 2846 ConstantRange(APInt::getMinValue(BitWidth), 2847 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2848 2849 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2850 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2851 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2852 X = X.add(getUnsignedRange(Add->getOperand(i))); 2853 return ConservativeResult.intersectWith(X); 2854 } 2855 2856 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2857 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2858 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2859 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2860 return ConservativeResult.intersectWith(X); 2861 } 2862 2863 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2864 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2865 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2866 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2867 return ConservativeResult.intersectWith(X); 2868 } 2869 2870 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2871 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2872 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2873 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2874 return ConservativeResult.intersectWith(X); 2875 } 2876 2877 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2878 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2879 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2880 return ConservativeResult.intersectWith(X.udiv(Y)); 2881 } 2882 2883 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2884 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2885 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2886 } 2887 2888 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2889 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2890 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2891 } 2892 2893 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2894 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2895 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 2896 } 2897 2898 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2899 // If there's no unsigned wrap, the value will never be less than its 2900 // initial value. 2901 if (AddRec->hasNoUnsignedWrap()) 2902 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2903 ConservativeResult = 2904 ConstantRange(C->getValue()->getValue(), 2905 APInt(getTypeSizeInBits(C->getType()), 0)); 2906 2907 // TODO: non-affine addrec 2908 if (AddRec->isAffine()) { 2909 const Type *Ty = AddRec->getType(); 2910 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2911 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 2912 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 2913 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2914 2915 const SCEV *Start = AddRec->getStart(); 2916 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2917 2918 // Check for overflow. 2919 if (!AddRec->hasNoUnsignedWrap()) 2920 return ConservativeResult; 2921 2922 ConstantRange StartRange = getUnsignedRange(Start); 2923 ConstantRange EndRange = getUnsignedRange(End); 2924 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2925 EndRange.getUnsignedMin()); 2926 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2927 EndRange.getUnsignedMax()); 2928 if (Min.isMinValue() && Max.isMaxValue()) 2929 return ConservativeResult; 2930 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 2931 } 2932 } 2933 2934 return ConservativeResult; 2935 } 2936 2937 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2938 // For a SCEVUnknown, ask ValueTracking. 2939 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2940 APInt Mask = APInt::getAllOnesValue(BitWidth); 2941 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2942 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2943 if (Ones == ~Zeros + 1) 2944 return ConservativeResult; 2945 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 2946 } 2947 2948 return ConservativeResult; 2949} 2950 2951/// getSignedRange - Determine the signed range for a particular SCEV. 2952/// 2953ConstantRange 2954ScalarEvolution::getSignedRange(const SCEV *S) { 2955 2956 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2957 return ConstantRange(C->getValue()->getValue()); 2958 2959 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2960 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2961 2962 // If the value has known zeros, the maximum signed value will have those 2963 // known zeros as well. 2964 uint32_t TZ = GetMinTrailingZeros(S); 2965 if (TZ != 0) 2966 ConservativeResult = 2967 ConstantRange(APInt::getSignedMinValue(BitWidth), 2968 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 2969 2970 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2971 ConstantRange X = getSignedRange(Add->getOperand(0)); 2972 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2973 X = X.add(getSignedRange(Add->getOperand(i))); 2974 return ConservativeResult.intersectWith(X); 2975 } 2976 2977 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2978 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2979 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2980 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2981 return ConservativeResult.intersectWith(X); 2982 } 2983 2984 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2985 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2986 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2987 X = X.smax(getSignedRange(SMax->getOperand(i))); 2988 return ConservativeResult.intersectWith(X); 2989 } 2990 2991 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2992 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2993 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2994 X = X.umax(getSignedRange(UMax->getOperand(i))); 2995 return ConservativeResult.intersectWith(X); 2996 } 2997 2998 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2999 ConstantRange X = getSignedRange(UDiv->getLHS()); 3000 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3001 return ConservativeResult.intersectWith(X.udiv(Y)); 3002 } 3003 3004 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3005 ConstantRange X = getSignedRange(ZExt->getOperand()); 3006 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3007 } 3008 3009 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3010 ConstantRange X = getSignedRange(SExt->getOperand()); 3011 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3012 } 3013 3014 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3015 ConstantRange X = getSignedRange(Trunc->getOperand()); 3016 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3017 } 3018 3019 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3020 // If there's no signed wrap, and all the operands have the same sign or 3021 // zero, the value won't ever change sign. 3022 if (AddRec->hasNoSignedWrap()) { 3023 bool AllNonNeg = true; 3024 bool AllNonPos = true; 3025 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3026 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3027 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3028 } 3029 if (AllNonNeg) 3030 ConservativeResult = ConservativeResult.intersectWith( 3031 ConstantRange(APInt(BitWidth, 0), 3032 APInt::getSignedMinValue(BitWidth))); 3033 else if (AllNonPos) 3034 ConservativeResult = ConservativeResult.intersectWith( 3035 ConstantRange(APInt::getSignedMinValue(BitWidth), 3036 APInt(BitWidth, 1))); 3037 } 3038 3039 // TODO: non-affine addrec 3040 if (AddRec->isAffine()) { 3041 const Type *Ty = AddRec->getType(); 3042 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3043 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3044 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3045 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3046 3047 const SCEV *Start = AddRec->getStart(); 3048 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 3049 3050 // Check for overflow. 3051 if (!AddRec->hasNoSignedWrap()) 3052 return ConservativeResult; 3053 3054 ConstantRange StartRange = getSignedRange(Start); 3055 ConstantRange EndRange = getSignedRange(End); 3056 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3057 EndRange.getSignedMin()); 3058 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3059 EndRange.getSignedMax()); 3060 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3061 return ConservativeResult; 3062 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3063 } 3064 } 3065 3066 return ConservativeResult; 3067 } 3068 3069 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3070 // For a SCEVUnknown, ask ValueTracking. 3071 if (!U->getValue()->getType()->isInteger() && !TD) 3072 return ConservativeResult; 3073 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3074 if (NS == 1) 3075 return ConservativeResult; 3076 return ConservativeResult.intersectWith( 3077 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3078 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3079 } 3080 3081 return ConservativeResult; 3082} 3083 3084/// createSCEV - We know that there is no SCEV for the specified value. 3085/// Analyze the expression. 3086/// 3087const SCEV *ScalarEvolution::createSCEV(Value *V) { 3088 if (!isSCEVable(V->getType())) 3089 return getUnknown(V); 3090 3091 unsigned Opcode = Instruction::UserOp1; 3092 if (Instruction *I = dyn_cast<Instruction>(V)) 3093 Opcode = I->getOpcode(); 3094 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3095 Opcode = CE->getOpcode(); 3096 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3097 return getConstant(CI); 3098 else if (isa<ConstantPointerNull>(V)) 3099 return getIntegerSCEV(0, V->getType()); 3100 else if (isa<UndefValue>(V)) 3101 return getIntegerSCEV(0, V->getType()); 3102 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3103 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3104 else 3105 return getUnknown(V); 3106 3107 Operator *U = cast<Operator>(V); 3108 switch (Opcode) { 3109 case Instruction::Add: 3110 // Don't transfer the NSW and NUW bits from the Add instruction to the 3111 // Add expression, because the Instruction may be guarded by control 3112 // flow and the no-overflow bits may not be valid for the expression in 3113 // any context. 3114 return getAddExpr(getSCEV(U->getOperand(0)), 3115 getSCEV(U->getOperand(1))); 3116 case Instruction::Mul: 3117 // Don't transfer the NSW and NUW bits from the Mul instruction to the 3118 // Mul expression, as with Add. 3119 return getMulExpr(getSCEV(U->getOperand(0)), 3120 getSCEV(U->getOperand(1))); 3121 case Instruction::UDiv: 3122 return getUDivExpr(getSCEV(U->getOperand(0)), 3123 getSCEV(U->getOperand(1))); 3124 case Instruction::Sub: 3125 return getMinusSCEV(getSCEV(U->getOperand(0)), 3126 getSCEV(U->getOperand(1))); 3127 case Instruction::And: 3128 // For an expression like x&255 that merely masks off the high bits, 3129 // use zext(trunc(x)) as the SCEV expression. 3130 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3131 if (CI->isNullValue()) 3132 return getSCEV(U->getOperand(1)); 3133 if (CI->isAllOnesValue()) 3134 return getSCEV(U->getOperand(0)); 3135 const APInt &A = CI->getValue(); 3136 3137 // Instcombine's ShrinkDemandedConstant may strip bits out of 3138 // constants, obscuring what would otherwise be a low-bits mask. 3139 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3140 // knew about to reconstruct a low-bits mask value. 3141 unsigned LZ = A.countLeadingZeros(); 3142 unsigned BitWidth = A.getBitWidth(); 3143 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3144 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3145 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3146 3147 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3148 3149 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3150 return 3151 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3152 IntegerType::get(getContext(), BitWidth - LZ)), 3153 U->getType()); 3154 } 3155 break; 3156 3157 case Instruction::Or: 3158 // If the RHS of the Or is a constant, we may have something like: 3159 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3160 // optimizations will transparently handle this case. 3161 // 3162 // In order for this transformation to be safe, the LHS must be of the 3163 // form X*(2^n) and the Or constant must be less than 2^n. 3164 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3165 const SCEV *LHS = getSCEV(U->getOperand(0)); 3166 const APInt &CIVal = CI->getValue(); 3167 if (GetMinTrailingZeros(LHS) >= 3168 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3169 // Build a plain add SCEV. 3170 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3171 // If the LHS of the add was an addrec and it has no-wrap flags, 3172 // transfer the no-wrap flags, since an or won't introduce a wrap. 3173 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3174 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3175 if (OldAR->hasNoUnsignedWrap()) 3176 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3177 if (OldAR->hasNoSignedWrap()) 3178 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3179 } 3180 return S; 3181 } 3182 } 3183 break; 3184 case Instruction::Xor: 3185 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3186 // If the RHS of the xor is a signbit, then this is just an add. 3187 // Instcombine turns add of signbit into xor as a strength reduction step. 3188 if (CI->getValue().isSignBit()) 3189 return getAddExpr(getSCEV(U->getOperand(0)), 3190 getSCEV(U->getOperand(1))); 3191 3192 // If the RHS of xor is -1, then this is a not operation. 3193 if (CI->isAllOnesValue()) 3194 return getNotSCEV(getSCEV(U->getOperand(0))); 3195 3196 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3197 // This is a variant of the check for xor with -1, and it handles 3198 // the case where instcombine has trimmed non-demanded bits out 3199 // of an xor with -1. 3200 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3201 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3202 if (BO->getOpcode() == Instruction::And && 3203 LCI->getValue() == CI->getValue()) 3204 if (const SCEVZeroExtendExpr *Z = 3205 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3206 const Type *UTy = U->getType(); 3207 const SCEV *Z0 = Z->getOperand(); 3208 const Type *Z0Ty = Z0->getType(); 3209 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3210 3211 // If C is a low-bits mask, the zero extend is zerving to 3212 // mask off the high bits. Complement the operand and 3213 // re-apply the zext. 3214 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3215 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3216 3217 // If C is a single bit, it may be in the sign-bit position 3218 // before the zero-extend. In this case, represent the xor 3219 // using an add, which is equivalent, and re-apply the zext. 3220 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3221 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3222 Trunc.isSignBit()) 3223 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3224 UTy); 3225 } 3226 } 3227 break; 3228 3229 case Instruction::Shl: 3230 // Turn shift left of a constant amount into a multiply. 3231 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3232 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3233 Constant *X = ConstantInt::get(getContext(), 3234 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3235 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3236 } 3237 break; 3238 3239 case Instruction::LShr: 3240 // Turn logical shift right of a constant into a unsigned divide. 3241 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3242 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3243 Constant *X = ConstantInt::get(getContext(), 3244 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3245 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3246 } 3247 break; 3248 3249 case Instruction::AShr: 3250 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3251 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3252 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3253 if (L->getOpcode() == Instruction::Shl && 3254 L->getOperand(1) == U->getOperand(1)) { 3255 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3256 uint64_t Amt = BitWidth - CI->getZExtValue(); 3257 if (Amt == BitWidth) 3258 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3259 if (Amt > BitWidth) 3260 return getIntegerSCEV(0, U->getType()); // value is undefined 3261 return 3262 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3263 IntegerType::get(getContext(), Amt)), 3264 U->getType()); 3265 } 3266 break; 3267 3268 case Instruction::Trunc: 3269 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3270 3271 case Instruction::ZExt: 3272 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3273 3274 case Instruction::SExt: 3275 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3276 3277 case Instruction::BitCast: 3278 // BitCasts are no-op casts so we just eliminate the cast. 3279 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3280 return getSCEV(U->getOperand(0)); 3281 break; 3282 3283 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3284 // lead to pointer expressions which cannot safely be expanded to GEPs, 3285 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3286 // simplifying integer expressions. 3287 3288 case Instruction::GetElementPtr: 3289 return createNodeForGEP(cast<GEPOperator>(U)); 3290 3291 case Instruction::PHI: 3292 return createNodeForPHI(cast<PHINode>(U)); 3293 3294 case Instruction::Select: 3295 // This could be a smax or umax that was lowered earlier. 3296 // Try to recover it. 3297 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3298 Value *LHS = ICI->getOperand(0); 3299 Value *RHS = ICI->getOperand(1); 3300 switch (ICI->getPredicate()) { 3301 case ICmpInst::ICMP_SLT: 3302 case ICmpInst::ICMP_SLE: 3303 std::swap(LHS, RHS); 3304 // fall through 3305 case ICmpInst::ICMP_SGT: 3306 case ICmpInst::ICMP_SGE: 3307 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3308 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3309 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3310 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3311 break; 3312 case ICmpInst::ICMP_ULT: 3313 case ICmpInst::ICMP_ULE: 3314 std::swap(LHS, RHS); 3315 // fall through 3316 case ICmpInst::ICMP_UGT: 3317 case ICmpInst::ICMP_UGE: 3318 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3319 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3320 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3321 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3322 break; 3323 case ICmpInst::ICMP_NE: 3324 // n != 0 ? n : 1 -> umax(n, 1) 3325 if (LHS == U->getOperand(1) && 3326 isa<ConstantInt>(U->getOperand(2)) && 3327 cast<ConstantInt>(U->getOperand(2))->isOne() && 3328 isa<ConstantInt>(RHS) && 3329 cast<ConstantInt>(RHS)->isZero()) 3330 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3331 break; 3332 case ICmpInst::ICMP_EQ: 3333 // n == 0 ? 1 : n -> umax(n, 1) 3334 if (LHS == U->getOperand(2) && 3335 isa<ConstantInt>(U->getOperand(1)) && 3336 cast<ConstantInt>(U->getOperand(1))->isOne() && 3337 isa<ConstantInt>(RHS) && 3338 cast<ConstantInt>(RHS)->isZero()) 3339 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3340 break; 3341 default: 3342 break; 3343 } 3344 } 3345 3346 default: // We cannot analyze this expression. 3347 break; 3348 } 3349 3350 return getUnknown(V); 3351} 3352 3353 3354 3355//===----------------------------------------------------------------------===// 3356// Iteration Count Computation Code 3357// 3358 3359/// getBackedgeTakenCount - If the specified loop has a predictable 3360/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3361/// object. The backedge-taken count is the number of times the loop header 3362/// will be branched to from within the loop. This is one less than the 3363/// trip count of the loop, since it doesn't count the first iteration, 3364/// when the header is branched to from outside the loop. 3365/// 3366/// Note that it is not valid to call this method on a loop without a 3367/// loop-invariant backedge-taken count (see 3368/// hasLoopInvariantBackedgeTakenCount). 3369/// 3370const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3371 return getBackedgeTakenInfo(L).Exact; 3372} 3373 3374/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3375/// return the least SCEV value that is known never to be less than the 3376/// actual backedge taken count. 3377const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3378 return getBackedgeTakenInfo(L).Max; 3379} 3380 3381/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3382/// onto the given Worklist. 3383static void 3384PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3385 BasicBlock *Header = L->getHeader(); 3386 3387 // Push all Loop-header PHIs onto the Worklist stack. 3388 for (BasicBlock::iterator I = Header->begin(); 3389 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3390 Worklist.push_back(PN); 3391} 3392 3393const ScalarEvolution::BackedgeTakenInfo & 3394ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3395 // Initially insert a CouldNotCompute for this loop. If the insertion 3396 // succeeds, procede to actually compute a backedge-taken count and 3397 // update the value. The temporary CouldNotCompute value tells SCEV 3398 // code elsewhere that it shouldn't attempt to request a new 3399 // backedge-taken count, which could result in infinite recursion. 3400 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3401 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3402 if (Pair.second) { 3403 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3404 if (BECount.Exact != getCouldNotCompute()) { 3405 assert(BECount.Exact->isLoopInvariant(L) && 3406 BECount.Max->isLoopInvariant(L) && 3407 "Computed backedge-taken count isn't loop invariant for loop!"); 3408 ++NumTripCountsComputed; 3409 3410 // Update the value in the map. 3411 Pair.first->second = BECount; 3412 } else { 3413 if (BECount.Max != getCouldNotCompute()) 3414 // Update the value in the map. 3415 Pair.first->second = BECount; 3416 if (isa<PHINode>(L->getHeader()->begin())) 3417 // Only count loops that have phi nodes as not being computable. 3418 ++NumTripCountsNotComputed; 3419 } 3420 3421 // Now that we know more about the trip count for this loop, forget any 3422 // existing SCEV values for PHI nodes in this loop since they are only 3423 // conservative estimates made without the benefit of trip count 3424 // information. This is similar to the code in forgetLoop, except that 3425 // it handles SCEVUnknown PHI nodes specially. 3426 if (BECount.hasAnyInfo()) { 3427 SmallVector<Instruction *, 16> Worklist; 3428 PushLoopPHIs(L, Worklist); 3429 3430 SmallPtrSet<Instruction *, 8> Visited; 3431 while (!Worklist.empty()) { 3432 Instruction *I = Worklist.pop_back_val(); 3433 if (!Visited.insert(I)) continue; 3434 3435 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3436 Scalars.find(static_cast<Value *>(I)); 3437 if (It != Scalars.end()) { 3438 // SCEVUnknown for a PHI either means that it has an unrecognized 3439 // structure, or it's a PHI that's in the progress of being computed 3440 // by createNodeForPHI. In the former case, additional loop trip 3441 // count information isn't going to change anything. In the later 3442 // case, createNodeForPHI will perform the necessary updates on its 3443 // own when it gets to that point. 3444 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3445 ValuesAtScopes.erase(It->second); 3446 Scalars.erase(It); 3447 } 3448 if (PHINode *PN = dyn_cast<PHINode>(I)) 3449 ConstantEvolutionLoopExitValue.erase(PN); 3450 } 3451 3452 PushDefUseChildren(I, Worklist); 3453 } 3454 } 3455 } 3456 return Pair.first->second; 3457} 3458 3459/// forgetLoop - This method should be called by the client when it has 3460/// changed a loop in a way that may effect ScalarEvolution's ability to 3461/// compute a trip count, or if the loop is deleted. 3462void ScalarEvolution::forgetLoop(const Loop *L) { 3463 // Drop any stored trip count value. 3464 BackedgeTakenCounts.erase(L); 3465 3466 // Drop information about expressions based on loop-header PHIs. 3467 SmallVector<Instruction *, 16> Worklist; 3468 PushLoopPHIs(L, Worklist); 3469 3470 SmallPtrSet<Instruction *, 8> Visited; 3471 while (!Worklist.empty()) { 3472 Instruction *I = Worklist.pop_back_val(); 3473 if (!Visited.insert(I)) continue; 3474 3475 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3476 Scalars.find(static_cast<Value *>(I)); 3477 if (It != Scalars.end()) { 3478 ValuesAtScopes.erase(It->second); 3479 Scalars.erase(It); 3480 if (PHINode *PN = dyn_cast<PHINode>(I)) 3481 ConstantEvolutionLoopExitValue.erase(PN); 3482 } 3483 3484 PushDefUseChildren(I, Worklist); 3485 } 3486} 3487 3488/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3489/// of the specified loop will execute. 3490ScalarEvolution::BackedgeTakenInfo 3491ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3492 SmallVector<BasicBlock *, 8> ExitingBlocks; 3493 L->getExitingBlocks(ExitingBlocks); 3494 3495 // Examine all exits and pick the most conservative values. 3496 const SCEV *BECount = getCouldNotCompute(); 3497 const SCEV *MaxBECount = getCouldNotCompute(); 3498 bool CouldNotComputeBECount = false; 3499 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3500 BackedgeTakenInfo NewBTI = 3501 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3502 3503 if (NewBTI.Exact == getCouldNotCompute()) { 3504 // We couldn't compute an exact value for this exit, so 3505 // we won't be able to compute an exact value for the loop. 3506 CouldNotComputeBECount = true; 3507 BECount = getCouldNotCompute(); 3508 } else if (!CouldNotComputeBECount) { 3509 if (BECount == getCouldNotCompute()) 3510 BECount = NewBTI.Exact; 3511 else 3512 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3513 } 3514 if (MaxBECount == getCouldNotCompute()) 3515 MaxBECount = NewBTI.Max; 3516 else if (NewBTI.Max != getCouldNotCompute()) 3517 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3518 } 3519 3520 return BackedgeTakenInfo(BECount, MaxBECount); 3521} 3522 3523/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3524/// of the specified loop will execute if it exits via the specified block. 3525ScalarEvolution::BackedgeTakenInfo 3526ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3527 BasicBlock *ExitingBlock) { 3528 3529 // Okay, we've chosen an exiting block. See what condition causes us to 3530 // exit at this block. 3531 // 3532 // FIXME: we should be able to handle switch instructions (with a single exit) 3533 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3534 if (ExitBr == 0) return getCouldNotCompute(); 3535 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3536 3537 // At this point, we know we have a conditional branch that determines whether 3538 // the loop is exited. However, we don't know if the branch is executed each 3539 // time through the loop. If not, then the execution count of the branch will 3540 // not be equal to the trip count of the loop. 3541 // 3542 // Currently we check for this by checking to see if the Exit branch goes to 3543 // the loop header. If so, we know it will always execute the same number of 3544 // times as the loop. We also handle the case where the exit block *is* the 3545 // loop header. This is common for un-rotated loops. 3546 // 3547 // If both of those tests fail, walk up the unique predecessor chain to the 3548 // header, stopping if there is an edge that doesn't exit the loop. If the 3549 // header is reached, the execution count of the branch will be equal to the 3550 // trip count of the loop. 3551 // 3552 // More extensive analysis could be done to handle more cases here. 3553 // 3554 if (ExitBr->getSuccessor(0) != L->getHeader() && 3555 ExitBr->getSuccessor(1) != L->getHeader() && 3556 ExitBr->getParent() != L->getHeader()) { 3557 // The simple checks failed, try climbing the unique predecessor chain 3558 // up to the header. 3559 bool Ok = false; 3560 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3561 BasicBlock *Pred = BB->getUniquePredecessor(); 3562 if (!Pred) 3563 return getCouldNotCompute(); 3564 TerminatorInst *PredTerm = Pred->getTerminator(); 3565 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3566 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3567 if (PredSucc == BB) 3568 continue; 3569 // If the predecessor has a successor that isn't BB and isn't 3570 // outside the loop, assume the worst. 3571 if (L->contains(PredSucc)) 3572 return getCouldNotCompute(); 3573 } 3574 if (Pred == L->getHeader()) { 3575 Ok = true; 3576 break; 3577 } 3578 BB = Pred; 3579 } 3580 if (!Ok) 3581 return getCouldNotCompute(); 3582 } 3583 3584 // Procede to the next level to examine the exit condition expression. 3585 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3586 ExitBr->getSuccessor(0), 3587 ExitBr->getSuccessor(1)); 3588} 3589 3590/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3591/// backedge of the specified loop will execute if its exit condition 3592/// were a conditional branch of ExitCond, TBB, and FBB. 3593ScalarEvolution::BackedgeTakenInfo 3594ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3595 Value *ExitCond, 3596 BasicBlock *TBB, 3597 BasicBlock *FBB) { 3598 // Check if the controlling expression for this loop is an And or Or. 3599 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3600 if (BO->getOpcode() == Instruction::And) { 3601 // Recurse on the operands of the and. 3602 BackedgeTakenInfo BTI0 = 3603 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3604 BackedgeTakenInfo BTI1 = 3605 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3606 const SCEV *BECount = getCouldNotCompute(); 3607 const SCEV *MaxBECount = getCouldNotCompute(); 3608 if (L->contains(TBB)) { 3609 // Both conditions must be true for the loop to continue executing. 3610 // Choose the less conservative count. 3611 if (BTI0.Exact == getCouldNotCompute() || 3612 BTI1.Exact == getCouldNotCompute()) 3613 BECount = getCouldNotCompute(); 3614 else 3615 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3616 if (BTI0.Max == getCouldNotCompute()) 3617 MaxBECount = BTI1.Max; 3618 else if (BTI1.Max == getCouldNotCompute()) 3619 MaxBECount = BTI0.Max; 3620 else 3621 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3622 } else { 3623 // Both conditions must be true for the loop to exit. 3624 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3625 if (BTI0.Exact != getCouldNotCompute() && 3626 BTI1.Exact != getCouldNotCompute()) 3627 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3628 if (BTI0.Max != getCouldNotCompute() && 3629 BTI1.Max != getCouldNotCompute()) 3630 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3631 } 3632 3633 return BackedgeTakenInfo(BECount, MaxBECount); 3634 } 3635 if (BO->getOpcode() == Instruction::Or) { 3636 // Recurse on the operands of the or. 3637 BackedgeTakenInfo BTI0 = 3638 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3639 BackedgeTakenInfo BTI1 = 3640 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3641 const SCEV *BECount = getCouldNotCompute(); 3642 const SCEV *MaxBECount = getCouldNotCompute(); 3643 if (L->contains(FBB)) { 3644 // Both conditions must be false for the loop to continue executing. 3645 // Choose the less conservative count. 3646 if (BTI0.Exact == getCouldNotCompute() || 3647 BTI1.Exact == getCouldNotCompute()) 3648 BECount = getCouldNotCompute(); 3649 else 3650 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3651 if (BTI0.Max == getCouldNotCompute()) 3652 MaxBECount = BTI1.Max; 3653 else if (BTI1.Max == getCouldNotCompute()) 3654 MaxBECount = BTI0.Max; 3655 else 3656 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3657 } else { 3658 // Both conditions must be false for the loop to exit. 3659 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3660 if (BTI0.Exact != getCouldNotCompute() && 3661 BTI1.Exact != getCouldNotCompute()) 3662 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3663 if (BTI0.Max != getCouldNotCompute() && 3664 BTI1.Max != getCouldNotCompute()) 3665 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3666 } 3667 3668 return BackedgeTakenInfo(BECount, MaxBECount); 3669 } 3670 } 3671 3672 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3673 // Procede to the next level to examine the icmp. 3674 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3675 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3676 3677 // If it's not an integer or pointer comparison then compute it the hard way. 3678 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3679} 3680 3681/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3682/// backedge of the specified loop will execute if its exit condition 3683/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3684ScalarEvolution::BackedgeTakenInfo 3685ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3686 ICmpInst *ExitCond, 3687 BasicBlock *TBB, 3688 BasicBlock *FBB) { 3689 3690 // If the condition was exit on true, convert the condition to exit on false 3691 ICmpInst::Predicate Cond; 3692 if (!L->contains(FBB)) 3693 Cond = ExitCond->getPredicate(); 3694 else 3695 Cond = ExitCond->getInversePredicate(); 3696 3697 // Handle common loops like: for (X = "string"; *X; ++X) 3698 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3699 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3700 const SCEV *ItCnt = 3701 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3702 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3703 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3704 return BackedgeTakenInfo(ItCnt, 3705 isa<SCEVConstant>(ItCnt) ? ItCnt : 3706 getConstant(APInt::getMaxValue(BitWidth)-1)); 3707 } 3708 } 3709 3710 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3711 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3712 3713 // Try to evaluate any dependencies out of the loop. 3714 LHS = getSCEVAtScope(LHS, L); 3715 RHS = getSCEVAtScope(RHS, L); 3716 3717 // At this point, we would like to compute how many iterations of the 3718 // loop the predicate will return true for these inputs. 3719 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3720 // If there is a loop-invariant, force it into the RHS. 3721 std::swap(LHS, RHS); 3722 Cond = ICmpInst::getSwappedPredicate(Cond); 3723 } 3724 3725 // If we have a comparison of a chrec against a constant, try to use value 3726 // ranges to answer this query. 3727 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3728 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3729 if (AddRec->getLoop() == L) { 3730 // Form the constant range. 3731 ConstantRange CompRange( 3732 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3733 3734 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3735 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3736 } 3737 3738 switch (Cond) { 3739 case ICmpInst::ICMP_NE: { // while (X != Y) 3740 // Convert to: while (X-Y != 0) 3741 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3742 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3743 break; 3744 } 3745 case ICmpInst::ICMP_EQ: { // while (X == Y) 3746 // Convert to: while (X-Y == 0) 3747 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3748 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3749 break; 3750 } 3751 case ICmpInst::ICMP_SLT: { 3752 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3753 if (BTI.hasAnyInfo()) return BTI; 3754 break; 3755 } 3756 case ICmpInst::ICMP_SGT: { 3757 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3758 getNotSCEV(RHS), L, true); 3759 if (BTI.hasAnyInfo()) return BTI; 3760 break; 3761 } 3762 case ICmpInst::ICMP_ULT: { 3763 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3764 if (BTI.hasAnyInfo()) return BTI; 3765 break; 3766 } 3767 case ICmpInst::ICMP_UGT: { 3768 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3769 getNotSCEV(RHS), L, false); 3770 if (BTI.hasAnyInfo()) return BTI; 3771 break; 3772 } 3773 default: 3774#if 0 3775 dbgs() << "ComputeBackedgeTakenCount "; 3776 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3777 dbgs() << "[unsigned] "; 3778 dbgs() << *LHS << " " 3779 << Instruction::getOpcodeName(Instruction::ICmp) 3780 << " " << *RHS << "\n"; 3781#endif 3782 break; 3783 } 3784 return 3785 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3786} 3787 3788static ConstantInt * 3789EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3790 ScalarEvolution &SE) { 3791 const SCEV *InVal = SE.getConstant(C); 3792 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3793 assert(isa<SCEVConstant>(Val) && 3794 "Evaluation of SCEV at constant didn't fold correctly?"); 3795 return cast<SCEVConstant>(Val)->getValue(); 3796} 3797 3798/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3799/// and a GEP expression (missing the pointer index) indexing into it, return 3800/// the addressed element of the initializer or null if the index expression is 3801/// invalid. 3802static Constant * 3803GetAddressedElementFromGlobal(GlobalVariable *GV, 3804 const std::vector<ConstantInt*> &Indices) { 3805 Constant *Init = GV->getInitializer(); 3806 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3807 uint64_t Idx = Indices[i]->getZExtValue(); 3808 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3809 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3810 Init = cast<Constant>(CS->getOperand(Idx)); 3811 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3812 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3813 Init = cast<Constant>(CA->getOperand(Idx)); 3814 } else if (isa<ConstantAggregateZero>(Init)) { 3815 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3816 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3817 Init = Constant::getNullValue(STy->getElementType(Idx)); 3818 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3819 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3820 Init = Constant::getNullValue(ATy->getElementType()); 3821 } else { 3822 llvm_unreachable("Unknown constant aggregate type!"); 3823 } 3824 return 0; 3825 } else { 3826 return 0; // Unknown initializer type 3827 } 3828 } 3829 return Init; 3830} 3831 3832/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3833/// 'icmp op load X, cst', try to see if we can compute the backedge 3834/// execution count. 3835const SCEV * 3836ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3837 LoadInst *LI, 3838 Constant *RHS, 3839 const Loop *L, 3840 ICmpInst::Predicate predicate) { 3841 if (LI->isVolatile()) return getCouldNotCompute(); 3842 3843 // Check to see if the loaded pointer is a getelementptr of a global. 3844 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3845 if (!GEP) return getCouldNotCompute(); 3846 3847 // Make sure that it is really a constant global we are gepping, with an 3848 // initializer, and make sure the first IDX is really 0. 3849 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3850 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3851 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3852 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3853 return getCouldNotCompute(); 3854 3855 // Okay, we allow one non-constant index into the GEP instruction. 3856 Value *VarIdx = 0; 3857 std::vector<ConstantInt*> Indexes; 3858 unsigned VarIdxNum = 0; 3859 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3860 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3861 Indexes.push_back(CI); 3862 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3863 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3864 VarIdx = GEP->getOperand(i); 3865 VarIdxNum = i-2; 3866 Indexes.push_back(0); 3867 } 3868 3869 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3870 // Check to see if X is a loop variant variable value now. 3871 const SCEV *Idx = getSCEV(VarIdx); 3872 Idx = getSCEVAtScope(Idx, L); 3873 3874 // We can only recognize very limited forms of loop index expressions, in 3875 // particular, only affine AddRec's like {C1,+,C2}. 3876 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3877 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3878 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3879 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3880 return getCouldNotCompute(); 3881 3882 unsigned MaxSteps = MaxBruteForceIterations; 3883 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3884 ConstantInt *ItCst = ConstantInt::get( 3885 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3886 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3887 3888 // Form the GEP offset. 3889 Indexes[VarIdxNum] = Val; 3890 3891 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3892 if (Result == 0) break; // Cannot compute! 3893 3894 // Evaluate the condition for this iteration. 3895 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3896 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3897 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3898#if 0 3899 dbgs() << "\n***\n*** Computed loop count " << *ItCst 3900 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3901 << "***\n"; 3902#endif 3903 ++NumArrayLenItCounts; 3904 return getConstant(ItCst); // Found terminating iteration! 3905 } 3906 } 3907 return getCouldNotCompute(); 3908} 3909 3910 3911/// CanConstantFold - Return true if we can constant fold an instruction of the 3912/// specified type, assuming that all operands were constants. 3913static bool CanConstantFold(const Instruction *I) { 3914 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3915 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3916 return true; 3917 3918 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3919 if (const Function *F = CI->getCalledFunction()) 3920 return canConstantFoldCallTo(F); 3921 return false; 3922} 3923 3924/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3925/// in the loop that V is derived from. We allow arbitrary operations along the 3926/// way, but the operands of an operation must either be constants or a value 3927/// derived from a constant PHI. If this expression does not fit with these 3928/// constraints, return null. 3929static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3930 // If this is not an instruction, or if this is an instruction outside of the 3931 // loop, it can't be derived from a loop PHI. 3932 Instruction *I = dyn_cast<Instruction>(V); 3933 if (I == 0 || !L->contains(I)) return 0; 3934 3935 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3936 if (L->getHeader() == I->getParent()) 3937 return PN; 3938 else 3939 // We don't currently keep track of the control flow needed to evaluate 3940 // PHIs, so we cannot handle PHIs inside of loops. 3941 return 0; 3942 } 3943 3944 // If we won't be able to constant fold this expression even if the operands 3945 // are constants, return early. 3946 if (!CanConstantFold(I)) return 0; 3947 3948 // Otherwise, we can evaluate this instruction if all of its operands are 3949 // constant or derived from a PHI node themselves. 3950 PHINode *PHI = 0; 3951 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3952 if (!(isa<Constant>(I->getOperand(Op)) || 3953 isa<GlobalValue>(I->getOperand(Op)))) { 3954 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3955 if (P == 0) return 0; // Not evolving from PHI 3956 if (PHI == 0) 3957 PHI = P; 3958 else if (PHI != P) 3959 return 0; // Evolving from multiple different PHIs. 3960 } 3961 3962 // This is a expression evolving from a constant PHI! 3963 return PHI; 3964} 3965 3966/// EvaluateExpression - Given an expression that passes the 3967/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3968/// in the loop has the value PHIVal. If we can't fold this expression for some 3969/// reason, return null. 3970static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 3971 const TargetData *TD) { 3972 if (isa<PHINode>(V)) return PHIVal; 3973 if (Constant *C = dyn_cast<Constant>(V)) return C; 3974 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3975 Instruction *I = cast<Instruction>(V); 3976 3977 std::vector<Constant*> Operands; 3978 Operands.resize(I->getNumOperands()); 3979 3980 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3981 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 3982 if (Operands[i] == 0) return 0; 3983 } 3984 3985 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3986 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 3987 Operands[1], TD); 3988 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3989 &Operands[0], Operands.size(), TD); 3990} 3991 3992/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3993/// in the header of its containing loop, we know the loop executes a 3994/// constant number of times, and the PHI node is just a recurrence 3995/// involving constants, fold it. 3996Constant * 3997ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3998 const APInt &BEs, 3999 const Loop *L) { 4000 std::map<PHINode*, Constant*>::iterator I = 4001 ConstantEvolutionLoopExitValue.find(PN); 4002 if (I != ConstantEvolutionLoopExitValue.end()) 4003 return I->second; 4004 4005 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 4006 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4007 4008 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4009 4010 // Since the loop is canonicalized, the PHI node must have two entries. One 4011 // entry must be a constant (coming in from outside of the loop), and the 4012 // second must be derived from the same PHI. 4013 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4014 Constant *StartCST = 4015 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4016 if (StartCST == 0) 4017 return RetVal = 0; // Must be a constant. 4018 4019 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4020 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4021 if (PN2 != PN) 4022 return RetVal = 0; // Not derived from same PHI. 4023 4024 // Execute the loop symbolically to determine the exit value. 4025 if (BEs.getActiveBits() >= 32) 4026 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4027 4028 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4029 unsigned IterationNum = 0; 4030 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4031 if (IterationNum == NumIterations) 4032 return RetVal = PHIVal; // Got exit value! 4033 4034 // Compute the value of the PHI node for the next iteration. 4035 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4036 if (NextPHI == PHIVal) 4037 return RetVal = NextPHI; // Stopped evolving! 4038 if (NextPHI == 0) 4039 return 0; // Couldn't evaluate! 4040 PHIVal = NextPHI; 4041 } 4042} 4043 4044/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4045/// constant number of times (the condition evolves only from constants), 4046/// try to evaluate a few iterations of the loop until we get the exit 4047/// condition gets a value of ExitWhen (true or false). If we cannot 4048/// evaluate the trip count of the loop, return getCouldNotCompute(). 4049const SCEV * 4050ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4051 Value *Cond, 4052 bool ExitWhen) { 4053 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4054 if (PN == 0) return getCouldNotCompute(); 4055 4056 // Since the loop is canonicalized, the PHI node must have two entries. One 4057 // entry must be a constant (coming in from outside of the loop), and the 4058 // second must be derived from the same PHI. 4059 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4060 Constant *StartCST = 4061 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4062 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4063 4064 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4065 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4066 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 4067 4068 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4069 // the loop symbolically to determine when the condition gets a value of 4070 // "ExitWhen". 4071 unsigned IterationNum = 0; 4072 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4073 for (Constant *PHIVal = StartCST; 4074 IterationNum != MaxIterations; ++IterationNum) { 4075 ConstantInt *CondVal = 4076 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4077 4078 // Couldn't symbolically evaluate. 4079 if (!CondVal) return getCouldNotCompute(); 4080 4081 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4082 ++NumBruteForceTripCountsComputed; 4083 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4084 } 4085 4086 // Compute the value of the PHI node for the next iteration. 4087 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4088 if (NextPHI == 0 || NextPHI == PHIVal) 4089 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4090 PHIVal = NextPHI; 4091 } 4092 4093 // Too many iterations were needed to evaluate. 4094 return getCouldNotCompute(); 4095} 4096 4097/// getSCEVAtScope - Return a SCEV expression for the specified value 4098/// at the specified scope in the program. The L value specifies a loop 4099/// nest to evaluate the expression at, where null is the top-level or a 4100/// specified loop is immediately inside of the loop. 4101/// 4102/// This method can be used to compute the exit value for a variable defined 4103/// in a loop by querying what the value will hold in the parent loop. 4104/// 4105/// In the case that a relevant loop exit value cannot be computed, the 4106/// original value V is returned. 4107const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4108 // Check to see if we've folded this expression at this loop before. 4109 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4110 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4111 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4112 if (!Pair.second) 4113 return Pair.first->second ? Pair.first->second : V; 4114 4115 // Otherwise compute it. 4116 const SCEV *C = computeSCEVAtScope(V, L); 4117 ValuesAtScopes[V][L] = C; 4118 return C; 4119} 4120 4121const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4122 if (isa<SCEVConstant>(V)) return V; 4123 4124 // If this instruction is evolved from a constant-evolving PHI, compute the 4125 // exit value from the loop without using SCEVs. 4126 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4127 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4128 const Loop *LI = (*this->LI)[I->getParent()]; 4129 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4130 if (PHINode *PN = dyn_cast<PHINode>(I)) 4131 if (PN->getParent() == LI->getHeader()) { 4132 // Okay, there is no closed form solution for the PHI node. Check 4133 // to see if the loop that contains it has a known backedge-taken 4134 // count. If so, we may be able to force computation of the exit 4135 // value. 4136 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4137 if (const SCEVConstant *BTCC = 4138 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4139 // Okay, we know how many times the containing loop executes. If 4140 // this is a constant evolving PHI node, get the final value at 4141 // the specified iteration number. 4142 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4143 BTCC->getValue()->getValue(), 4144 LI); 4145 if (RV) return getSCEV(RV); 4146 } 4147 } 4148 4149 // Okay, this is an expression that we cannot symbolically evaluate 4150 // into a SCEV. Check to see if it's possible to symbolically evaluate 4151 // the arguments into constants, and if so, try to constant propagate the 4152 // result. This is particularly useful for computing loop exit values. 4153 if (CanConstantFold(I)) { 4154 std::vector<Constant*> Operands; 4155 Operands.reserve(I->getNumOperands()); 4156 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4157 Value *Op = I->getOperand(i); 4158 if (Constant *C = dyn_cast<Constant>(Op)) { 4159 Operands.push_back(C); 4160 } else { 4161 // If any of the operands is non-constant and if they are 4162 // non-integer and non-pointer, don't even try to analyze them 4163 // with scev techniques. 4164 if (!isSCEVable(Op->getType())) 4165 return V; 4166 4167 const SCEV *OpV = getSCEVAtScope(Op, L); 4168 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4169 Constant *C = SC->getValue(); 4170 if (C->getType() != Op->getType()) 4171 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4172 Op->getType(), 4173 false), 4174 C, Op->getType()); 4175 Operands.push_back(C); 4176 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4177 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4178 if (C->getType() != Op->getType()) 4179 C = 4180 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4181 Op->getType(), 4182 false), 4183 C, Op->getType()); 4184 Operands.push_back(C); 4185 } else 4186 return V; 4187 } else { 4188 return V; 4189 } 4190 } 4191 } 4192 4193 Constant *C; 4194 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4195 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4196 Operands[0], Operands[1], TD); 4197 else 4198 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4199 &Operands[0], Operands.size(), TD); 4200 return getSCEV(C); 4201 } 4202 } 4203 4204 // This is some other type of SCEVUnknown, just return it. 4205 return V; 4206 } 4207 4208 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4209 // Avoid performing the look-up in the common case where the specified 4210 // expression has no loop-variant portions. 4211 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4212 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4213 if (OpAtScope != Comm->getOperand(i)) { 4214 // Okay, at least one of these operands is loop variant but might be 4215 // foldable. Build a new instance of the folded commutative expression. 4216 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4217 Comm->op_begin()+i); 4218 NewOps.push_back(OpAtScope); 4219 4220 for (++i; i != e; ++i) { 4221 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4222 NewOps.push_back(OpAtScope); 4223 } 4224 if (isa<SCEVAddExpr>(Comm)) 4225 return getAddExpr(NewOps); 4226 if (isa<SCEVMulExpr>(Comm)) 4227 return getMulExpr(NewOps); 4228 if (isa<SCEVSMaxExpr>(Comm)) 4229 return getSMaxExpr(NewOps); 4230 if (isa<SCEVUMaxExpr>(Comm)) 4231 return getUMaxExpr(NewOps); 4232 llvm_unreachable("Unknown commutative SCEV type!"); 4233 } 4234 } 4235 // If we got here, all operands are loop invariant. 4236 return Comm; 4237 } 4238 4239 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4240 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4241 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4242 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4243 return Div; // must be loop invariant 4244 return getUDivExpr(LHS, RHS); 4245 } 4246 4247 // If this is a loop recurrence for a loop that does not contain L, then we 4248 // are dealing with the final value computed by the loop. 4249 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4250 if (!L || !AddRec->getLoop()->contains(L)) { 4251 // To evaluate this recurrence, we need to know how many times the AddRec 4252 // loop iterates. Compute this now. 4253 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4254 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4255 4256 // Then, evaluate the AddRec. 4257 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4258 } 4259 return AddRec; 4260 } 4261 4262 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4263 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4264 if (Op == Cast->getOperand()) 4265 return Cast; // must be loop invariant 4266 return getZeroExtendExpr(Op, Cast->getType()); 4267 } 4268 4269 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4270 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4271 if (Op == Cast->getOperand()) 4272 return Cast; // must be loop invariant 4273 return getSignExtendExpr(Op, Cast->getType()); 4274 } 4275 4276 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4277 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4278 if (Op == Cast->getOperand()) 4279 return Cast; // must be loop invariant 4280 return getTruncateExpr(Op, Cast->getType()); 4281 } 4282 4283 llvm_unreachable("Unknown SCEV type!"); 4284 return 0; 4285} 4286 4287/// getSCEVAtScope - This is a convenience function which does 4288/// getSCEVAtScope(getSCEV(V), L). 4289const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4290 return getSCEVAtScope(getSCEV(V), L); 4291} 4292 4293/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4294/// following equation: 4295/// 4296/// A * X = B (mod N) 4297/// 4298/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4299/// A and B isn't important. 4300/// 4301/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4302static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4303 ScalarEvolution &SE) { 4304 uint32_t BW = A.getBitWidth(); 4305 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4306 assert(A != 0 && "A must be non-zero."); 4307 4308 // 1. D = gcd(A, N) 4309 // 4310 // The gcd of A and N may have only one prime factor: 2. The number of 4311 // trailing zeros in A is its multiplicity 4312 uint32_t Mult2 = A.countTrailingZeros(); 4313 // D = 2^Mult2 4314 4315 // 2. Check if B is divisible by D. 4316 // 4317 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4318 // is not less than multiplicity of this prime factor for D. 4319 if (B.countTrailingZeros() < Mult2) 4320 return SE.getCouldNotCompute(); 4321 4322 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4323 // modulo (N / D). 4324 // 4325 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4326 // bit width during computations. 4327 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4328 APInt Mod(BW + 1, 0); 4329 Mod.set(BW - Mult2); // Mod = N / D 4330 APInt I = AD.multiplicativeInverse(Mod); 4331 4332 // 4. Compute the minimum unsigned root of the equation: 4333 // I * (B / D) mod (N / D) 4334 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4335 4336 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4337 // bits. 4338 return SE.getConstant(Result.trunc(BW)); 4339} 4340 4341/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4342/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4343/// might be the same) or two SCEVCouldNotCompute objects. 4344/// 4345static std::pair<const SCEV *,const SCEV *> 4346SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4347 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4348 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4349 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4350 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4351 4352 // We currently can only solve this if the coefficients are constants. 4353 if (!LC || !MC || !NC) { 4354 const SCEV *CNC = SE.getCouldNotCompute(); 4355 return std::make_pair(CNC, CNC); 4356 } 4357 4358 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4359 const APInt &L = LC->getValue()->getValue(); 4360 const APInt &M = MC->getValue()->getValue(); 4361 const APInt &N = NC->getValue()->getValue(); 4362 APInt Two(BitWidth, 2); 4363 APInt Four(BitWidth, 4); 4364 4365 { 4366 using namespace APIntOps; 4367 const APInt& C = L; 4368 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4369 // The B coefficient is M-N/2 4370 APInt B(M); 4371 B -= sdiv(N,Two); 4372 4373 // The A coefficient is N/2 4374 APInt A(N.sdiv(Two)); 4375 4376 // Compute the B^2-4ac term. 4377 APInt SqrtTerm(B); 4378 SqrtTerm *= B; 4379 SqrtTerm -= Four * (A * C); 4380 4381 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4382 // integer value or else APInt::sqrt() will assert. 4383 APInt SqrtVal(SqrtTerm.sqrt()); 4384 4385 // Compute the two solutions for the quadratic formula. 4386 // The divisions must be performed as signed divisions. 4387 APInt NegB(-B); 4388 APInt TwoA( A << 1 ); 4389 if (TwoA.isMinValue()) { 4390 const SCEV *CNC = SE.getCouldNotCompute(); 4391 return std::make_pair(CNC, CNC); 4392 } 4393 4394 LLVMContext &Context = SE.getContext(); 4395 4396 ConstantInt *Solution1 = 4397 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4398 ConstantInt *Solution2 = 4399 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4400 4401 return std::make_pair(SE.getConstant(Solution1), 4402 SE.getConstant(Solution2)); 4403 } // end APIntOps namespace 4404} 4405 4406/// HowFarToZero - Return the number of times a backedge comparing the specified 4407/// value to zero will execute. If not computable, return CouldNotCompute. 4408const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4409 // If the value is a constant 4410 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4411 // If the value is already zero, the branch will execute zero times. 4412 if (C->getValue()->isZero()) return C; 4413 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4414 } 4415 4416 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4417 if (!AddRec || AddRec->getLoop() != L) 4418 return getCouldNotCompute(); 4419 4420 if (AddRec->isAffine()) { 4421 // If this is an affine expression, the execution count of this branch is 4422 // the minimum unsigned root of the following equation: 4423 // 4424 // Start + Step*N = 0 (mod 2^BW) 4425 // 4426 // equivalent to: 4427 // 4428 // Step*N = -Start (mod 2^BW) 4429 // 4430 // where BW is the common bit width of Start and Step. 4431 4432 // Get the initial value for the loop. 4433 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4434 L->getParentLoop()); 4435 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4436 L->getParentLoop()); 4437 4438 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4439 // For now we handle only constant steps. 4440 4441 // First, handle unitary steps. 4442 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4443 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4444 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4445 return Start; // N = Start (as unsigned) 4446 4447 // Then, try to solve the above equation provided that Start is constant. 4448 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4449 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4450 -StartC->getValue()->getValue(), 4451 *this); 4452 } 4453 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4454 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4455 // the quadratic equation to solve it. 4456 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4457 *this); 4458 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4459 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4460 if (R1) { 4461#if 0 4462 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4463 << " sol#2: " << *R2 << "\n"; 4464#endif 4465 // Pick the smallest positive root value. 4466 if (ConstantInt *CB = 4467 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4468 R1->getValue(), R2->getValue()))) { 4469 if (CB->getZExtValue() == false) 4470 std::swap(R1, R2); // R1 is the minimum root now. 4471 4472 // We can only use this value if the chrec ends up with an exact zero 4473 // value at this index. When solving for "X*X != 5", for example, we 4474 // should not accept a root of 2. 4475 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4476 if (Val->isZero()) 4477 return R1; // We found a quadratic root! 4478 } 4479 } 4480 } 4481 4482 return getCouldNotCompute(); 4483} 4484 4485/// HowFarToNonZero - Return the number of times a backedge checking the 4486/// specified value for nonzero will execute. If not computable, return 4487/// CouldNotCompute 4488const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4489 // Loops that look like: while (X == 0) are very strange indeed. We don't 4490 // handle them yet except for the trivial case. This could be expanded in the 4491 // future as needed. 4492 4493 // If the value is a constant, check to see if it is known to be non-zero 4494 // already. If so, the backedge will execute zero times. 4495 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4496 if (!C->getValue()->isNullValue()) 4497 return getIntegerSCEV(0, C->getType()); 4498 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4499 } 4500 4501 // We could implement others, but I really doubt anyone writes loops like 4502 // this, and if they did, they would already be constant folded. 4503 return getCouldNotCompute(); 4504} 4505 4506/// getLoopPredecessor - If the given loop's header has exactly one unique 4507/// predecessor outside the loop, return it. Otherwise return null. 4508/// 4509BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4510 BasicBlock *Header = L->getHeader(); 4511 BasicBlock *Pred = 0; 4512 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4513 PI != E; ++PI) 4514 if (!L->contains(*PI)) { 4515 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4516 Pred = *PI; 4517 } 4518 return Pred; 4519} 4520 4521/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4522/// (which may not be an immediate predecessor) which has exactly one 4523/// successor from which BB is reachable, or null if no such block is 4524/// found. 4525/// 4526BasicBlock * 4527ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4528 // If the block has a unique predecessor, then there is no path from the 4529 // predecessor to the block that does not go through the direct edge 4530 // from the predecessor to the block. 4531 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4532 return Pred; 4533 4534 // A loop's header is defined to be a block that dominates the loop. 4535 // If the header has a unique predecessor outside the loop, it must be 4536 // a block that has exactly one successor that can reach the loop. 4537 if (Loop *L = LI->getLoopFor(BB)) 4538 return getLoopPredecessor(L); 4539 4540 return 0; 4541} 4542 4543/// HasSameValue - SCEV structural equivalence is usually sufficient for 4544/// testing whether two expressions are equal, however for the purposes of 4545/// looking for a condition guarding a loop, it can be useful to be a little 4546/// more general, since a front-end may have replicated the controlling 4547/// expression. 4548/// 4549static bool HasSameValue(const SCEV *A, const SCEV *B) { 4550 // Quick check to see if they are the same SCEV. 4551 if (A == B) return true; 4552 4553 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4554 // two different instructions with the same value. Check for this case. 4555 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4556 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4557 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4558 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4559 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4560 return true; 4561 4562 // Otherwise assume they may have a different value. 4563 return false; 4564} 4565 4566bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4567 return getSignedRange(S).getSignedMax().isNegative(); 4568} 4569 4570bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4571 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4572} 4573 4574bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4575 return !getSignedRange(S).getSignedMin().isNegative(); 4576} 4577 4578bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4579 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4580} 4581 4582bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4583 return isKnownNegative(S) || isKnownPositive(S); 4584} 4585 4586bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4587 const SCEV *LHS, const SCEV *RHS) { 4588 4589 if (HasSameValue(LHS, RHS)) 4590 return ICmpInst::isTrueWhenEqual(Pred); 4591 4592 switch (Pred) { 4593 default: 4594 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4595 break; 4596 case ICmpInst::ICMP_SGT: 4597 Pred = ICmpInst::ICMP_SLT; 4598 std::swap(LHS, RHS); 4599 case ICmpInst::ICMP_SLT: { 4600 ConstantRange LHSRange = getSignedRange(LHS); 4601 ConstantRange RHSRange = getSignedRange(RHS); 4602 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4603 return true; 4604 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4605 return false; 4606 break; 4607 } 4608 case ICmpInst::ICMP_SGE: 4609 Pred = ICmpInst::ICMP_SLE; 4610 std::swap(LHS, RHS); 4611 case ICmpInst::ICMP_SLE: { 4612 ConstantRange LHSRange = getSignedRange(LHS); 4613 ConstantRange RHSRange = getSignedRange(RHS); 4614 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4615 return true; 4616 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4617 return false; 4618 break; 4619 } 4620 case ICmpInst::ICMP_UGT: 4621 Pred = ICmpInst::ICMP_ULT; 4622 std::swap(LHS, RHS); 4623 case ICmpInst::ICMP_ULT: { 4624 ConstantRange LHSRange = getUnsignedRange(LHS); 4625 ConstantRange RHSRange = getUnsignedRange(RHS); 4626 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4627 return true; 4628 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4629 return false; 4630 break; 4631 } 4632 case ICmpInst::ICMP_UGE: 4633 Pred = ICmpInst::ICMP_ULE; 4634 std::swap(LHS, RHS); 4635 case ICmpInst::ICMP_ULE: { 4636 ConstantRange LHSRange = getUnsignedRange(LHS); 4637 ConstantRange RHSRange = getUnsignedRange(RHS); 4638 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4639 return true; 4640 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4641 return false; 4642 break; 4643 } 4644 case ICmpInst::ICMP_NE: { 4645 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4646 return true; 4647 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4648 return true; 4649 4650 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4651 if (isKnownNonZero(Diff)) 4652 return true; 4653 break; 4654 } 4655 case ICmpInst::ICMP_EQ: 4656 // The check at the top of the function catches the case where 4657 // the values are known to be equal. 4658 break; 4659 } 4660 return false; 4661} 4662 4663/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4664/// protected by a conditional between LHS and RHS. This is used to 4665/// to eliminate casts. 4666bool 4667ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4668 ICmpInst::Predicate Pred, 4669 const SCEV *LHS, const SCEV *RHS) { 4670 // Interpret a null as meaning no loop, where there is obviously no guard 4671 // (interprocedural conditions notwithstanding). 4672 if (!L) return true; 4673 4674 BasicBlock *Latch = L->getLoopLatch(); 4675 if (!Latch) 4676 return false; 4677 4678 BranchInst *LoopContinuePredicate = 4679 dyn_cast<BranchInst>(Latch->getTerminator()); 4680 if (!LoopContinuePredicate || 4681 LoopContinuePredicate->isUnconditional()) 4682 return false; 4683 4684 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4685 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4686} 4687 4688/// isLoopGuardedByCond - Test whether entry to the loop is protected 4689/// by a conditional between LHS and RHS. This is used to help avoid max 4690/// expressions in loop trip counts, and to eliminate casts. 4691bool 4692ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4693 ICmpInst::Predicate Pred, 4694 const SCEV *LHS, const SCEV *RHS) { 4695 // Interpret a null as meaning no loop, where there is obviously no guard 4696 // (interprocedural conditions notwithstanding). 4697 if (!L) return false; 4698 4699 BasicBlock *Predecessor = getLoopPredecessor(L); 4700 BasicBlock *PredecessorDest = L->getHeader(); 4701 4702 // Starting at the loop predecessor, climb up the predecessor chain, as long 4703 // as there are predecessors that can be found that have unique successors 4704 // leading to the original header. 4705 for (; Predecessor; 4706 PredecessorDest = Predecessor, 4707 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4708 4709 BranchInst *LoopEntryPredicate = 4710 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4711 if (!LoopEntryPredicate || 4712 LoopEntryPredicate->isUnconditional()) 4713 continue; 4714 4715 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4716 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4717 return true; 4718 } 4719 4720 return false; 4721} 4722 4723/// isImpliedCond - Test whether the condition described by Pred, LHS, 4724/// and RHS is true whenever the given Cond value evaluates to true. 4725bool ScalarEvolution::isImpliedCond(Value *CondValue, 4726 ICmpInst::Predicate Pred, 4727 const SCEV *LHS, const SCEV *RHS, 4728 bool Inverse) { 4729 // Recursivly handle And and Or conditions. 4730 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4731 if (BO->getOpcode() == Instruction::And) { 4732 if (!Inverse) 4733 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4734 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4735 } else if (BO->getOpcode() == Instruction::Or) { 4736 if (Inverse) 4737 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4738 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4739 } 4740 } 4741 4742 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4743 if (!ICI) return false; 4744 4745 // Bail if the ICmp's operands' types are wider than the needed type 4746 // before attempting to call getSCEV on them. This avoids infinite 4747 // recursion, since the analysis of widening casts can require loop 4748 // exit condition information for overflow checking, which would 4749 // lead back here. 4750 if (getTypeSizeInBits(LHS->getType()) < 4751 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4752 return false; 4753 4754 // Now that we found a conditional branch that dominates the loop, check to 4755 // see if it is the comparison we are looking for. 4756 ICmpInst::Predicate FoundPred; 4757 if (Inverse) 4758 FoundPred = ICI->getInversePredicate(); 4759 else 4760 FoundPred = ICI->getPredicate(); 4761 4762 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4763 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4764 4765 // Balance the types. The case where FoundLHS' type is wider than 4766 // LHS' type is checked for above. 4767 if (getTypeSizeInBits(LHS->getType()) > 4768 getTypeSizeInBits(FoundLHS->getType())) { 4769 if (CmpInst::isSigned(Pred)) { 4770 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4771 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4772 } else { 4773 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4774 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4775 } 4776 } 4777 4778 // Canonicalize the query to match the way instcombine will have 4779 // canonicalized the comparison. 4780 // First, put a constant operand on the right. 4781 if (isa<SCEVConstant>(LHS)) { 4782 std::swap(LHS, RHS); 4783 Pred = ICmpInst::getSwappedPredicate(Pred); 4784 } 4785 // Then, canonicalize comparisons with boundary cases. 4786 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4787 const APInt &RA = RC->getValue()->getValue(); 4788 switch (Pred) { 4789 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4790 case ICmpInst::ICMP_EQ: 4791 case ICmpInst::ICMP_NE: 4792 break; 4793 case ICmpInst::ICMP_UGE: 4794 if ((RA - 1).isMinValue()) { 4795 Pred = ICmpInst::ICMP_NE; 4796 RHS = getConstant(RA - 1); 4797 break; 4798 } 4799 if (RA.isMaxValue()) { 4800 Pred = ICmpInst::ICMP_EQ; 4801 break; 4802 } 4803 if (RA.isMinValue()) return true; 4804 break; 4805 case ICmpInst::ICMP_ULE: 4806 if ((RA + 1).isMaxValue()) { 4807 Pred = ICmpInst::ICMP_NE; 4808 RHS = getConstant(RA + 1); 4809 break; 4810 } 4811 if (RA.isMinValue()) { 4812 Pred = ICmpInst::ICMP_EQ; 4813 break; 4814 } 4815 if (RA.isMaxValue()) return true; 4816 break; 4817 case ICmpInst::ICMP_SGE: 4818 if ((RA - 1).isMinSignedValue()) { 4819 Pred = ICmpInst::ICMP_NE; 4820 RHS = getConstant(RA - 1); 4821 break; 4822 } 4823 if (RA.isMaxSignedValue()) { 4824 Pred = ICmpInst::ICMP_EQ; 4825 break; 4826 } 4827 if (RA.isMinSignedValue()) return true; 4828 break; 4829 case ICmpInst::ICMP_SLE: 4830 if ((RA + 1).isMaxSignedValue()) { 4831 Pred = ICmpInst::ICMP_NE; 4832 RHS = getConstant(RA + 1); 4833 break; 4834 } 4835 if (RA.isMinSignedValue()) { 4836 Pred = ICmpInst::ICMP_EQ; 4837 break; 4838 } 4839 if (RA.isMaxSignedValue()) return true; 4840 break; 4841 case ICmpInst::ICMP_UGT: 4842 if (RA.isMinValue()) { 4843 Pred = ICmpInst::ICMP_NE; 4844 break; 4845 } 4846 if ((RA + 1).isMaxValue()) { 4847 Pred = ICmpInst::ICMP_EQ; 4848 RHS = getConstant(RA + 1); 4849 break; 4850 } 4851 if (RA.isMaxValue()) return false; 4852 break; 4853 case ICmpInst::ICMP_ULT: 4854 if (RA.isMaxValue()) { 4855 Pred = ICmpInst::ICMP_NE; 4856 break; 4857 } 4858 if ((RA - 1).isMinValue()) { 4859 Pred = ICmpInst::ICMP_EQ; 4860 RHS = getConstant(RA - 1); 4861 break; 4862 } 4863 if (RA.isMinValue()) return false; 4864 break; 4865 case ICmpInst::ICMP_SGT: 4866 if (RA.isMinSignedValue()) { 4867 Pred = ICmpInst::ICMP_NE; 4868 break; 4869 } 4870 if ((RA + 1).isMaxSignedValue()) { 4871 Pred = ICmpInst::ICMP_EQ; 4872 RHS = getConstant(RA + 1); 4873 break; 4874 } 4875 if (RA.isMaxSignedValue()) return false; 4876 break; 4877 case ICmpInst::ICMP_SLT: 4878 if (RA.isMaxSignedValue()) { 4879 Pred = ICmpInst::ICMP_NE; 4880 break; 4881 } 4882 if ((RA - 1).isMinSignedValue()) { 4883 Pred = ICmpInst::ICMP_EQ; 4884 RHS = getConstant(RA - 1); 4885 break; 4886 } 4887 if (RA.isMinSignedValue()) return false; 4888 break; 4889 } 4890 } 4891 4892 // Check to see if we can make the LHS or RHS match. 4893 if (LHS == FoundRHS || RHS == FoundLHS) { 4894 if (isa<SCEVConstant>(RHS)) { 4895 std::swap(FoundLHS, FoundRHS); 4896 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4897 } else { 4898 std::swap(LHS, RHS); 4899 Pred = ICmpInst::getSwappedPredicate(Pred); 4900 } 4901 } 4902 4903 // Check whether the found predicate is the same as the desired predicate. 4904 if (FoundPred == Pred) 4905 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4906 4907 // Check whether swapping the found predicate makes it the same as the 4908 // desired predicate. 4909 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4910 if (isa<SCEVConstant>(RHS)) 4911 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4912 else 4913 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4914 RHS, LHS, FoundLHS, FoundRHS); 4915 } 4916 4917 // Check whether the actual condition is beyond sufficient. 4918 if (FoundPred == ICmpInst::ICMP_EQ) 4919 if (ICmpInst::isTrueWhenEqual(Pred)) 4920 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4921 return true; 4922 if (Pred == ICmpInst::ICMP_NE) 4923 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4924 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4925 return true; 4926 4927 // Otherwise assume the worst. 4928 return false; 4929} 4930 4931/// isImpliedCondOperands - Test whether the condition described by Pred, 4932/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS, 4933/// and FoundRHS is true. 4934bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4935 const SCEV *LHS, const SCEV *RHS, 4936 const SCEV *FoundLHS, 4937 const SCEV *FoundRHS) { 4938 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4939 FoundLHS, FoundRHS) || 4940 // ~x < ~y --> x > y 4941 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4942 getNotSCEV(FoundRHS), 4943 getNotSCEV(FoundLHS)); 4944} 4945 4946/// isImpliedCondOperandsHelper - Test whether the condition described by 4947/// Pred, LHS, and RHS is true whenever the condition desribed by Pred, 4948/// FoundLHS, and FoundRHS is true. 4949bool 4950ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 4951 const SCEV *LHS, const SCEV *RHS, 4952 const SCEV *FoundLHS, 4953 const SCEV *FoundRHS) { 4954 switch (Pred) { 4955 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4956 case ICmpInst::ICMP_EQ: 4957 case ICmpInst::ICMP_NE: 4958 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 4959 return true; 4960 break; 4961 case ICmpInst::ICMP_SLT: 4962 case ICmpInst::ICMP_SLE: 4963 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4964 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4965 return true; 4966 break; 4967 case ICmpInst::ICMP_SGT: 4968 case ICmpInst::ICMP_SGE: 4969 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4970 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4971 return true; 4972 break; 4973 case ICmpInst::ICMP_ULT: 4974 case ICmpInst::ICMP_ULE: 4975 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4976 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4977 return true; 4978 break; 4979 case ICmpInst::ICMP_UGT: 4980 case ICmpInst::ICMP_UGE: 4981 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4982 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4983 return true; 4984 break; 4985 } 4986 4987 return false; 4988} 4989 4990/// getBECount - Subtract the end and start values and divide by the step, 4991/// rounding up, to get the number of times the backedge is executed. Return 4992/// CouldNotCompute if an intermediate computation overflows. 4993const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4994 const SCEV *End, 4995 const SCEV *Step, 4996 bool NoWrap) { 4997 assert(!isKnownNegative(Step) && 4998 "This code doesn't handle negative strides yet!"); 4999 5000 const Type *Ty = Start->getType(); 5001 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 5002 const SCEV *Diff = getMinusSCEV(End, Start); 5003 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5004 5005 // Add an adjustment to the difference between End and Start so that 5006 // the division will effectively round up. 5007 const SCEV *Add = getAddExpr(Diff, RoundUp); 5008 5009 if (!NoWrap) { 5010 // Check Add for unsigned overflow. 5011 // TODO: More sophisticated things could be done here. 5012 const Type *WideTy = IntegerType::get(getContext(), 5013 getTypeSizeInBits(Ty) + 1); 5014 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5015 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5016 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5017 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5018 return getCouldNotCompute(); 5019 } 5020 5021 return getUDivExpr(Add, Step); 5022} 5023 5024/// HowManyLessThans - Return the number of times a backedge containing the 5025/// specified less-than comparison will execute. If not computable, return 5026/// CouldNotCompute. 5027ScalarEvolution::BackedgeTakenInfo 5028ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5029 const Loop *L, bool isSigned) { 5030 // Only handle: "ADDREC < LoopInvariant". 5031 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5032 5033 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5034 if (!AddRec || AddRec->getLoop() != L) 5035 return getCouldNotCompute(); 5036 5037 // Check to see if we have a flag which makes analysis easy. 5038 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5039 AddRec->hasNoUnsignedWrap(); 5040 5041 if (AddRec->isAffine()) { 5042 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5043 const SCEV *Step = AddRec->getStepRecurrence(*this); 5044 5045 if (Step->isZero()) 5046 return getCouldNotCompute(); 5047 if (Step->isOne()) { 5048 // With unit stride, the iteration never steps past the limit value. 5049 } else if (isKnownPositive(Step)) { 5050 // Test whether a positive iteration can step past the limit 5051 // value and past the maximum value for its type in a single step. 5052 // Note that it's not sufficient to check NoWrap here, because even 5053 // though the value after a wrap is undefined, it's not undefined 5054 // behavior, so if wrap does occur, the loop could either terminate or 5055 // loop infinitely, but in either case, the loop is guaranteed to 5056 // iterate at least until the iteration where the wrapping occurs. 5057 const SCEV *One = getIntegerSCEV(1, Step->getType()); 5058 if (isSigned) { 5059 APInt Max = APInt::getSignedMaxValue(BitWidth); 5060 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5061 .slt(getSignedRange(RHS).getSignedMax())) 5062 return getCouldNotCompute(); 5063 } else { 5064 APInt Max = APInt::getMaxValue(BitWidth); 5065 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5066 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5067 return getCouldNotCompute(); 5068 } 5069 } else 5070 // TODO: Handle negative strides here and below. 5071 return getCouldNotCompute(); 5072 5073 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5074 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5075 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5076 // treat m-n as signed nor unsigned due to overflow possibility. 5077 5078 // First, we get the value of the LHS in the first iteration: n 5079 const SCEV *Start = AddRec->getOperand(0); 5080 5081 // Determine the minimum constant start value. 5082 const SCEV *MinStart = getConstant(isSigned ? 5083 getSignedRange(Start).getSignedMin() : 5084 getUnsignedRange(Start).getUnsignedMin()); 5085 5086 // If we know that the condition is true in order to enter the loop, 5087 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5088 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5089 // the division must round up. 5090 const SCEV *End = RHS; 5091 if (!isLoopGuardedByCond(L, 5092 isSigned ? ICmpInst::ICMP_SLT : 5093 ICmpInst::ICMP_ULT, 5094 getMinusSCEV(Start, Step), RHS)) 5095 End = isSigned ? getSMaxExpr(RHS, Start) 5096 : getUMaxExpr(RHS, Start); 5097 5098 // Determine the maximum constant end value. 5099 const SCEV *MaxEnd = getConstant(isSigned ? 5100 getSignedRange(End).getSignedMax() : 5101 getUnsignedRange(End).getUnsignedMax()); 5102 5103 // If MaxEnd is within a step of the maximum integer value in its type, 5104 // adjust it down to the minimum value which would produce the same effect. 5105 // This allows the subsequent ceiling divison of (N+(step-1))/step to 5106 // compute the correct value. 5107 const SCEV *StepMinusOne = getMinusSCEV(Step, 5108 getIntegerSCEV(1, Step->getType())); 5109 MaxEnd = isSigned ? 5110 getSMinExpr(MaxEnd, 5111 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5112 StepMinusOne)) : 5113 getUMinExpr(MaxEnd, 5114 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5115 StepMinusOne)); 5116 5117 // Finally, we subtract these two values and divide, rounding up, to get 5118 // the number of times the backedge is executed. 5119 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5120 5121 // The maximum backedge count is similar, except using the minimum start 5122 // value and the maximum end value. 5123 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5124 5125 return BackedgeTakenInfo(BECount, MaxBECount); 5126 } 5127 5128 return getCouldNotCompute(); 5129} 5130 5131/// getNumIterationsInRange - Return the number of iterations of this loop that 5132/// produce values in the specified constant range. Another way of looking at 5133/// this is that it returns the first iteration number where the value is not in 5134/// the condition, thus computing the exit count. If the iteration count can't 5135/// be computed, an instance of SCEVCouldNotCompute is returned. 5136const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5137 ScalarEvolution &SE) const { 5138 if (Range.isFullSet()) // Infinite loop. 5139 return SE.getCouldNotCompute(); 5140 5141 // If the start is a non-zero constant, shift the range to simplify things. 5142 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5143 if (!SC->getValue()->isZero()) { 5144 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5145 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 5146 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5147 if (const SCEVAddRecExpr *ShiftedAddRec = 5148 dyn_cast<SCEVAddRecExpr>(Shifted)) 5149 return ShiftedAddRec->getNumIterationsInRange( 5150 Range.subtract(SC->getValue()->getValue()), SE); 5151 // This is strange and shouldn't happen. 5152 return SE.getCouldNotCompute(); 5153 } 5154 5155 // The only time we can solve this is when we have all constant indices. 5156 // Otherwise, we cannot determine the overflow conditions. 5157 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5158 if (!isa<SCEVConstant>(getOperand(i))) 5159 return SE.getCouldNotCompute(); 5160 5161 5162 // Okay at this point we know that all elements of the chrec are constants and 5163 // that the start element is zero. 5164 5165 // First check to see if the range contains zero. If not, the first 5166 // iteration exits. 5167 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5168 if (!Range.contains(APInt(BitWidth, 0))) 5169 return SE.getIntegerSCEV(0, getType()); 5170 5171 if (isAffine()) { 5172 // If this is an affine expression then we have this situation: 5173 // Solve {0,+,A} in Range === Ax in Range 5174 5175 // We know that zero is in the range. If A is positive then we know that 5176 // the upper value of the range must be the first possible exit value. 5177 // If A is negative then the lower of the range is the last possible loop 5178 // value. Also note that we already checked for a full range. 5179 APInt One(BitWidth,1); 5180 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5181 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5182 5183 // The exit value should be (End+A)/A. 5184 APInt ExitVal = (End + A).udiv(A); 5185 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5186 5187 // Evaluate at the exit value. If we really did fall out of the valid 5188 // range, then we computed our trip count, otherwise wrap around or other 5189 // things must have happened. 5190 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5191 if (Range.contains(Val->getValue())) 5192 return SE.getCouldNotCompute(); // Something strange happened 5193 5194 // Ensure that the previous value is in the range. This is a sanity check. 5195 assert(Range.contains( 5196 EvaluateConstantChrecAtConstant(this, 5197 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5198 "Linear scev computation is off in a bad way!"); 5199 return SE.getConstant(ExitValue); 5200 } else if (isQuadratic()) { 5201 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5202 // quadratic equation to solve it. To do this, we must frame our problem in 5203 // terms of figuring out when zero is crossed, instead of when 5204 // Range.getUpper() is crossed. 5205 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5206 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5207 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5208 5209 // Next, solve the constructed addrec 5210 std::pair<const SCEV *,const SCEV *> Roots = 5211 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5212 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5213 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5214 if (R1) { 5215 // Pick the smallest positive root value. 5216 if (ConstantInt *CB = 5217 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5218 R1->getValue(), R2->getValue()))) { 5219 if (CB->getZExtValue() == false) 5220 std::swap(R1, R2); // R1 is the minimum root now. 5221 5222 // Make sure the root is not off by one. The returned iteration should 5223 // not be in the range, but the previous one should be. When solving 5224 // for "X*X < 5", for example, we should not return a root of 2. 5225 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5226 R1->getValue(), 5227 SE); 5228 if (Range.contains(R1Val->getValue())) { 5229 // The next iteration must be out of the range... 5230 ConstantInt *NextVal = 5231 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5232 5233 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5234 if (!Range.contains(R1Val->getValue())) 5235 return SE.getConstant(NextVal); 5236 return SE.getCouldNotCompute(); // Something strange happened 5237 } 5238 5239 // If R1 was not in the range, then it is a good return value. Make 5240 // sure that R1-1 WAS in the range though, just in case. 5241 ConstantInt *NextVal = 5242 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5243 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5244 if (Range.contains(R1Val->getValue())) 5245 return R1; 5246 return SE.getCouldNotCompute(); // Something strange happened 5247 } 5248 } 5249 } 5250 5251 return SE.getCouldNotCompute(); 5252} 5253 5254 5255 5256//===----------------------------------------------------------------------===// 5257// SCEVCallbackVH Class Implementation 5258//===----------------------------------------------------------------------===// 5259 5260void ScalarEvolution::SCEVCallbackVH::deleted() { 5261 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5262 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5263 SE->ConstantEvolutionLoopExitValue.erase(PN); 5264 SE->Scalars.erase(getValPtr()); 5265 // this now dangles! 5266} 5267 5268void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5269 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5270 5271 // Forget all the expressions associated with users of the old value, 5272 // so that future queries will recompute the expressions using the new 5273 // value. 5274 SmallVector<User *, 16> Worklist; 5275 SmallPtrSet<User *, 8> Visited; 5276 Value *Old = getValPtr(); 5277 bool DeleteOld = false; 5278 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5279 UI != UE; ++UI) 5280 Worklist.push_back(*UI); 5281 while (!Worklist.empty()) { 5282 User *U = Worklist.pop_back_val(); 5283 // Deleting the Old value will cause this to dangle. Postpone 5284 // that until everything else is done. 5285 if (U == Old) { 5286 DeleteOld = true; 5287 continue; 5288 } 5289 if (!Visited.insert(U)) 5290 continue; 5291 if (PHINode *PN = dyn_cast<PHINode>(U)) 5292 SE->ConstantEvolutionLoopExitValue.erase(PN); 5293 SE->Scalars.erase(U); 5294 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5295 UI != UE; ++UI) 5296 Worklist.push_back(*UI); 5297 } 5298 // Delete the Old value if it (indirectly) references itself. 5299 if (DeleteOld) { 5300 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5301 SE->ConstantEvolutionLoopExitValue.erase(PN); 5302 SE->Scalars.erase(Old); 5303 // this now dangles! 5304 } 5305 // this may dangle! 5306} 5307 5308ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5309 : CallbackVH(V), SE(se) {} 5310 5311//===----------------------------------------------------------------------===// 5312// ScalarEvolution Class Implementation 5313//===----------------------------------------------------------------------===// 5314 5315ScalarEvolution::ScalarEvolution() 5316 : FunctionPass(&ID) { 5317} 5318 5319bool ScalarEvolution::runOnFunction(Function &F) { 5320 this->F = &F; 5321 LI = &getAnalysis<LoopInfo>(); 5322 DT = &getAnalysis<DominatorTree>(); 5323 TD = getAnalysisIfAvailable<TargetData>(); 5324 return false; 5325} 5326 5327void ScalarEvolution::releaseMemory() { 5328 Scalars.clear(); 5329 BackedgeTakenCounts.clear(); 5330 ConstantEvolutionLoopExitValue.clear(); 5331 ValuesAtScopes.clear(); 5332 UniqueSCEVs.clear(); 5333 SCEVAllocator.Reset(); 5334} 5335 5336void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5337 AU.setPreservesAll(); 5338 AU.addRequiredTransitive<LoopInfo>(); 5339 AU.addRequiredTransitive<DominatorTree>(); 5340} 5341 5342bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5343 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5344} 5345 5346static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5347 const Loop *L) { 5348 // Print all inner loops first 5349 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5350 PrintLoopInfo(OS, SE, *I); 5351 5352 OS << "Loop "; 5353 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5354 OS << ": "; 5355 5356 SmallVector<BasicBlock *, 8> ExitBlocks; 5357 L->getExitBlocks(ExitBlocks); 5358 if (ExitBlocks.size() != 1) 5359 OS << "<multiple exits> "; 5360 5361 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5362 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5363 } else { 5364 OS << "Unpredictable backedge-taken count. "; 5365 } 5366 5367 OS << "\n" 5368 "Loop "; 5369 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5370 OS << ": "; 5371 5372 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5373 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5374 } else { 5375 OS << "Unpredictable max backedge-taken count. "; 5376 } 5377 5378 OS << "\n"; 5379} 5380 5381void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5382 // ScalarEvolution's implementaiton of the print method is to print 5383 // out SCEV values of all instructions that are interesting. Doing 5384 // this potentially causes it to create new SCEV objects though, 5385 // which technically conflicts with the const qualifier. This isn't 5386 // observable from outside the class though, so casting away the 5387 // const isn't dangerous. 5388 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5389 5390 OS << "Classifying expressions for: "; 5391 WriteAsOperand(OS, F, /*PrintType=*/false); 5392 OS << "\n"; 5393 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5394 if (isSCEVable(I->getType())) { 5395 OS << *I << '\n'; 5396 OS << " --> "; 5397 const SCEV *SV = SE.getSCEV(&*I); 5398 SV->print(OS); 5399 5400 const Loop *L = LI->getLoopFor((*I).getParent()); 5401 5402 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5403 if (AtUse != SV) { 5404 OS << " --> "; 5405 AtUse->print(OS); 5406 } 5407 5408 if (L) { 5409 OS << "\t\t" "Exits: "; 5410 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5411 if (!ExitValue->isLoopInvariant(L)) { 5412 OS << "<<Unknown>>"; 5413 } else { 5414 OS << *ExitValue; 5415 } 5416 } 5417 5418 OS << "\n"; 5419 } 5420 5421 OS << "Determining loop execution counts for: "; 5422 WriteAsOperand(OS, F, /*PrintType=*/false); 5423 OS << "\n"; 5424 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5425 PrintLoopInfo(OS, &SE, *I); 5426} 5427 5428