ScalarEvolution.cpp revision b06432c2761ecb84f4149544b56362ac00ef68be
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by the LLVM research group and is distributed under 6// the University of Illinois Open Source 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. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/Instructions.h" 66#include "llvm/Type.h" 67#include "llvm/Value.h" 68#include "llvm/Analysis/LoopInfo.h" 69#include "llvm/Assembly/Writer.h" 70#include "llvm/Transforms/Scalar.h" 71#include "llvm/Transforms/Utils/Local.h" 72#include "llvm/Support/CFG.h" 73#include "llvm/Support/ConstantRange.h" 74#include "llvm/Support/InstIterator.h" 75#include "Support/CommandLine.h" 76#include "Support/Statistic.h" 77#include <cmath> 78using namespace llvm; 79 80namespace { 81 RegisterAnalysis<ScalarEvolution> 82 R("scalar-evolution", "Scalar Evolution Analysis"); 83 84 Statistic<> 85 NumBruteForceEvaluations("scalar-evolution", 86 "Number of brute force evaluations needed to calculate high-order polynomial exit values"); 87 Statistic<> 88 NumTripCountsComputed("scalar-evolution", 89 "Number of loops with predictable loop counts"); 90 Statistic<> 91 NumTripCountsNotComputed("scalar-evolution", 92 "Number of loops without predictable loop counts"); 93 Statistic<> 94 NumBruteForceTripCountsComputed("scalar-evolution", 95 "Number of loops with trip counts computed by force"); 96 97 cl::opt<unsigned> 98 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 99 cl::desc("Maximum number of iterations SCEV will symbolically execute a constant derived loop"), 100 cl::init(100)); 101} 102 103//===----------------------------------------------------------------------===// 104// SCEV class definitions 105//===----------------------------------------------------------------------===// 106 107//===----------------------------------------------------------------------===// 108// Implementation of the SCEV class. 109// 110namespace { 111 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 112 /// than the complexity of the RHS. If the SCEVs have identical complexity, 113 /// order them by their addresses. This comparator is used to canonicalize 114 /// expressions. 115 struct SCEVComplexityCompare { 116 bool operator()(SCEV *LHS, SCEV *RHS) { 117 if (LHS->getSCEVType() < RHS->getSCEVType()) 118 return true; 119 if (LHS->getSCEVType() == RHS->getSCEVType()) 120 return LHS < RHS; 121 return false; 122 } 123 }; 124} 125 126SCEV::~SCEV() {} 127void SCEV::dump() const { 128 print(std::cerr); 129} 130 131/// getValueRange - Return the tightest constant bounds that this value is 132/// known to have. This method is only valid on integer SCEV objects. 133ConstantRange SCEV::getValueRange() const { 134 const Type *Ty = getType(); 135 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 136 Ty = Ty->getUnsignedVersion(); 137 // Default to a full range if no better information is available. 138 return ConstantRange(getType()); 139} 140 141 142SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 143 144bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 146 return false; 147} 148 149const Type *SCEVCouldNotCompute::getType() const { 150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 151 return 0; 152} 153 154bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 155 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 156 return false; 157} 158 159void SCEVCouldNotCompute::print(std::ostream &OS) const { 160 OS << "***COULDNOTCOMPUTE***"; 161} 162 163bool SCEVCouldNotCompute::classof(const SCEV *S) { 164 return S->getSCEVType() == scCouldNotCompute; 165} 166 167 168// SCEVConstants - Only allow the creation of one SCEVConstant for any 169// particular value. Don't use a SCEVHandle here, or else the object will 170// never be deleted! 171static std::map<ConstantInt*, SCEVConstant*> SCEVConstants; 172 173 174SCEVConstant::~SCEVConstant() { 175 SCEVConstants.erase(V); 176} 177 178SCEVHandle SCEVConstant::get(ConstantInt *V) { 179 // Make sure that SCEVConstant instances are all unsigned. 180 if (V->getType()->isSigned()) { 181 const Type *NewTy = V->getType()->getUnsignedVersion(); 182 V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy)); 183 } 184 185 SCEVConstant *&R = SCEVConstants[V]; 186 if (R == 0) R = new SCEVConstant(V); 187 return R; 188} 189 190ConstantRange SCEVConstant::getValueRange() const { 191 return ConstantRange(V); 192} 193 194const Type *SCEVConstant::getType() const { return V->getType(); } 195 196void SCEVConstant::print(std::ostream &OS) const { 197 WriteAsOperand(OS, V, false); 198} 199 200// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 201// particular input. Don't use a SCEVHandle here, or else the object will 202// never be deleted! 203static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates; 204 205SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 206 : SCEV(scTruncate), Op(op), Ty(ty) { 207 assert(Op->getType()->isInteger() && Ty->isInteger() && 208 Ty->isUnsigned() && 209 "Cannot truncate non-integer value!"); 210 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 211 "This is not a truncating conversion!"); 212} 213 214SCEVTruncateExpr::~SCEVTruncateExpr() { 215 SCEVTruncates.erase(std::make_pair(Op, Ty)); 216} 217 218ConstantRange SCEVTruncateExpr::getValueRange() const { 219 return getOperand()->getValueRange().truncate(getType()); 220} 221 222void SCEVTruncateExpr::print(std::ostream &OS) const { 223 OS << "(truncate " << *Op << " to " << *Ty << ")"; 224} 225 226// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 227// particular input. Don't use a SCEVHandle here, or else the object will never 228// be deleted! 229static std::map<std::pair<SCEV*, const Type*>, 230 SCEVZeroExtendExpr*> SCEVZeroExtends; 231 232SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 233 : SCEV(scTruncate), Op(Op), Ty(ty) { 234 assert(Op->getType()->isInteger() && Ty->isInteger() && 235 Ty->isUnsigned() && 236 "Cannot zero extend non-integer value!"); 237 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 238 "This is not an extending conversion!"); 239} 240 241SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 242 SCEVZeroExtends.erase(std::make_pair(Op, Ty)); 243} 244 245ConstantRange SCEVZeroExtendExpr::getValueRange() const { 246 return getOperand()->getValueRange().zeroExtend(getType()); 247} 248 249void SCEVZeroExtendExpr::print(std::ostream &OS) const { 250 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 251} 252 253// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 254// particular input. Don't use a SCEVHandle here, or else the object will never 255// be deleted! 256static std::map<std::pair<unsigned, std::vector<SCEV*> >, 257 SCEVCommutativeExpr*> SCEVCommExprs; 258 259SCEVCommutativeExpr::~SCEVCommutativeExpr() { 260 SCEVCommExprs.erase(std::make_pair(getSCEVType(), 261 std::vector<SCEV*>(Operands.begin(), 262 Operands.end()))); 263} 264 265void SCEVCommutativeExpr::print(std::ostream &OS) const { 266 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 267 const char *OpStr = getOperationStr(); 268 OS << "(" << *Operands[0]; 269 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 270 OS << OpStr << *Operands[i]; 271 OS << ")"; 272} 273 274// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 275// input. Don't use a SCEVHandle here, or else the object will never be 276// deleted! 277static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs; 278 279SCEVUDivExpr::~SCEVUDivExpr() { 280 SCEVUDivs.erase(std::make_pair(LHS, RHS)); 281} 282 283void SCEVUDivExpr::print(std::ostream &OS) const { 284 OS << "(" << *LHS << " /u " << *RHS << ")"; 285} 286 287const Type *SCEVUDivExpr::getType() const { 288 const Type *Ty = LHS->getType(); 289 if (Ty->isSigned()) Ty = Ty->getUnsignedVersion(); 290 return Ty; 291} 292 293// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 294// particular input. Don't use a SCEVHandle here, or else the object will never 295// be deleted! 296static std::map<std::pair<const Loop *, std::vector<SCEV*> >, 297 SCEVAddRecExpr*> SCEVAddRecExprs; 298 299SCEVAddRecExpr::~SCEVAddRecExpr() { 300 SCEVAddRecExprs.erase(std::make_pair(L, 301 std::vector<SCEV*>(Operands.begin(), 302 Operands.end()))); 303} 304 305bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 306 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 307 // contain L. 308 return !QueryLoop->contains(L->getHeader()); 309} 310 311 312void SCEVAddRecExpr::print(std::ostream &OS) const { 313 OS << "{" << *Operands[0]; 314 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 315 OS << ",+," << *Operands[i]; 316 OS << "}<" << L->getHeader()->getName() + ">"; 317} 318 319// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 320// value. Don't use a SCEVHandle here, or else the object will never be 321// deleted! 322static std::map<Value*, SCEVUnknown*> SCEVUnknowns; 323 324SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); } 325 326bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 327 // All non-instruction values are loop invariant. All instructions are loop 328 // invariant if they are not contained in the specified loop. 329 if (Instruction *I = dyn_cast<Instruction>(V)) 330 return !L->contains(I->getParent()); 331 return true; 332} 333 334const Type *SCEVUnknown::getType() const { 335 return V->getType(); 336} 337 338void SCEVUnknown::print(std::ostream &OS) const { 339 WriteAsOperand(OS, V, false); 340} 341 342 343 344//===----------------------------------------------------------------------===// 345// Simple SCEV method implementations 346//===----------------------------------------------------------------------===// 347 348/// getIntegerSCEV - Given an integer or FP type, create a constant for the 349/// specified signed integer value and return a SCEV for the constant. 350SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 351 Constant *C; 352 if (Val == 0) 353 C = Constant::getNullValue(Ty); 354 else if (Ty->isFloatingPoint()) 355 C = ConstantFP::get(Ty, Val); 356 else if (Ty->isSigned()) 357 C = ConstantSInt::get(Ty, Val); 358 else { 359 C = ConstantSInt::get(Ty->getSignedVersion(), Val); 360 C = ConstantExpr::getCast(C, Ty); 361 } 362 return SCEVUnknown::get(C); 363} 364 365/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 366/// input value to the specified type. If the type must be extended, it is zero 367/// extended. 368static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 369 const Type *SrcTy = V->getType(); 370 assert(SrcTy->isInteger() && Ty->isInteger() && 371 "Cannot truncate or zero extend with non-integer arguments!"); 372 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 373 return V; // No conversion 374 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 375 return SCEVTruncateExpr::get(V, Ty); 376 return SCEVZeroExtendExpr::get(V, Ty); 377} 378 379/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 380/// 381static SCEVHandle getNegativeSCEV(const SCEVHandle &V) { 382 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 383 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 384 385 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 386} 387 388/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 389/// 390static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 391 // X - Y --> X + -Y 392 return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS)); 393} 394 395 396/// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is 397/// often very small, so we try to reduce the number of N! terms we need to 398/// evaluate by evaluating this as (N!/(N-M)!)/M! 399static ConstantInt *Binomial(ConstantInt *N, unsigned M) { 400 uint64_t NVal = N->getRawValue(); 401 uint64_t FirstTerm = 1; 402 for (unsigned i = 0; i != M; ++i) 403 FirstTerm *= NVal-i; 404 405 unsigned MFactorial = 1; 406 for (; M; --M) 407 MFactorial *= M; 408 409 Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial); 410 Result = ConstantExpr::getCast(Result, N->getType()); 411 assert(isa<ConstantInt>(Result) && "Cast of integer not folded??"); 412 return cast<ConstantInt>(Result); 413} 414 415/// PartialFact - Compute V!/(V-NumSteps)! 416static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 417 // Handle this case efficiently, it is common to have constant iteration 418 // counts while computing loop exit values. 419 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 420 uint64_t Val = SC->getValue()->getRawValue(); 421 uint64_t Result = 1; 422 for (; NumSteps; --NumSteps) 423 Result *= Val-(NumSteps-1); 424 Constant *Res = ConstantUInt::get(Type::ULongTy, Result); 425 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType())); 426 } 427 428 const Type *Ty = V->getType(); 429 if (NumSteps == 0) 430 return SCEVUnknown::getIntegerSCEV(1, Ty); 431 432 SCEVHandle Result = V; 433 for (unsigned i = 1; i != NumSteps; ++i) 434 Result = SCEVMulExpr::get(Result, getMinusSCEV(V, 435 SCEVUnknown::getIntegerSCEV(i, Ty))); 436 return Result; 437} 438 439 440/// evaluateAtIteration - Return the value of this chain of recurrences at 441/// the specified iteration number. We can evaluate this recurrence by 442/// multiplying each element in the chain by the binomial coefficient 443/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 444/// 445/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 446/// 447/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 448/// Is the binomial equation safe using modular arithmetic?? 449/// 450SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 451 SCEVHandle Result = getStart(); 452 int Divisor = 1; 453 const Type *Ty = It->getType(); 454 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 455 SCEVHandle BC = PartialFact(It, i); 456 Divisor *= i; 457 SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 458 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 459 Result = SCEVAddExpr::get(Result, Val); 460 } 461 return Result; 462} 463 464 465//===----------------------------------------------------------------------===// 466// SCEV Expression folder implementations 467//===----------------------------------------------------------------------===// 468 469SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 470 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 471 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 472 473 // If the input value is a chrec scev made out of constants, truncate 474 // all of the constants. 475 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 476 std::vector<SCEVHandle> Operands; 477 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 478 // FIXME: This should allow truncation of other expression types! 479 if (isa<SCEVConstant>(AddRec->getOperand(i))) 480 Operands.push_back(get(AddRec->getOperand(i), Ty)); 481 else 482 break; 483 if (Operands.size() == AddRec->getNumOperands()) 484 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 485 } 486 487 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)]; 488 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 489 return Result; 490} 491 492SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 493 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 494 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 495 496 // FIXME: If the input value is a chrec scev, and we can prove that the value 497 // did not overflow the old, smaller, value, we can zero extend all of the 498 // operands (often constants). This would allow analysis of something like 499 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 500 501 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)]; 502 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 503 return Result; 504} 505 506// get - Get a canonical add expression, or something simpler if possible. 507SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 508 assert(!Ops.empty() && "Cannot get empty add!"); 509 if (Ops.size() == 1) return Ops[0]; 510 511 // Sort by complexity, this groups all similar expression types together. 512 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 513 514 // If there are any constants, fold them together. 515 unsigned Idx = 0; 516 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 517 ++Idx; 518 assert(Idx < Ops.size()); 519 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 520 // We found two constants, fold them together! 521 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 522 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 523 Ops[0] = SCEVConstant::get(CI); 524 Ops.erase(Ops.begin()+1); // Erase the folded element 525 if (Ops.size() == 1) return Ops[0]; 526 } else { 527 // If we couldn't fold the expression, move to the next constant. Note 528 // that this is impossible to happen in practice because we always 529 // constant fold constant ints to constant ints. 530 ++Idx; 531 } 532 } 533 534 // If we are left with a constant zero being added, strip it off. 535 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 536 Ops.erase(Ops.begin()); 537 --Idx; 538 } 539 } 540 541 if (Ops.size() == 1) return Ops[0]; 542 543 // Okay, check to see if the same value occurs in the operand list twice. If 544 // so, merge them together into an multiply expression. Since we sorted the 545 // list, these values are required to be adjacent. 546 const Type *Ty = Ops[0]->getType(); 547 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 548 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 549 // Found a match, merge the two values into a multiply, and add any 550 // remaining values to the result. 551 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 552 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 553 if (Ops.size() == 2) 554 return Mul; 555 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 556 Ops.push_back(Mul); 557 return SCEVAddExpr::get(Ops); 558 } 559 560 // Okay, now we know the first non-constant operand. If there are add 561 // operands they would be next. 562 if (Idx < Ops.size()) { 563 bool DeletedAdd = false; 564 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 565 // If we have an add, expand the add operands onto the end of the operands 566 // list. 567 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 568 Ops.erase(Ops.begin()+Idx); 569 DeletedAdd = true; 570 } 571 572 // If we deleted at least one add, we added operands to the end of the list, 573 // and they are not necessarily sorted. Recurse to resort and resimplify 574 // any operands we just aquired. 575 if (DeletedAdd) 576 return get(Ops); 577 } 578 579 // Skip over the add expression until we get to a multiply. 580 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 581 ++Idx; 582 583 // If we are adding something to a multiply expression, make sure the 584 // something is not already an operand of the multiply. If so, merge it into 585 // the multiply. 586 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 587 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 588 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 589 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 590 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 591 if (MulOpSCEV == Ops[AddOp] && 592 (Mul->getNumOperands() != 2 || !isa<SCEVConstant>(MulOpSCEV))) { 593 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 594 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 595 if (Mul->getNumOperands() != 2) { 596 // If the multiply has more than two operands, we must get the 597 // Y*Z term. 598 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 599 MulOps.erase(MulOps.begin()+MulOp); 600 InnerMul = SCEVMulExpr::get(MulOps); 601 } 602 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 603 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 604 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 605 if (Ops.size() == 2) return OuterMul; 606 if (AddOp < Idx) { 607 Ops.erase(Ops.begin()+AddOp); 608 Ops.erase(Ops.begin()+Idx-1); 609 } else { 610 Ops.erase(Ops.begin()+Idx); 611 Ops.erase(Ops.begin()+AddOp-1); 612 } 613 Ops.push_back(OuterMul); 614 return SCEVAddExpr::get(Ops); 615 } 616 617 // Check this multiply against other multiplies being added together. 618 for (unsigned OtherMulIdx = Idx+1; 619 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 620 ++OtherMulIdx) { 621 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 622 // If MulOp occurs in OtherMul, we can fold the two multiplies 623 // together. 624 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 625 OMulOp != e; ++OMulOp) 626 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 627 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 628 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 629 if (Mul->getNumOperands() != 2) { 630 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 631 MulOps.erase(MulOps.begin()+MulOp); 632 InnerMul1 = SCEVMulExpr::get(MulOps); 633 } 634 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 635 if (OtherMul->getNumOperands() != 2) { 636 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 637 OtherMul->op_end()); 638 MulOps.erase(MulOps.begin()+OMulOp); 639 InnerMul2 = SCEVMulExpr::get(MulOps); 640 } 641 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 642 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 643 if (Ops.size() == 2) return OuterMul; 644 Ops.erase(Ops.begin()+Idx); 645 Ops.erase(Ops.begin()+OtherMulIdx-1); 646 Ops.push_back(OuterMul); 647 return SCEVAddExpr::get(Ops); 648 } 649 } 650 } 651 } 652 653 // If there are any add recurrences in the operands list, see if any other 654 // added values are loop invariant. If so, we can fold them into the 655 // recurrence. 656 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 657 ++Idx; 658 659 // Scan over all recurrences, trying to fold loop invariants into them. 660 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 661 // Scan all of the other operands to this add and add them to the vector if 662 // they are loop invariant w.r.t. the recurrence. 663 std::vector<SCEVHandle> LIOps; 664 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 665 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 666 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 667 LIOps.push_back(Ops[i]); 668 Ops.erase(Ops.begin()+i); 669 --i; --e; 670 } 671 672 // If we found some loop invariants, fold them into the recurrence. 673 if (!LIOps.empty()) { 674 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 675 LIOps.push_back(AddRec->getStart()); 676 677 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 678 AddRecOps[0] = SCEVAddExpr::get(LIOps); 679 680 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 681 // If all of the other operands were loop invariant, we are done. 682 if (Ops.size() == 1) return NewRec; 683 684 // Otherwise, add the folded AddRec by the non-liv parts. 685 for (unsigned i = 0;; ++i) 686 if (Ops[i] == AddRec) { 687 Ops[i] = NewRec; 688 break; 689 } 690 return SCEVAddExpr::get(Ops); 691 } 692 693 // Okay, if there weren't any loop invariants to be folded, check to see if 694 // there are multiple AddRec's with the same loop induction variable being 695 // added together. If so, we can fold them. 696 for (unsigned OtherIdx = Idx+1; 697 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 698 if (OtherIdx != Idx) { 699 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 700 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 701 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 702 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 703 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 704 if (i >= NewOps.size()) { 705 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 706 OtherAddRec->op_end()); 707 break; 708 } 709 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 710 } 711 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 712 713 if (Ops.size() == 2) return NewAddRec; 714 715 Ops.erase(Ops.begin()+Idx); 716 Ops.erase(Ops.begin()+OtherIdx-1); 717 Ops.push_back(NewAddRec); 718 return SCEVAddExpr::get(Ops); 719 } 720 } 721 722 // Otherwise couldn't fold anything into this recurrence. Move onto the 723 // next one. 724 } 725 726 // Okay, it looks like we really DO need an add expr. Check to see if we 727 // already have one, otherwise create a new one. 728 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 729 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr, 730 SCEVOps)]; 731 if (Result == 0) Result = new SCEVAddExpr(Ops); 732 return Result; 733} 734 735 736SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 737 assert(!Ops.empty() && "Cannot get empty mul!"); 738 739 // Sort by complexity, this groups all similar expression types together. 740 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 741 742 // If there are any constants, fold them together. 743 unsigned Idx = 0; 744 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 745 746 // C1*(C2+V) -> C1*C2 + C1*V 747 if (Ops.size() == 2) 748 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 749 if (Add->getNumOperands() == 2 && 750 isa<SCEVConstant>(Add->getOperand(0))) 751 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 752 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 753 754 755 ++Idx; 756 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 757 // We found two constants, fold them together! 758 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 759 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 760 Ops[0] = SCEVConstant::get(CI); 761 Ops.erase(Ops.begin()+1); // Erase the folded element 762 if (Ops.size() == 1) return Ops[0]; 763 } else { 764 // If we couldn't fold the expression, move to the next constant. Note 765 // that this is impossible to happen in practice because we always 766 // constant fold constant ints to constant ints. 767 ++Idx; 768 } 769 } 770 771 // If we are left with a constant one being multiplied, strip it off. 772 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 773 Ops.erase(Ops.begin()); 774 --Idx; 775 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 776 // If we have a multiply of zero, it will always be zero. 777 return Ops[0]; 778 } 779 } 780 781 // Skip over the add expression until we get to a multiply. 782 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 783 ++Idx; 784 785 if (Ops.size() == 1) 786 return Ops[0]; 787 788 // If there are mul operands inline them all into this expression. 789 if (Idx < Ops.size()) { 790 bool DeletedMul = false; 791 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 792 // If we have an mul, expand the mul operands onto the end of the operands 793 // list. 794 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 795 Ops.erase(Ops.begin()+Idx); 796 DeletedMul = true; 797 } 798 799 // If we deleted at least one mul, we added operands to the end of the list, 800 // and they are not necessarily sorted. Recurse to resort and resimplify 801 // any operands we just aquired. 802 if (DeletedMul) 803 return get(Ops); 804 } 805 806 // If there are any add recurrences in the operands list, see if any other 807 // added values are loop invariant. If so, we can fold them into the 808 // recurrence. 809 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 810 ++Idx; 811 812 // Scan over all recurrences, trying to fold loop invariants into them. 813 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 814 // Scan all of the other operands to this mul and add them to the vector if 815 // they are loop invariant w.r.t. the recurrence. 816 std::vector<SCEVHandle> LIOps; 817 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 818 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 819 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 820 LIOps.push_back(Ops[i]); 821 Ops.erase(Ops.begin()+i); 822 --i; --e; 823 } 824 825 // If we found some loop invariants, fold them into the recurrence. 826 if (!LIOps.empty()) { 827 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 828 std::vector<SCEVHandle> NewOps; 829 NewOps.reserve(AddRec->getNumOperands()); 830 if (LIOps.size() == 1) { 831 SCEV *Scale = LIOps[0]; 832 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 833 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 834 } else { 835 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 836 std::vector<SCEVHandle> MulOps(LIOps); 837 MulOps.push_back(AddRec->getOperand(i)); 838 NewOps.push_back(SCEVMulExpr::get(MulOps)); 839 } 840 } 841 842 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 843 844 // If all of the other operands were loop invariant, we are done. 845 if (Ops.size() == 1) return NewRec; 846 847 // Otherwise, multiply the folded AddRec by the non-liv parts. 848 for (unsigned i = 0;; ++i) 849 if (Ops[i] == AddRec) { 850 Ops[i] = NewRec; 851 break; 852 } 853 return SCEVMulExpr::get(Ops); 854 } 855 856 // Okay, if there weren't any loop invariants to be folded, check to see if 857 // there are multiple AddRec's with the same loop induction variable being 858 // multiplied together. If so, we can fold them. 859 for (unsigned OtherIdx = Idx+1; 860 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 861 if (OtherIdx != Idx) { 862 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 863 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 864 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 865 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 866 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 867 G->getStart()); 868 SCEVHandle B = F->getStepRecurrence(); 869 SCEVHandle D = G->getStepRecurrence(); 870 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 871 SCEVMulExpr::get(G, B), 872 SCEVMulExpr::get(B, D)); 873 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 874 F->getLoop()); 875 if (Ops.size() == 2) return NewAddRec; 876 877 Ops.erase(Ops.begin()+Idx); 878 Ops.erase(Ops.begin()+OtherIdx-1); 879 Ops.push_back(NewAddRec); 880 return SCEVMulExpr::get(Ops); 881 } 882 } 883 884 // Otherwise couldn't fold anything into this recurrence. Move onto the 885 // next one. 886 } 887 888 // Okay, it looks like we really DO need an mul expr. Check to see if we 889 // already have one, otherwise create a new one. 890 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 891 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr, 892 SCEVOps)]; 893 if (Result == 0) Result = new SCEVMulExpr(Ops); 894 return Result; 895} 896 897SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 898 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 899 if (RHSC->getValue()->equalsInt(1)) 900 return LHS; // X /u 1 --> x 901 if (RHSC->getValue()->isAllOnesValue()) 902 return getNegativeSCEV(LHS); // X /u -1 --> -x 903 904 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 905 Constant *LHSCV = LHSC->getValue(); 906 Constant *RHSCV = RHSC->getValue(); 907 if (LHSCV->getType()->isSigned()) 908 LHSCV = ConstantExpr::getCast(LHSCV, 909 LHSCV->getType()->getUnsignedVersion()); 910 if (RHSCV->getType()->isSigned()) 911 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType()); 912 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV)); 913 } 914 } 915 916 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 917 918 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)]; 919 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 920 return Result; 921} 922 923 924/// SCEVAddRecExpr::get - Get a add recurrence expression for the 925/// specified loop. Simplify the expression as much as possible. 926SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 927 const SCEVHandle &Step, const Loop *L) { 928 std::vector<SCEVHandle> Operands; 929 Operands.push_back(Start); 930 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 931 if (StepChrec->getLoop() == L) { 932 Operands.insert(Operands.end(), StepChrec->op_begin(), 933 StepChrec->op_end()); 934 return get(Operands, L); 935 } 936 937 Operands.push_back(Step); 938 return get(Operands, L); 939} 940 941/// SCEVAddRecExpr::get - Get a add recurrence expression for the 942/// specified loop. Simplify the expression as much as possible. 943SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 944 const Loop *L) { 945 if (Operands.size() == 1) return Operands[0]; 946 947 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 948 if (StepC->getValue()->isNullValue()) { 949 Operands.pop_back(); 950 return get(Operands, L); // { X,+,0 } --> X 951 } 952 953 SCEVAddRecExpr *&Result = 954 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 955 Operands.end()))]; 956 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 957 return Result; 958} 959 960SCEVHandle SCEVUnknown::get(Value *V) { 961 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 962 return SCEVConstant::get(CI); 963 SCEVUnknown *&Result = SCEVUnknowns[V]; 964 if (Result == 0) Result = new SCEVUnknown(V); 965 return Result; 966} 967 968 969//===----------------------------------------------------------------------===// 970// ScalarEvolutionsImpl Definition and Implementation 971//===----------------------------------------------------------------------===// 972// 973/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 974/// evolution code. 975/// 976namespace { 977 struct ScalarEvolutionsImpl { 978 /// F - The function we are analyzing. 979 /// 980 Function &F; 981 982 /// LI - The loop information for the function we are currently analyzing. 983 /// 984 LoopInfo &LI; 985 986 /// UnknownValue - This SCEV is used to represent unknown trip counts and 987 /// things. 988 SCEVHandle UnknownValue; 989 990 /// Scalars - This is a cache of the scalars we have analyzed so far. 991 /// 992 std::map<Value*, SCEVHandle> Scalars; 993 994 /// IterationCounts - Cache the iteration count of the loops for this 995 /// function as they are computed. 996 std::map<const Loop*, SCEVHandle> IterationCounts; 997 998 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 999 /// the PHI instructions that we attempt to compute constant evolutions for. 1000 /// This allows us to avoid potentially expensive recomputation of these 1001 /// properties. An instruction maps to null if we are unable to compute its 1002 /// exit value. 1003 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1004 1005 public: 1006 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1007 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1008 1009 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1010 /// expression and create a new one. 1011 SCEVHandle getSCEV(Value *V); 1012 1013 /// getSCEVAtScope - Compute the value of the specified expression within 1014 /// the indicated loop (which may be null to indicate in no loop). If the 1015 /// expression cannot be evaluated, return UnknownValue itself. 1016 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1017 1018 1019 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1020 /// an analyzable loop-invariant iteration count. 1021 bool hasLoopInvariantIterationCount(const Loop *L); 1022 1023 /// getIterationCount - If the specified loop has a predictable iteration 1024 /// count, return it. Note that it is not valid to call this method on a 1025 /// loop without a loop-invariant iteration count. 1026 SCEVHandle getIterationCount(const Loop *L); 1027 1028 /// deleteInstructionFromRecords - This method should be called by the 1029 /// client before it removes an instruction from the program, to make sure 1030 /// that no dangling references are left around. 1031 void deleteInstructionFromRecords(Instruction *I); 1032 1033 private: 1034 /// createSCEV - We know that there is no SCEV for the specified value. 1035 /// Analyze the expression. 1036 SCEVHandle createSCEV(Value *V); 1037 SCEVHandle createNodeForCast(CastInst *CI); 1038 1039 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1040 /// SCEVs. 1041 SCEVHandle createNodeForPHI(PHINode *PN); 1042 void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN, 1043 std::set<Instruction*> &UpdatedInsts); 1044 1045 /// ComputeIterationCount - Compute the number of times the specified loop 1046 /// will iterate. 1047 SCEVHandle ComputeIterationCount(const Loop *L); 1048 1049 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1050 /// constant number of times (the condition evolves only from constants), 1051 /// try to evaluate a few iterations of the loop until we get the exit 1052 /// condition gets a value of ExitWhen (true or false). If we cannot 1053 /// evaluate the trip count of the loop, return UnknownValue. 1054 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1055 bool ExitWhen); 1056 1057 /// HowFarToZero - Return the number of times a backedge comparing the 1058 /// specified value to zero will execute. If not computable, return 1059 /// UnknownValue 1060 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1061 1062 /// HowFarToNonZero - Return the number of times a backedge checking the 1063 /// specified value for nonzero will execute. If not computable, return 1064 /// UnknownValue 1065 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1066 1067 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1068 /// in the header of its containing loop, we know the loop executes a 1069 /// constant number of times, and the PHI node is just a recurrence 1070 /// involving constants, fold it. 1071 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1072 const Loop *L); 1073 }; 1074} 1075 1076//===----------------------------------------------------------------------===// 1077// Basic SCEV Analysis and PHI Idiom Recognition Code 1078// 1079 1080/// deleteInstructionFromRecords - This method should be called by the 1081/// client before it removes an instruction from the program, to make sure 1082/// that no dangling references are left around. 1083void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1084 Scalars.erase(I); 1085 if (PHINode *PN = dyn_cast<PHINode>(I)) 1086 ConstantEvolutionLoopExitValue.erase(PN); 1087} 1088 1089 1090/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1091/// expression and create a new one. 1092SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1093 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1094 1095 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1096 if (I != Scalars.end()) return I->second; 1097 SCEVHandle S = createSCEV(V); 1098 Scalars.insert(std::make_pair(V, S)); 1099 return S; 1100} 1101 1102 1103/// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of 1104/// entries in the scalar map that refer to the "symbolic" PHI value instead of 1105/// the recurrence value. After we resolve the PHI we must loop over all of the 1106/// using instructions that have scalar map entries and update them. 1107void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I, 1108 PHINode *PN, 1109 std::set<Instruction*> &UpdatedInsts) { 1110 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1111 if (SI == Scalars.end()) return; // This scalar wasn't previous processed. 1112 if (UpdatedInsts.insert(I).second) { 1113 Scalars.erase(SI); // Remove the old entry 1114 getSCEV(I); // Calculate the new entry 1115 1116 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1117 UI != E; ++UI) 1118 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts); 1119 } 1120} 1121 1122 1123/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1124/// a loop header, making it a potential recurrence, or it doesn't. 1125/// 1126SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1127 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1128 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1129 if (L->getHeader() == PN->getParent()) { 1130 // If it lives in the loop header, it has two incoming values, one 1131 // from outside the loop, and one from inside. 1132 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1133 unsigned BackEdge = IncomingEdge^1; 1134 1135 // While we are analyzing this PHI node, handle its value symbolically. 1136 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1137 assert(Scalars.find(PN) == Scalars.end() && 1138 "PHI node already processed?"); 1139 Scalars.insert(std::make_pair(PN, SymbolicName)); 1140 1141 // Using this symbolic name for the PHI, analyze the value coming around 1142 // the back-edge. 1143 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1144 1145 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1146 // has a special value for the first iteration of the loop. 1147 1148 // If the value coming around the backedge is an add with the symbolic 1149 // value we just inserted, then we found a simple induction variable! 1150 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1151 // If there is a single occurrence of the symbolic value, replace it 1152 // with a recurrence. 1153 unsigned FoundIndex = Add->getNumOperands(); 1154 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1155 if (Add->getOperand(i) == SymbolicName) 1156 if (FoundIndex == e) { 1157 FoundIndex = i; 1158 break; 1159 } 1160 1161 if (FoundIndex != Add->getNumOperands()) { 1162 // Create an add with everything but the specified operand. 1163 std::vector<SCEVHandle> Ops; 1164 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1165 if (i != FoundIndex) 1166 Ops.push_back(Add->getOperand(i)); 1167 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1168 1169 // This is not a valid addrec if the step amount is varying each 1170 // loop iteration, but is not itself an addrec in this loop. 1171 if (Accum->isLoopInvariant(L) || 1172 (isa<SCEVAddRecExpr>(Accum) && 1173 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1174 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1175 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1176 1177 // Okay, for the entire analysis of this edge we assumed the PHI 1178 // to be symbolic. We now need to go back and update all of the 1179 // entries for the scalars that use the PHI (except for the PHI 1180 // itself) to use the new analyzed value instead of the "symbolic" 1181 // value. 1182 Scalars.find(PN)->second = PHISCEV; // Update the PHI value 1183 std::set<Instruction*> UpdatedInsts; 1184 UpdatedInsts.insert(PN); 1185 for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end(); 1186 UI != E; ++UI) 1187 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, 1188 UpdatedInsts); 1189 return PHISCEV; 1190 } 1191 } 1192 } 1193 1194 return SymbolicName; 1195 } 1196 1197 // If it's not a loop phi, we can't handle it yet. 1198 return SCEVUnknown::get(PN); 1199} 1200 1201/// createNodeForCast - Handle the various forms of casts that we support. 1202/// 1203SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) { 1204 const Type *SrcTy = CI->getOperand(0)->getType(); 1205 const Type *DestTy = CI->getType(); 1206 1207 // If this is a noop cast (ie, conversion from int to uint), ignore it. 1208 if (SrcTy->isLosslesslyConvertibleTo(DestTy)) 1209 return getSCEV(CI->getOperand(0)); 1210 1211 if (SrcTy->isInteger() && DestTy->isInteger()) { 1212 // Otherwise, if this is a truncating integer cast, we can represent this 1213 // cast. 1214 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1215 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)), 1216 CI->getType()->getUnsignedVersion()); 1217 if (SrcTy->isUnsigned() && 1218 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1219 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)), 1220 CI->getType()->getUnsignedVersion()); 1221 } 1222 1223 // If this is an sign or zero extending cast and we can prove that the value 1224 // will never overflow, we could do similar transformations. 1225 1226 // Otherwise, we can't handle this cast! 1227 return SCEVUnknown::get(CI); 1228} 1229 1230 1231/// createSCEV - We know that there is no SCEV for the specified value. 1232/// Analyze the expression. 1233/// 1234SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1235 if (Instruction *I = dyn_cast<Instruction>(V)) { 1236 switch (I->getOpcode()) { 1237 case Instruction::Add: 1238 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1239 getSCEV(I->getOperand(1))); 1240 case Instruction::Mul: 1241 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1242 getSCEV(I->getOperand(1))); 1243 case Instruction::Div: 1244 if (V->getType()->isInteger() && V->getType()->isUnsigned()) 1245 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), 1246 getSCEV(I->getOperand(1))); 1247 break; 1248 1249 case Instruction::Sub: 1250 return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1))); 1251 1252 case Instruction::Shl: 1253 // Turn shift left of a constant amount into a multiply. 1254 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1255 Constant *X = ConstantInt::get(V->getType(), 1); 1256 X = ConstantExpr::getShl(X, SA); 1257 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1258 } 1259 break; 1260 1261 case Instruction::Shr: 1262 if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1))) 1263 if (V->getType()->isUnsigned()) { 1264 Constant *X = ConstantInt::get(V->getType(), 1); 1265 X = ConstantExpr::getShl(X, SA); 1266 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1267 } 1268 break; 1269 1270 case Instruction::Cast: 1271 return createNodeForCast(cast<CastInst>(I)); 1272 1273 case Instruction::PHI: 1274 return createNodeForPHI(cast<PHINode>(I)); 1275 1276 default: // We cannot analyze this expression. 1277 break; 1278 } 1279 } 1280 1281 return SCEVUnknown::get(V); 1282} 1283 1284 1285 1286//===----------------------------------------------------------------------===// 1287// Iteration Count Computation Code 1288// 1289 1290/// getIterationCount - If the specified loop has a predictable iteration 1291/// count, return it. Note that it is not valid to call this method on a 1292/// loop without a loop-invariant iteration count. 1293SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1294 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1295 if (I == IterationCounts.end()) { 1296 SCEVHandle ItCount = ComputeIterationCount(L); 1297 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1298 if (ItCount != UnknownValue) { 1299 assert(ItCount->isLoopInvariant(L) && 1300 "Computed trip count isn't loop invariant for loop!"); 1301 ++NumTripCountsComputed; 1302 } else if (isa<PHINode>(L->getHeader()->begin())) { 1303 // Only count loops that have phi nodes as not being computable. 1304 ++NumTripCountsNotComputed; 1305 } 1306 } 1307 return I->second; 1308} 1309 1310/// ComputeIterationCount - Compute the number of times the specified loop 1311/// will iterate. 1312SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1313 // If the loop has a non-one exit block count, we can't analyze it. 1314 std::vector<BasicBlock*> ExitBlocks; 1315 L->getExitBlocks(ExitBlocks); 1316 if (ExitBlocks.size() != 1) return UnknownValue; 1317 1318 // Okay, there is one exit block. Try to find the condition that causes the 1319 // loop to be exited. 1320 BasicBlock *ExitBlock = ExitBlocks[0]; 1321 1322 BasicBlock *ExitingBlock = 0; 1323 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1324 PI != E; ++PI) 1325 if (L->contains(*PI)) { 1326 if (ExitingBlock == 0) 1327 ExitingBlock = *PI; 1328 else 1329 return UnknownValue; // More than one block exiting! 1330 } 1331 assert(ExitingBlock && "No exits from loop, something is broken!"); 1332 1333 // Okay, we've computed the exiting block. See what condition causes us to 1334 // exit. 1335 // 1336 // FIXME: we should be able to handle switch instructions (with a single exit) 1337 // FIXME: We should handle cast of int to bool as well 1338 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1339 if (ExitBr == 0) return UnknownValue; 1340 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1341 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1342 if (ExitCond == 0) // Not a setcc 1343 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1344 ExitBr->getSuccessor(0) == ExitBlock); 1345 1346 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1347 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1348 1349 // Try to evaluate any dependencies out of the loop. 1350 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1351 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1352 Tmp = getSCEVAtScope(RHS, L); 1353 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1354 1355 // If the condition was exit on true, convert the condition to exit on false. 1356 Instruction::BinaryOps Cond; 1357 if (ExitBr->getSuccessor(1) == ExitBlock) 1358 Cond = ExitCond->getOpcode(); 1359 else 1360 Cond = ExitCond->getInverseCondition(); 1361 1362 // At this point, we would like to compute how many iterations of the loop the 1363 // predicate will return true for these inputs. 1364 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1365 // If there is a constant, force it into the RHS. 1366 std::swap(LHS, RHS); 1367 Cond = SetCondInst::getSwappedCondition(Cond); 1368 } 1369 1370 // FIXME: think about handling pointer comparisons! i.e.: 1371 // while (P != P+100) ++P; 1372 1373 // If we have a comparison of a chrec against a constant, try to use value 1374 // ranges to answer this query. 1375 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1376 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1377 if (AddRec->getLoop() == L) { 1378 // Form the comparison range using the constant of the correct type so 1379 // that the ConstantRange class knows to do a signed or unsigned 1380 // comparison. 1381 ConstantInt *CompVal = RHSC->getValue(); 1382 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1383 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy)); 1384 if (CompVal) { 1385 // Form the constant range. 1386 ConstantRange CompRange(Cond, CompVal); 1387 1388 // Now that we have it, if it's signed, convert it to an unsigned 1389 // range. 1390 if (CompRange.getLower()->getType()->isSigned()) { 1391 const Type *NewTy = RHSC->getValue()->getType(); 1392 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy); 1393 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy); 1394 CompRange = ConstantRange(NewL, NewU); 1395 } 1396 1397 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1398 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1399 } 1400 } 1401 1402 switch (Cond) { 1403 case Instruction::SetNE: // while (X != Y) 1404 // Convert to: while (X-Y != 0) 1405 if (LHS->getType()->isInteger()) { 1406 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 1407 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1408 } 1409 break; 1410 case Instruction::SetEQ: 1411 // Convert to: while (X-Y == 0) // while (X == Y) 1412 if (LHS->getType()->isInteger()) { 1413 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 1414 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1415 } 1416 break; 1417 default: 1418#if 0 1419 std::cerr << "ComputeIterationCount "; 1420 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1421 std::cerr << "[unsigned] "; 1422 std::cerr << *LHS << " " 1423 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1424#endif 1425 break; 1426 } 1427 1428 return ComputeIterationCountExhaustively(L, ExitCond, 1429 ExitBr->getSuccessor(0) == ExitBlock); 1430} 1431 1432/// CanConstantFold - Return true if we can constant fold an instruction of the 1433/// specified type, assuming that all operands were constants. 1434static bool CanConstantFold(const Instruction *I) { 1435 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1436 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1437 return true; 1438 1439 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1440 if (const Function *F = CI->getCalledFunction()) 1441 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1442 return false; 1443} 1444 1445/// ConstantFold - Constant fold an instruction of the specified type with the 1446/// specified constant operands. This function may modify the operands vector. 1447static Constant *ConstantFold(const Instruction *I, 1448 std::vector<Constant*> &Operands) { 1449 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1450 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1451 1452 switch (I->getOpcode()) { 1453 case Instruction::Cast: 1454 return ConstantExpr::getCast(Operands[0], I->getType()); 1455 case Instruction::Select: 1456 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1457 case Instruction::Call: 1458 if (ConstantPointerRef *CPR = dyn_cast<ConstantPointerRef>(Operands[0])) { 1459 Operands.erase(Operands.begin()); 1460 return ConstantFoldCall(cast<Function>(CPR->getValue()), Operands); 1461 } 1462 1463 return 0; 1464 case Instruction::GetElementPtr: 1465 Constant *Base = Operands[0]; 1466 Operands.erase(Operands.begin()); 1467 return ConstantExpr::getGetElementPtr(Base, Operands); 1468 } 1469 return 0; 1470} 1471 1472 1473/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1474/// in the loop that V is derived from. We allow arbitrary operations along the 1475/// way, but the operands of an operation must either be constants or a value 1476/// derived from a constant PHI. If this expression does not fit with these 1477/// constraints, return null. 1478static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1479 // If this is not an instruction, or if this is an instruction outside of the 1480 // loop, it can't be derived from a loop PHI. 1481 Instruction *I = dyn_cast<Instruction>(V); 1482 if (I == 0 || !L->contains(I->getParent())) return 0; 1483 1484 if (PHINode *PN = dyn_cast<PHINode>(I)) 1485 if (L->getHeader() == I->getParent()) 1486 return PN; 1487 else 1488 // We don't currently keep track of the control flow needed to evaluate 1489 // PHIs, so we cannot handle PHIs inside of loops. 1490 return 0; 1491 1492 // If we won't be able to constant fold this expression even if the operands 1493 // are constants, return early. 1494 if (!CanConstantFold(I)) return 0; 1495 1496 // Otherwise, we can evaluate this instruction if all of its operands are 1497 // constant or derived from a PHI node themselves. 1498 PHINode *PHI = 0; 1499 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1500 if (!(isa<Constant>(I->getOperand(Op)) || 1501 isa<GlobalValue>(I->getOperand(Op)))) { 1502 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1503 if (P == 0) return 0; // Not evolving from PHI 1504 if (PHI == 0) 1505 PHI = P; 1506 else if (PHI != P) 1507 return 0; // Evolving from multiple different PHIs. 1508 } 1509 1510 // This is a expression evolving from a constant PHI! 1511 return PHI; 1512} 1513 1514/// EvaluateExpression - Given an expression that passes the 1515/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1516/// in the loop has the value PHIVal. If we can't fold this expression for some 1517/// reason, return null. 1518static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1519 if (isa<PHINode>(V)) return PHIVal; 1520 if (Constant *C = dyn_cast<Constant>(V)) return C; 1521 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1522 return ConstantPointerRef::get(GV); 1523 Instruction *I = cast<Instruction>(V); 1524 1525 std::vector<Constant*> Operands; 1526 Operands.resize(I->getNumOperands()); 1527 1528 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1529 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1530 if (Operands[i] == 0) return 0; 1531 } 1532 1533 return ConstantFold(I, Operands); 1534} 1535 1536/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1537/// in the header of its containing loop, we know the loop executes a 1538/// constant number of times, and the PHI node is just a recurrence 1539/// involving constants, fold it. 1540Constant *ScalarEvolutionsImpl:: 1541getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1542 std::map<PHINode*, Constant*>::iterator I = 1543 ConstantEvolutionLoopExitValue.find(PN); 1544 if (I != ConstantEvolutionLoopExitValue.end()) 1545 return I->second; 1546 1547 if (Its > MaxBruteForceIterations) 1548 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1549 1550 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1551 1552 // Since the loop is canonicalized, the PHI node must have two entries. One 1553 // entry must be a constant (coming in from outside of the loop), and the 1554 // second must be derived from the same PHI. 1555 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1556 Constant *StartCST = 1557 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1558 if (StartCST == 0) 1559 return RetVal = 0; // Must be a constant. 1560 1561 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1562 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1563 if (PN2 != PN) 1564 return RetVal = 0; // Not derived from same PHI. 1565 1566 // Execute the loop symbolically to determine the exit value. 1567 unsigned IterationNum = 0; 1568 unsigned NumIterations = Its; 1569 if (NumIterations != Its) 1570 return RetVal = 0; // More than 2^32 iterations?? 1571 1572 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1573 if (IterationNum == NumIterations) 1574 return RetVal = PHIVal; // Got exit value! 1575 1576 // Compute the value of the PHI node for the next iteration. 1577 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1578 if (NextPHI == PHIVal) 1579 return RetVal = NextPHI; // Stopped evolving! 1580 if (NextPHI == 0) 1581 return 0; // Couldn't evaluate! 1582 PHIVal = NextPHI; 1583 } 1584} 1585 1586/// ComputeIterationCountExhaustively - If the trip is known to execute a 1587/// constant number of times (the condition evolves only from constants), 1588/// try to evaluate a few iterations of the loop until we get the exit 1589/// condition gets a value of ExitWhen (true or false). If we cannot 1590/// evaluate the trip count of the loop, return UnknownValue. 1591SCEVHandle ScalarEvolutionsImpl:: 1592ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1593 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1594 if (PN == 0) return UnknownValue; 1595 1596 // Since the loop is canonicalized, the PHI node must have two entries. One 1597 // entry must be a constant (coming in from outside of the loop), and the 1598 // second must be derived from the same PHI. 1599 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1600 Constant *StartCST = 1601 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1602 if (StartCST == 0) return UnknownValue; // Must be a constant. 1603 1604 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1605 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1606 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1607 1608 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1609 // the loop symbolically to determine when the condition gets a value of 1610 // "ExitWhen". 1611 unsigned IterationNum = 0; 1612 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1613 for (Constant *PHIVal = StartCST; 1614 IterationNum != MaxIterations; ++IterationNum) { 1615 ConstantBool *CondVal = 1616 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1617 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1618 1619 if (CondVal->getValue() == ExitWhen) { 1620 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1621 ++NumBruteForceTripCountsComputed; 1622 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum)); 1623 } 1624 1625 // Compute the value of the PHI node for the next iteration. 1626 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1627 if (NextPHI == 0 || NextPHI == PHIVal) 1628 return UnknownValue; // Couldn't evaluate or not making progress... 1629 PHIVal = NextPHI; 1630 } 1631 1632 // Too many iterations were needed to evaluate. 1633 return UnknownValue; 1634} 1635 1636/// getSCEVAtScope - Compute the value of the specified expression within the 1637/// indicated loop (which may be null to indicate in no loop). If the 1638/// expression cannot be evaluated, return UnknownValue. 1639SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1640 // FIXME: this should be turned into a virtual method on SCEV! 1641 1642 if (isa<SCEVConstant>(V)) return V; 1643 1644 // If this instruction is evolves from a constant-evolving PHI, compute the 1645 // exit value from the loop without using SCEVs. 1646 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1647 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1648 const Loop *LI = this->LI[I->getParent()]; 1649 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1650 if (PHINode *PN = dyn_cast<PHINode>(I)) 1651 if (PN->getParent() == LI->getHeader()) { 1652 // Okay, there is no closed form solution for the PHI node. Check 1653 // to see if the loop that contains it has a known iteration count. 1654 // If so, we may be able to force computation of the exit value. 1655 SCEVHandle IterationCount = getIterationCount(LI); 1656 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1657 // Okay, we know how many times the containing loop executes. If 1658 // this is a constant evolving PHI node, get the final value at 1659 // the specified iteration number. 1660 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1661 ICC->getValue()->getRawValue(), 1662 LI); 1663 if (RV) return SCEVUnknown::get(RV); 1664 } 1665 } 1666 1667 // Okay, this is a some expression that we cannot symbolically evaluate 1668 // into a SCEV. Check to see if it's possible to symbolically evaluate 1669 // the arguments into constants, and if see, try to constant propagate the 1670 // result. This is particularly useful for computing loop exit values. 1671 if (CanConstantFold(I)) { 1672 std::vector<Constant*> Operands; 1673 Operands.reserve(I->getNumOperands()); 1674 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1675 Value *Op = I->getOperand(i); 1676 if (Constant *C = dyn_cast<Constant>(Op)) { 1677 Operands.push_back(C); 1678 } else if (GlobalValue *GV = dyn_cast<GlobalValue>(Op)) { 1679 Operands.push_back(ConstantPointerRef::get(GV)); 1680 } else { 1681 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1682 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1683 Operands.push_back(ConstantExpr::getCast(SC->getValue(), 1684 Op->getType())); 1685 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1686 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1687 Operands.push_back(ConstantExpr::getCast(C, Op->getType())); 1688 else 1689 return V; 1690 } else { 1691 return V; 1692 } 1693 } 1694 } 1695 return SCEVUnknown::get(ConstantFold(I, Operands)); 1696 } 1697 } 1698 1699 // This is some other type of SCEVUnknown, just return it. 1700 return V; 1701 } 1702 1703 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1704 // Avoid performing the look-up in the common case where the specified 1705 // expression has no loop-variant portions. 1706 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1707 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1708 if (OpAtScope != Comm->getOperand(i)) { 1709 if (OpAtScope == UnknownValue) return UnknownValue; 1710 // Okay, at least one of these operands is loop variant but might be 1711 // foldable. Build a new instance of the folded commutative expression. 1712 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 1713 NewOps.push_back(OpAtScope); 1714 1715 for (++i; i != e; ++i) { 1716 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1717 if (OpAtScope == UnknownValue) return UnknownValue; 1718 NewOps.push_back(OpAtScope); 1719 } 1720 if (isa<SCEVAddExpr>(Comm)) 1721 return SCEVAddExpr::get(NewOps); 1722 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 1723 return SCEVMulExpr::get(NewOps); 1724 } 1725 } 1726 // If we got here, all operands are loop invariant. 1727 return Comm; 1728 } 1729 1730 if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) { 1731 SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L); 1732 if (LHS == UnknownValue) return LHS; 1733 SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L); 1734 if (RHS == UnknownValue) return RHS; 1735 if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS()) 1736 return UDiv; // must be loop invariant 1737 return SCEVUDivExpr::get(LHS, RHS); 1738 } 1739 1740 // If this is a loop recurrence for a loop that does not contain L, then we 1741 // are dealing with the final value computed by the loop. 1742 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 1743 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 1744 // To evaluate this recurrence, we need to know how many times the AddRec 1745 // loop iterates. Compute this now. 1746 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 1747 if (IterationCount == UnknownValue) return UnknownValue; 1748 IterationCount = getTruncateOrZeroExtend(IterationCount, 1749 AddRec->getType()); 1750 1751 // If the value is affine, simplify the expression evaluation to just 1752 // Start + Step*IterationCount. 1753 if (AddRec->isAffine()) 1754 return SCEVAddExpr::get(AddRec->getStart(), 1755 SCEVMulExpr::get(IterationCount, 1756 AddRec->getOperand(1))); 1757 1758 // Otherwise, evaluate it the hard way. 1759 return AddRec->evaluateAtIteration(IterationCount); 1760 } 1761 return UnknownValue; 1762 } 1763 1764 //assert(0 && "Unknown SCEV type!"); 1765 return UnknownValue; 1766} 1767 1768 1769/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 1770/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 1771/// might be the same) or two SCEVCouldNotCompute objects. 1772/// 1773static std::pair<SCEVHandle,SCEVHandle> 1774SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 1775 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 1776 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 1777 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 1778 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 1779 1780 // We currently can only solve this if the coefficients are constants. 1781 if (!L || !M || !N) { 1782 SCEV *CNC = new SCEVCouldNotCompute(); 1783 return std::make_pair(CNC, CNC); 1784 } 1785 1786 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2); 1787 1788 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 1789 Constant *C = L->getValue(); 1790 // The B coefficient is M-N/2 1791 Constant *B = ConstantExpr::getSub(M->getValue(), 1792 ConstantExpr::getDiv(N->getValue(), 1793 Two)); 1794 // The A coefficient is N/2 1795 Constant *A = ConstantExpr::getDiv(N->getValue(), Two); 1796 1797 // Compute the B^2-4ac term. 1798 Constant *SqrtTerm = 1799 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 1800 ConstantExpr::getMul(A, C)); 1801 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 1802 1803 // Compute floor(sqrt(B^2-4ac)) 1804 ConstantUInt *SqrtVal = 1805 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm, 1806 SqrtTerm->getType()->getUnsignedVersion())); 1807 uint64_t SqrtValV = SqrtVal->getValue(); 1808 uint64_t SqrtValV2 = (uint64_t)sqrt(SqrtValV); 1809 // The square root might not be precise for arbitrary 64-bit integer 1810 // values. Do some sanity checks to ensure it's correct. 1811 if (SqrtValV2*SqrtValV2 > SqrtValV || 1812 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 1813 SCEV *CNC = new SCEVCouldNotCompute(); 1814 return std::make_pair(CNC, CNC); 1815 } 1816 1817 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2); 1818 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType()); 1819 1820 Constant *NegB = ConstantExpr::getNeg(B); 1821 Constant *TwoA = ConstantExpr::getMul(A, Two); 1822 1823 // The divisions must be performed as signed divisions. 1824 const Type *SignedTy = NegB->getType()->getSignedVersion(); 1825 NegB = ConstantExpr::getCast(NegB, SignedTy); 1826 TwoA = ConstantExpr::getCast(TwoA, SignedTy); 1827 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy); 1828 1829 Constant *Solution1 = 1830 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 1831 Constant *Solution2 = 1832 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 1833 return std::make_pair(SCEVUnknown::get(Solution1), 1834 SCEVUnknown::get(Solution2)); 1835} 1836 1837/// HowFarToZero - Return the number of times a backedge comparing the specified 1838/// value to zero will execute. If not computable, return UnknownValue 1839SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 1840 // If the value is a constant 1841 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 1842 // If the value is already zero, the branch will execute zero times. 1843 if (C->getValue()->isNullValue()) return C; 1844 return UnknownValue; // Otherwise it will loop infinitely. 1845 } 1846 1847 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 1848 if (!AddRec || AddRec->getLoop() != L) 1849 return UnknownValue; 1850 1851 if (AddRec->isAffine()) { 1852 // If this is an affine expression the execution count of this branch is 1853 // equal to: 1854 // 1855 // (0 - Start/Step) iff Start % Step == 0 1856 // 1857 // Get the initial value for the loop. 1858 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 1859 SCEVHandle Step = AddRec->getOperand(1); 1860 1861 Step = getSCEVAtScope(Step, L->getParentLoop()); 1862 1863 // Figure out if Start % Step == 0. 1864 // FIXME: We should add DivExpr and RemExpr operations to our AST. 1865 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 1866 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 1867 return getNegativeSCEV(Start); // 0 - Start/1 == -Start 1868 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 1869 return Start; // 0 - Start/-1 == Start 1870 1871 // Check to see if Start is divisible by SC with no remainder. 1872 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 1873 ConstantInt *StartCC = StartC->getValue(); 1874 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 1875 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue()); 1876 if (Rem->isNullValue()) { 1877 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue()); 1878 return SCEVUnknown::get(Result); 1879 } 1880 } 1881 } 1882 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 1883 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 1884 // the quadratic equation to solve it. 1885 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 1886 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 1887 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 1888 if (R1) { 1889#if 0 1890 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1 1891 << " sol#2: " << *R2 << "\n"; 1892#endif 1893 // Pick the smallest positive root value. 1894 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 1895 if (ConstantBool *CB = 1896 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 1897 R2->getValue()))) { 1898 if (CB != ConstantBool::True) 1899 std::swap(R1, R2); // R1 is the minimum root now. 1900 1901 // We can only use this value if the chrec ends up with an exact zero 1902 // value at this index. When solving for "X*X != 5", for example, we 1903 // should not accept a root of 2. 1904 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 1905 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 1906 if (EvalVal->getValue()->isNullValue()) 1907 return R1; // We found a quadratic root! 1908 } 1909 } 1910 } 1911 1912 return UnknownValue; 1913} 1914 1915/// HowFarToNonZero - Return the number of times a backedge checking the 1916/// specified value for nonzero will execute. If not computable, return 1917/// UnknownValue 1918SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 1919 // Loops that look like: while (X == 0) are very strange indeed. We don't 1920 // handle them yet except for the trivial case. This could be expanded in the 1921 // future as needed. 1922 1923 // If the value is a constant, check to see if it is known to be non-zero 1924 // already. If so, the backedge will execute zero times. 1925 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 1926 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 1927 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 1928 if (NonZero == ConstantBool::True) 1929 return getSCEV(Zero); 1930 return UnknownValue; // Otherwise it will loop infinitely. 1931 } 1932 1933 // We could implement others, but I really doubt anyone writes loops like 1934 // this, and if they did, they would already be constant folded. 1935 return UnknownValue; 1936} 1937 1938static ConstantInt * 1939EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1940 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1941 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1942 assert(isa<SCEVConstant>(Val) && 1943 "Evaluation of SCEV at constant didn't fold correctly?"); 1944 return cast<SCEVConstant>(Val)->getValue(); 1945} 1946 1947 1948/// getNumIterationsInRange - Return the number of iterations of this loop that 1949/// produce values in the specified constant range. Another way of looking at 1950/// this is that it returns the first iteration number where the value is not in 1951/// the condition, thus computing the exit count. If the iteration count can't 1952/// be computed, an instance of SCEVCouldNotCompute is returned. 1953SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 1954 if (Range.isFullSet()) // Infinite loop. 1955 return new SCEVCouldNotCompute(); 1956 1957 // If the start is a non-zero constant, shift the range to simplify things. 1958 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 1959 if (!SC->getValue()->isNullValue()) { 1960 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 1961 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 1962 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 1963 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 1964 return ShiftedAddRec->getNumIterationsInRange( 1965 Range.subtract(SC->getValue())); 1966 // This is strange and shouldn't happen. 1967 return new SCEVCouldNotCompute(); 1968 } 1969 1970 // The only time we can solve this is when we have all constant indices. 1971 // Otherwise, we cannot determine the overflow conditions. 1972 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 1973 if (!isa<SCEVConstant>(getOperand(i))) 1974 return new SCEVCouldNotCompute(); 1975 1976 1977 // Okay at this point we know that all elements of the chrec are constants and 1978 // that the start element is zero. 1979 1980 // First check to see if the range contains zero. If not, the first 1981 // iteration exits. 1982 ConstantInt *Zero = ConstantInt::get(getType(), 0); 1983 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 1984 1985 if (isAffine()) { 1986 // If this is an affine expression then we have this situation: 1987 // Solve {0,+,A} in Range === Ax in Range 1988 1989 // Since we know that zero is in the range, we know that the upper value of 1990 // the range must be the first possible exit value. Also note that we 1991 // already checked for a full range. 1992 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 1993 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 1994 ConstantInt *One = ConstantInt::get(getType(), 1); 1995 1996 // The exit value should be (Upper+A-1)/A. 1997 Constant *ExitValue = Upper; 1998 if (A != One) { 1999 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2000 ExitValue = ConstantExpr::getDiv(ExitValue, A); 2001 } 2002 assert(isa<ConstantInt>(ExitValue) && 2003 "Constant folding of integers not implemented?"); 2004 2005 // Evaluate at the exit value. If we really did fall out of the valid 2006 // range, then we computed our trip count, otherwise wrap around or other 2007 // things must have happened. 2008 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2009 if (Range.contains(Val)) 2010 return new SCEVCouldNotCompute(); // Something strange happened 2011 2012 // Ensure that the previous value is in the range. This is a sanity check. 2013 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2014 ConstantExpr::getSub(ExitValue, One))) && 2015 "Linear scev computation is off in a bad way!"); 2016 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2017 } else if (isQuadratic()) { 2018 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2019 // quadratic equation to solve it. To do this, we must frame our problem in 2020 // terms of figuring out when zero is crossed, instead of when 2021 // Range.getUpper() is crossed. 2022 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2023 NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2024 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2025 2026 // Next, solve the constructed addrec 2027 std::pair<SCEVHandle,SCEVHandle> Roots = 2028 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2029 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2030 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2031 if (R1) { 2032 // Pick the smallest positive root value. 2033 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2034 if (ConstantBool *CB = 2035 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2036 R2->getValue()))) { 2037 if (CB != ConstantBool::True) 2038 std::swap(R1, R2); // R1 is the minimum root now. 2039 2040 // Make sure the root is not off by one. The returned iteration should 2041 // not be in the range, but the previous one should be. When solving 2042 // for "X*X < 5", for example, we should not return a root of 2. 2043 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2044 R1->getValue()); 2045 if (Range.contains(R1Val)) { 2046 // The next iteration must be out of the range... 2047 Constant *NextVal = 2048 ConstantExpr::getAdd(R1->getValue(), 2049 ConstantInt::get(R1->getType(), 1)); 2050 2051 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2052 if (!Range.contains(R1Val)) 2053 return SCEVUnknown::get(NextVal); 2054 return new SCEVCouldNotCompute(); // Something strange happened 2055 } 2056 2057 // If R1 was not in the range, then it is a good return value. Make 2058 // sure that R1-1 WAS in the range though, just in case. 2059 Constant *NextVal = 2060 ConstantExpr::getSub(R1->getValue(), 2061 ConstantInt::get(R1->getType(), 1)); 2062 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2063 if (Range.contains(R1Val)) 2064 return R1; 2065 return new SCEVCouldNotCompute(); // Something strange happened 2066 } 2067 } 2068 } 2069 2070 // Fallback, if this is a general polynomial, figure out the progression 2071 // through brute force: evaluate until we find an iteration that fails the 2072 // test. This is likely to be slow, but getting an accurate trip count is 2073 // incredibly important, we will be able to simplify the exit test a lot, and 2074 // we are almost guaranteed to get a trip count in this case. 2075 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2076 ConstantInt *One = ConstantInt::get(getType(), 1); 2077 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2078 do { 2079 ++NumBruteForceEvaluations; 2080 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2081 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2082 return new SCEVCouldNotCompute(); 2083 2084 // Check to see if we found the value! 2085 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2086 return SCEVConstant::get(TestVal); 2087 2088 // Increment to test the next index. 2089 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2090 } while (TestVal != EndVal); 2091 2092 return new SCEVCouldNotCompute(); 2093} 2094 2095 2096 2097//===----------------------------------------------------------------------===// 2098// ScalarEvolution Class Implementation 2099//===----------------------------------------------------------------------===// 2100 2101bool ScalarEvolution::runOnFunction(Function &F) { 2102 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2103 return false; 2104} 2105 2106void ScalarEvolution::releaseMemory() { 2107 delete (ScalarEvolutionsImpl*)Impl; 2108 Impl = 0; 2109} 2110 2111void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2112 AU.setPreservesAll(); 2113 AU.addRequiredID(LoopSimplifyID); 2114 AU.addRequiredTransitive<LoopInfo>(); 2115} 2116 2117SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2118 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2119} 2120 2121SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2122 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2123} 2124 2125bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2126 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2127} 2128 2129SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2130 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2131} 2132 2133void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2134 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2135} 2136 2137 2138/// shouldSubstituteIndVar - Return true if we should perform induction variable 2139/// substitution for this variable. This is a hack because we don't have a 2140/// strength reduction pass yet. When we do we will promote all vars, because 2141/// we can strength reduce them later as desired. 2142bool ScalarEvolution::shouldSubstituteIndVar(const SCEV *S) const { 2143 // Don't substitute high degree polynomials. 2144 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) 2145 if (AddRec->getNumOperands() > 3) return false; 2146 return true; 2147} 2148 2149 2150static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2151 const Loop *L) { 2152 // Print all inner loops first 2153 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2154 PrintLoopInfo(OS, SE, *I); 2155 2156 std::cerr << "Loop " << L->getHeader()->getName() << ": "; 2157 2158 std::vector<BasicBlock*> ExitBlocks; 2159 L->getExitBlocks(ExitBlocks); 2160 if (ExitBlocks.size() != 1) 2161 std::cerr << "<multiple exits> "; 2162 2163 if (SE->hasLoopInvariantIterationCount(L)) { 2164 std::cerr << *SE->getIterationCount(L) << " iterations! "; 2165 } else { 2166 std::cerr << "Unpredictable iteration count. "; 2167 } 2168 2169 std::cerr << "\n"; 2170} 2171 2172void ScalarEvolution::print(std::ostream &OS) const { 2173 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2174 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2175 2176 OS << "Classifying expressions for: " << F.getName() << "\n"; 2177 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2178 if ((*I)->getType()->isInteger()) { 2179 OS << **I; 2180 OS << " --> "; 2181 SCEVHandle SV = getSCEV(*I); 2182 SV->print(OS); 2183 OS << "\t\t"; 2184 2185 if ((*I)->getType()->isIntegral()) { 2186 ConstantRange Bounds = SV->getValueRange(); 2187 if (!Bounds.isFullSet()) 2188 OS << "Bounds: " << Bounds << " "; 2189 } 2190 2191 if (const Loop *L = LI.getLoopFor((*I)->getParent())) { 2192 OS << "Exits: "; 2193 SCEVHandle ExitValue = getSCEVAtScope(*I, L->getParentLoop()); 2194 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2195 OS << "<<Unknown>>"; 2196 } else { 2197 OS << *ExitValue; 2198 } 2199 } 2200 2201 2202 OS << "\n"; 2203 } 2204 2205 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2206 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2207 PrintLoopInfo(OS, this, *I); 2208} 2209 2210