ScalarEvolution.cpp revision 5aa20212cc8dd1008d05915bf23dd02143fc5de9
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// 110SCEV::~SCEV() {} 111void SCEV::dump() const { 112 print(std::cerr); 113} 114 115/// getValueRange - Return the tightest constant bounds that this value is 116/// known to have. This method is only valid on integer SCEV objects. 117ConstantRange SCEV::getValueRange() const { 118 const Type *Ty = getType(); 119 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 120 Ty = Ty->getUnsignedVersion(); 121 // Default to a full range if no better information is available. 122 return ConstantRange(getType()); 123} 124 125 126SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 127 128bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 129 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 130 return false; 131} 132 133const Type *SCEVCouldNotCompute::getType() const { 134 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 135 return 0; 136} 137 138bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 140 return false; 141} 142 143void SCEVCouldNotCompute::print(std::ostream &OS) const { 144 OS << "***COULDNOTCOMPUTE***"; 145} 146 147bool SCEVCouldNotCompute::classof(const SCEV *S) { 148 return S->getSCEVType() == scCouldNotCompute; 149} 150 151 152// SCEVConstants - Only allow the creation of one SCEVConstant for any 153// particular value. Don't use a SCEVHandle here, or else the object will 154// never be deleted! 155static std::map<ConstantInt*, SCEVConstant*> SCEVConstants; 156 157 158SCEVConstant::~SCEVConstant() { 159 SCEVConstants.erase(V); 160} 161 162SCEVHandle SCEVConstant::get(ConstantInt *V) { 163 // Make sure that SCEVConstant instances are all unsigned. 164 if (V->getType()->isSigned()) { 165 const Type *NewTy = V->getType()->getUnsignedVersion(); 166 V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy)); 167 } 168 169 SCEVConstant *&R = SCEVConstants[V]; 170 if (R == 0) R = new SCEVConstant(V); 171 return R; 172} 173 174ConstantRange SCEVConstant::getValueRange() const { 175 return ConstantRange(V); 176} 177 178const Type *SCEVConstant::getType() const { return V->getType(); } 179 180void SCEVConstant::print(std::ostream &OS) const { 181 WriteAsOperand(OS, V, false); 182} 183 184// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 185// particular input. Don't use a SCEVHandle here, or else the object will 186// never be deleted! 187static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates; 188 189SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 190 : SCEV(scTruncate), Op(op), Ty(ty) { 191 assert(Op->getType()->isInteger() && Ty->isInteger() && 192 Ty->isUnsigned() && 193 "Cannot truncate non-integer value!"); 194 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 195 "This is not a truncating conversion!"); 196} 197 198SCEVTruncateExpr::~SCEVTruncateExpr() { 199 SCEVTruncates.erase(std::make_pair(Op, Ty)); 200} 201 202ConstantRange SCEVTruncateExpr::getValueRange() const { 203 return getOperand()->getValueRange().truncate(getType()); 204} 205 206void SCEVTruncateExpr::print(std::ostream &OS) const { 207 OS << "(truncate " << *Op << " to " << *Ty << ")"; 208} 209 210// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 211// particular input. Don't use a SCEVHandle here, or else the object will never 212// be deleted! 213static std::map<std::pair<SCEV*, const Type*>, 214 SCEVZeroExtendExpr*> SCEVZeroExtends; 215 216SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 217 : SCEV(scTruncate), Op(Op), Ty(ty) { 218 assert(Op->getType()->isInteger() && Ty->isInteger() && 219 Ty->isUnsigned() && 220 "Cannot zero extend non-integer value!"); 221 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 222 "This is not an extending conversion!"); 223} 224 225SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 226 SCEVZeroExtends.erase(std::make_pair(Op, Ty)); 227} 228 229ConstantRange SCEVZeroExtendExpr::getValueRange() const { 230 return getOperand()->getValueRange().zeroExtend(getType()); 231} 232 233void SCEVZeroExtendExpr::print(std::ostream &OS) const { 234 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 235} 236 237// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 238// particular input. Don't use a SCEVHandle here, or else the object will never 239// be deleted! 240static std::map<std::pair<unsigned, std::vector<SCEV*> >, 241 SCEVCommutativeExpr*> SCEVCommExprs; 242 243SCEVCommutativeExpr::~SCEVCommutativeExpr() { 244 SCEVCommExprs.erase(std::make_pair(getSCEVType(), 245 std::vector<SCEV*>(Operands.begin(), 246 Operands.end()))); 247} 248 249void SCEVCommutativeExpr::print(std::ostream &OS) const { 250 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 251 const char *OpStr = getOperationStr(); 252 OS << "(" << *Operands[0]; 253 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 254 OS << OpStr << *Operands[i]; 255 OS << ")"; 256} 257 258// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 259// input. Don't use a SCEVHandle here, or else the object will never be 260// deleted! 261static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs; 262 263SCEVUDivExpr::~SCEVUDivExpr() { 264 SCEVUDivs.erase(std::make_pair(LHS, RHS)); 265} 266 267void SCEVUDivExpr::print(std::ostream &OS) const { 268 OS << "(" << *LHS << " /u " << *RHS << ")"; 269} 270 271const Type *SCEVUDivExpr::getType() const { 272 const Type *Ty = LHS->getType(); 273 if (Ty->isSigned()) Ty = Ty->getUnsignedVersion(); 274 return Ty; 275} 276 277// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 278// particular input. Don't use a SCEVHandle here, or else the object will never 279// be deleted! 280static std::map<std::pair<const Loop *, std::vector<SCEV*> >, 281 SCEVAddRecExpr*> SCEVAddRecExprs; 282 283SCEVAddRecExpr::~SCEVAddRecExpr() { 284 SCEVAddRecExprs.erase(std::make_pair(L, 285 std::vector<SCEV*>(Operands.begin(), 286 Operands.end()))); 287} 288 289bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 290 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 291 // contain L. 292 return !QueryLoop->contains(L->getHeader()); 293} 294 295 296void SCEVAddRecExpr::print(std::ostream &OS) const { 297 OS << "{" << *Operands[0]; 298 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 299 OS << ",+," << *Operands[i]; 300 OS << "}<" << L->getHeader()->getName() + ">"; 301} 302 303// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 304// value. Don't use a SCEVHandle here, or else the object will never be 305// deleted! 306static std::map<Value*, SCEVUnknown*> SCEVUnknowns; 307 308SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); } 309 310bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 311 // All non-instruction values are loop invariant. All instructions are loop 312 // invariant if they are not contained in the specified loop. 313 if (Instruction *I = dyn_cast<Instruction>(V)) 314 return !L->contains(I->getParent()); 315 return true; 316} 317 318const Type *SCEVUnknown::getType() const { 319 return V->getType(); 320} 321 322void SCEVUnknown::print(std::ostream &OS) const { 323 WriteAsOperand(OS, V, false); 324} 325 326//===----------------------------------------------------------------------===// 327// SCEV Utilities 328//===----------------------------------------------------------------------===// 329 330namespace { 331 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 332 /// than the complexity of the RHS. This comparator is used to canonicalize 333 /// expressions. 334 struct SCEVComplexityCompare { 335 bool operator()(SCEV *LHS, SCEV *RHS) { 336 return LHS->getSCEVType() < RHS->getSCEVType(); 337 } 338 }; 339} 340 341/// GroupByComplexity - Given a list of SCEV objects, order them by their 342/// complexity, and group objects of the same complexity together by value. 343/// When this routine is finished, we know that any duplicates in the vector are 344/// consecutive and that complexity is monotonically increasing. 345/// 346/// Note that we go take special precautions to ensure that we get determinstic 347/// results from this routine. In other words, we don't want the results of 348/// this to depend on where the addresses of various SCEV objects happened to 349/// land in memory. 350/// 351static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 352 if (Ops.size() < 2) return; // Noop 353 if (Ops.size() == 2) { 354 // This is the common case, which also happens to be trivially simple. 355 // Special case it. 356 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 357 std::swap(Ops[0], Ops[1]); 358 return; 359 } 360 361 // Do the rough sort by complexity. 362 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 363 364 // Now that we are sorted by complexity, group elements of the same 365 // complexity. Note that this is, at worst, N^2, but the vector is likely to 366 // be extremely short in practice. Note that we take this approach because we 367 // do not want to depend on the addresses of the objects we are grouping. 368 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 369 SCEV *S = Ops[i]; 370 unsigned Complexity = S->getSCEVType(); 371 372 // If there are any objects of the same complexity and same value as this 373 // one, group them. 374 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 375 if (Ops[j] == S) { // Found a duplicate. 376 // Move it to immediately after i'th element. 377 std::swap(Ops[i+1], Ops[j]); 378 ++i; // no need to rescan it. 379 if (i == e-2) return; // Done! 380 } 381 } 382 } 383} 384 385 386 387//===----------------------------------------------------------------------===// 388// Simple SCEV method implementations 389//===----------------------------------------------------------------------===// 390 391/// getIntegerSCEV - Given an integer or FP type, create a constant for the 392/// specified signed integer value and return a SCEV for the constant. 393SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 394 Constant *C; 395 if (Val == 0) 396 C = Constant::getNullValue(Ty); 397 else if (Ty->isFloatingPoint()) 398 C = ConstantFP::get(Ty, Val); 399 else if (Ty->isSigned()) 400 C = ConstantSInt::get(Ty, Val); 401 else { 402 C = ConstantSInt::get(Ty->getSignedVersion(), Val); 403 C = ConstantExpr::getCast(C, Ty); 404 } 405 return SCEVUnknown::get(C); 406} 407 408/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 409/// input value to the specified type. If the type must be extended, it is zero 410/// extended. 411static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 412 const Type *SrcTy = V->getType(); 413 assert(SrcTy->isInteger() && Ty->isInteger() && 414 "Cannot truncate or zero extend with non-integer arguments!"); 415 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 416 return V; // No conversion 417 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 418 return SCEVTruncateExpr::get(V, Ty); 419 return SCEVZeroExtendExpr::get(V, Ty); 420} 421 422/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 423/// 424static SCEVHandle getNegativeSCEV(const SCEVHandle &V) { 425 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 426 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 427 428 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 429} 430 431/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 432/// 433static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 434 // X - Y --> X + -Y 435 return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS)); 436} 437 438 439/// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is 440/// often very small, so we try to reduce the number of N! terms we need to 441/// evaluate by evaluating this as (N!/(N-M)!)/M! 442static ConstantInt *Binomial(ConstantInt *N, unsigned M) { 443 uint64_t NVal = N->getRawValue(); 444 uint64_t FirstTerm = 1; 445 for (unsigned i = 0; i != M; ++i) 446 FirstTerm *= NVal-i; 447 448 unsigned MFactorial = 1; 449 for (; M; --M) 450 MFactorial *= M; 451 452 Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial); 453 Result = ConstantExpr::getCast(Result, N->getType()); 454 assert(isa<ConstantInt>(Result) && "Cast of integer not folded??"); 455 return cast<ConstantInt>(Result); 456} 457 458/// PartialFact - Compute V!/(V-NumSteps)! 459static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 460 // Handle this case efficiently, it is common to have constant iteration 461 // counts while computing loop exit values. 462 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 463 uint64_t Val = SC->getValue()->getRawValue(); 464 uint64_t Result = 1; 465 for (; NumSteps; --NumSteps) 466 Result *= Val-(NumSteps-1); 467 Constant *Res = ConstantUInt::get(Type::ULongTy, Result); 468 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType())); 469 } 470 471 const Type *Ty = V->getType(); 472 if (NumSteps == 0) 473 return SCEVUnknown::getIntegerSCEV(1, Ty); 474 475 SCEVHandle Result = V; 476 for (unsigned i = 1; i != NumSteps; ++i) 477 Result = SCEVMulExpr::get(Result, getMinusSCEV(V, 478 SCEVUnknown::getIntegerSCEV(i, Ty))); 479 return Result; 480} 481 482 483/// evaluateAtIteration - Return the value of this chain of recurrences at 484/// the specified iteration number. We can evaluate this recurrence by 485/// multiplying each element in the chain by the binomial coefficient 486/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 487/// 488/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 489/// 490/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 491/// Is the binomial equation safe using modular arithmetic?? 492/// 493SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 494 SCEVHandle Result = getStart(); 495 int Divisor = 1; 496 const Type *Ty = It->getType(); 497 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 498 SCEVHandle BC = PartialFact(It, i); 499 Divisor *= i; 500 SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 501 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 502 Result = SCEVAddExpr::get(Result, Val); 503 } 504 return Result; 505} 506 507 508//===----------------------------------------------------------------------===// 509// SCEV Expression folder implementations 510//===----------------------------------------------------------------------===// 511 512SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 513 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 514 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 515 516 // If the input value is a chrec scev made out of constants, truncate 517 // all of the constants. 518 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 519 std::vector<SCEVHandle> Operands; 520 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 521 // FIXME: This should allow truncation of other expression types! 522 if (isa<SCEVConstant>(AddRec->getOperand(i))) 523 Operands.push_back(get(AddRec->getOperand(i), Ty)); 524 else 525 break; 526 if (Operands.size() == AddRec->getNumOperands()) 527 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 528 } 529 530 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)]; 531 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 532 return Result; 533} 534 535SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 536 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 537 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 538 539 // FIXME: If the input value is a chrec scev, and we can prove that the value 540 // did not overflow the old, smaller, value, we can zero extend all of the 541 // operands (often constants). This would allow analysis of something like 542 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 543 544 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)]; 545 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 546 return Result; 547} 548 549// get - Get a canonical add expression, or something simpler if possible. 550SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 551 assert(!Ops.empty() && "Cannot get empty add!"); 552 if (Ops.size() == 1) return Ops[0]; 553 554 // Sort by complexity, this groups all similar expression types together. 555 GroupByComplexity(Ops); 556 557 // If there are any constants, fold them together. 558 unsigned Idx = 0; 559 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 560 ++Idx; 561 assert(Idx < Ops.size()); 562 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 563 // We found two constants, fold them together! 564 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 565 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 566 Ops[0] = SCEVConstant::get(CI); 567 Ops.erase(Ops.begin()+1); // Erase the folded element 568 if (Ops.size() == 1) return Ops[0]; 569 } else { 570 // If we couldn't fold the expression, move to the next constant. Note 571 // that this is impossible to happen in practice because we always 572 // constant fold constant ints to constant ints. 573 ++Idx; 574 } 575 } 576 577 // If we are left with a constant zero being added, strip it off. 578 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 579 Ops.erase(Ops.begin()); 580 --Idx; 581 } 582 } 583 584 if (Ops.size() == 1) return Ops[0]; 585 586 // Okay, check to see if the same value occurs in the operand list twice. If 587 // so, merge them together into an multiply expression. Since we sorted the 588 // list, these values are required to be adjacent. 589 const Type *Ty = Ops[0]->getType(); 590 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 591 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 592 // Found a match, merge the two values into a multiply, and add any 593 // remaining values to the result. 594 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 595 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 596 if (Ops.size() == 2) 597 return Mul; 598 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 599 Ops.push_back(Mul); 600 return SCEVAddExpr::get(Ops); 601 } 602 603 // Okay, now we know the first non-constant operand. If there are add 604 // operands they would be next. 605 if (Idx < Ops.size()) { 606 bool DeletedAdd = false; 607 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 608 // If we have an add, expand the add operands onto the end of the operands 609 // list. 610 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 611 Ops.erase(Ops.begin()+Idx); 612 DeletedAdd = true; 613 } 614 615 // If we deleted at least one add, we added operands to the end of the list, 616 // and they are not necessarily sorted. Recurse to resort and resimplify 617 // any operands we just aquired. 618 if (DeletedAdd) 619 return get(Ops); 620 } 621 622 // Skip over the add expression until we get to a multiply. 623 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 624 ++Idx; 625 626 // If we are adding something to a multiply expression, make sure the 627 // something is not already an operand of the multiply. If so, merge it into 628 // the multiply. 629 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 630 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 631 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 632 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 633 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 634 if (MulOpSCEV == Ops[AddOp] && 635 (Mul->getNumOperands() != 2 || !isa<SCEVConstant>(MulOpSCEV))) { 636 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 637 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 638 if (Mul->getNumOperands() != 2) { 639 // If the multiply has more than two operands, we must get the 640 // Y*Z term. 641 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 642 MulOps.erase(MulOps.begin()+MulOp); 643 InnerMul = SCEVMulExpr::get(MulOps); 644 } 645 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 646 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 647 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 648 if (Ops.size() == 2) return OuterMul; 649 if (AddOp < Idx) { 650 Ops.erase(Ops.begin()+AddOp); 651 Ops.erase(Ops.begin()+Idx-1); 652 } else { 653 Ops.erase(Ops.begin()+Idx); 654 Ops.erase(Ops.begin()+AddOp-1); 655 } 656 Ops.push_back(OuterMul); 657 return SCEVAddExpr::get(Ops); 658 } 659 660 // Check this multiply against other multiplies being added together. 661 for (unsigned OtherMulIdx = Idx+1; 662 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 663 ++OtherMulIdx) { 664 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 665 // If MulOp occurs in OtherMul, we can fold the two multiplies 666 // together. 667 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 668 OMulOp != e; ++OMulOp) 669 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 670 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 671 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 672 if (Mul->getNumOperands() != 2) { 673 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 674 MulOps.erase(MulOps.begin()+MulOp); 675 InnerMul1 = SCEVMulExpr::get(MulOps); 676 } 677 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 678 if (OtherMul->getNumOperands() != 2) { 679 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 680 OtherMul->op_end()); 681 MulOps.erase(MulOps.begin()+OMulOp); 682 InnerMul2 = SCEVMulExpr::get(MulOps); 683 } 684 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 685 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 686 if (Ops.size() == 2) return OuterMul; 687 Ops.erase(Ops.begin()+Idx); 688 Ops.erase(Ops.begin()+OtherMulIdx-1); 689 Ops.push_back(OuterMul); 690 return SCEVAddExpr::get(Ops); 691 } 692 } 693 } 694 } 695 696 // If there are any add recurrences in the operands list, see if any other 697 // added values are loop invariant. If so, we can fold them into the 698 // recurrence. 699 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 700 ++Idx; 701 702 // Scan over all recurrences, trying to fold loop invariants into them. 703 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 704 // Scan all of the other operands to this add and add them to the vector if 705 // they are loop invariant w.r.t. the recurrence. 706 std::vector<SCEVHandle> LIOps; 707 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 708 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 709 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 710 LIOps.push_back(Ops[i]); 711 Ops.erase(Ops.begin()+i); 712 --i; --e; 713 } 714 715 // If we found some loop invariants, fold them into the recurrence. 716 if (!LIOps.empty()) { 717 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 718 LIOps.push_back(AddRec->getStart()); 719 720 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 721 AddRecOps[0] = SCEVAddExpr::get(LIOps); 722 723 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 724 // If all of the other operands were loop invariant, we are done. 725 if (Ops.size() == 1) return NewRec; 726 727 // Otherwise, add the folded AddRec by the non-liv parts. 728 for (unsigned i = 0;; ++i) 729 if (Ops[i] == AddRec) { 730 Ops[i] = NewRec; 731 break; 732 } 733 return SCEVAddExpr::get(Ops); 734 } 735 736 // Okay, if there weren't any loop invariants to be folded, check to see if 737 // there are multiple AddRec's with the same loop induction variable being 738 // added together. If so, we can fold them. 739 for (unsigned OtherIdx = Idx+1; 740 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 741 if (OtherIdx != Idx) { 742 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 743 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 744 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 745 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 746 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 747 if (i >= NewOps.size()) { 748 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 749 OtherAddRec->op_end()); 750 break; 751 } 752 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 753 } 754 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 755 756 if (Ops.size() == 2) return NewAddRec; 757 758 Ops.erase(Ops.begin()+Idx); 759 Ops.erase(Ops.begin()+OtherIdx-1); 760 Ops.push_back(NewAddRec); 761 return SCEVAddExpr::get(Ops); 762 } 763 } 764 765 // Otherwise couldn't fold anything into this recurrence. Move onto the 766 // next one. 767 } 768 769 // Okay, it looks like we really DO need an add expr. Check to see if we 770 // already have one, otherwise create a new one. 771 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 772 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr, 773 SCEVOps)]; 774 if (Result == 0) Result = new SCEVAddExpr(Ops); 775 return Result; 776} 777 778 779SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 780 assert(!Ops.empty() && "Cannot get empty mul!"); 781 782 // Sort by complexity, this groups all similar expression types together. 783 GroupByComplexity(Ops); 784 785 // If there are any constants, fold them together. 786 unsigned Idx = 0; 787 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 788 789 // C1*(C2+V) -> C1*C2 + C1*V 790 if (Ops.size() == 2) 791 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 792 if (Add->getNumOperands() == 2 && 793 isa<SCEVConstant>(Add->getOperand(0))) 794 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 795 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 796 797 798 ++Idx; 799 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 800 // We found two constants, fold them together! 801 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 802 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 803 Ops[0] = SCEVConstant::get(CI); 804 Ops.erase(Ops.begin()+1); // Erase the folded element 805 if (Ops.size() == 1) return Ops[0]; 806 } else { 807 // If we couldn't fold the expression, move to the next constant. Note 808 // that this is impossible to happen in practice because we always 809 // constant fold constant ints to constant ints. 810 ++Idx; 811 } 812 } 813 814 // If we are left with a constant one being multiplied, strip it off. 815 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 816 Ops.erase(Ops.begin()); 817 --Idx; 818 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 819 // If we have a multiply of zero, it will always be zero. 820 return Ops[0]; 821 } 822 } 823 824 // Skip over the add expression until we get to a multiply. 825 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 826 ++Idx; 827 828 if (Ops.size() == 1) 829 return Ops[0]; 830 831 // If there are mul operands inline them all into this expression. 832 if (Idx < Ops.size()) { 833 bool DeletedMul = false; 834 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 835 // If we have an mul, expand the mul operands onto the end of the operands 836 // list. 837 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 838 Ops.erase(Ops.begin()+Idx); 839 DeletedMul = true; 840 } 841 842 // If we deleted at least one mul, we added operands to the end of the list, 843 // and they are not necessarily sorted. Recurse to resort and resimplify 844 // any operands we just aquired. 845 if (DeletedMul) 846 return get(Ops); 847 } 848 849 // If there are any add recurrences in the operands list, see if any other 850 // added values are loop invariant. If so, we can fold them into the 851 // recurrence. 852 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 853 ++Idx; 854 855 // Scan over all recurrences, trying to fold loop invariants into them. 856 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 857 // Scan all of the other operands to this mul and add them to the vector if 858 // they are loop invariant w.r.t. the recurrence. 859 std::vector<SCEVHandle> LIOps; 860 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 861 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 862 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 863 LIOps.push_back(Ops[i]); 864 Ops.erase(Ops.begin()+i); 865 --i; --e; 866 } 867 868 // If we found some loop invariants, fold them into the recurrence. 869 if (!LIOps.empty()) { 870 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 871 std::vector<SCEVHandle> NewOps; 872 NewOps.reserve(AddRec->getNumOperands()); 873 if (LIOps.size() == 1) { 874 SCEV *Scale = LIOps[0]; 875 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 876 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 877 } else { 878 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 879 std::vector<SCEVHandle> MulOps(LIOps); 880 MulOps.push_back(AddRec->getOperand(i)); 881 NewOps.push_back(SCEVMulExpr::get(MulOps)); 882 } 883 } 884 885 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 886 887 // If all of the other operands were loop invariant, we are done. 888 if (Ops.size() == 1) return NewRec; 889 890 // Otherwise, multiply the folded AddRec by the non-liv parts. 891 for (unsigned i = 0;; ++i) 892 if (Ops[i] == AddRec) { 893 Ops[i] = NewRec; 894 break; 895 } 896 return SCEVMulExpr::get(Ops); 897 } 898 899 // Okay, if there weren't any loop invariants to be folded, check to see if 900 // there are multiple AddRec's with the same loop induction variable being 901 // multiplied together. If so, we can fold them. 902 for (unsigned OtherIdx = Idx+1; 903 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 904 if (OtherIdx != Idx) { 905 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 906 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 907 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 908 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 909 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 910 G->getStart()); 911 SCEVHandle B = F->getStepRecurrence(); 912 SCEVHandle D = G->getStepRecurrence(); 913 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 914 SCEVMulExpr::get(G, B), 915 SCEVMulExpr::get(B, D)); 916 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 917 F->getLoop()); 918 if (Ops.size() == 2) return NewAddRec; 919 920 Ops.erase(Ops.begin()+Idx); 921 Ops.erase(Ops.begin()+OtherIdx-1); 922 Ops.push_back(NewAddRec); 923 return SCEVMulExpr::get(Ops); 924 } 925 } 926 927 // Otherwise couldn't fold anything into this recurrence. Move onto the 928 // next one. 929 } 930 931 // Okay, it looks like we really DO need an mul expr. Check to see if we 932 // already have one, otherwise create a new one. 933 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 934 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr, 935 SCEVOps)]; 936 if (Result == 0) Result = new SCEVMulExpr(Ops); 937 return Result; 938} 939 940SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 941 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 942 if (RHSC->getValue()->equalsInt(1)) 943 return LHS; // X /u 1 --> x 944 if (RHSC->getValue()->isAllOnesValue()) 945 return getNegativeSCEV(LHS); // X /u -1 --> -x 946 947 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 948 Constant *LHSCV = LHSC->getValue(); 949 Constant *RHSCV = RHSC->getValue(); 950 if (LHSCV->getType()->isSigned()) 951 LHSCV = ConstantExpr::getCast(LHSCV, 952 LHSCV->getType()->getUnsignedVersion()); 953 if (RHSCV->getType()->isSigned()) 954 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType()); 955 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV)); 956 } 957 } 958 959 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 960 961 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)]; 962 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 963 return Result; 964} 965 966 967/// SCEVAddRecExpr::get - Get a add recurrence expression for the 968/// specified loop. Simplify the expression as much as possible. 969SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 970 const SCEVHandle &Step, const Loop *L) { 971 std::vector<SCEVHandle> Operands; 972 Operands.push_back(Start); 973 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 974 if (StepChrec->getLoop() == L) { 975 Operands.insert(Operands.end(), StepChrec->op_begin(), 976 StepChrec->op_end()); 977 return get(Operands, L); 978 } 979 980 Operands.push_back(Step); 981 return get(Operands, L); 982} 983 984/// SCEVAddRecExpr::get - Get a add recurrence expression for the 985/// specified loop. Simplify the expression as much as possible. 986SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 987 const Loop *L) { 988 if (Operands.size() == 1) return Operands[0]; 989 990 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 991 if (StepC->getValue()->isNullValue()) { 992 Operands.pop_back(); 993 return get(Operands, L); // { X,+,0 } --> X 994 } 995 996 SCEVAddRecExpr *&Result = 997 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 998 Operands.end()))]; 999 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1000 return Result; 1001} 1002 1003SCEVHandle SCEVUnknown::get(Value *V) { 1004 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1005 return SCEVConstant::get(CI); 1006 SCEVUnknown *&Result = SCEVUnknowns[V]; 1007 if (Result == 0) Result = new SCEVUnknown(V); 1008 return Result; 1009} 1010 1011 1012//===----------------------------------------------------------------------===// 1013// ScalarEvolutionsImpl Definition and Implementation 1014//===----------------------------------------------------------------------===// 1015// 1016/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1017/// evolution code. 1018/// 1019namespace { 1020 struct ScalarEvolutionsImpl { 1021 /// F - The function we are analyzing. 1022 /// 1023 Function &F; 1024 1025 /// LI - The loop information for the function we are currently analyzing. 1026 /// 1027 LoopInfo &LI; 1028 1029 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1030 /// things. 1031 SCEVHandle UnknownValue; 1032 1033 /// Scalars - This is a cache of the scalars we have analyzed so far. 1034 /// 1035 std::map<Value*, SCEVHandle> Scalars; 1036 1037 /// IterationCounts - Cache the iteration count of the loops for this 1038 /// function as they are computed. 1039 std::map<const Loop*, SCEVHandle> IterationCounts; 1040 1041 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1042 /// the PHI instructions that we attempt to compute constant evolutions for. 1043 /// This allows us to avoid potentially expensive recomputation of these 1044 /// properties. An instruction maps to null if we are unable to compute its 1045 /// exit value. 1046 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1047 1048 public: 1049 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1050 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1051 1052 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1053 /// expression and create a new one. 1054 SCEVHandle getSCEV(Value *V); 1055 1056 /// getSCEVAtScope - Compute the value of the specified expression within 1057 /// the indicated loop (which may be null to indicate in no loop). If the 1058 /// expression cannot be evaluated, return UnknownValue itself. 1059 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1060 1061 1062 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1063 /// an analyzable loop-invariant iteration count. 1064 bool hasLoopInvariantIterationCount(const Loop *L); 1065 1066 /// getIterationCount - If the specified loop has a predictable iteration 1067 /// count, return it. Note that it is not valid to call this method on a 1068 /// loop without a loop-invariant iteration count. 1069 SCEVHandle getIterationCount(const Loop *L); 1070 1071 /// deleteInstructionFromRecords - This method should be called by the 1072 /// client before it removes an instruction from the program, to make sure 1073 /// that no dangling references are left around. 1074 void deleteInstructionFromRecords(Instruction *I); 1075 1076 private: 1077 /// createSCEV - We know that there is no SCEV for the specified value. 1078 /// Analyze the expression. 1079 SCEVHandle createSCEV(Value *V); 1080 SCEVHandle createNodeForCast(CastInst *CI); 1081 1082 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1083 /// SCEVs. 1084 SCEVHandle createNodeForPHI(PHINode *PN); 1085 void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN, 1086 std::set<Instruction*> &UpdatedInsts); 1087 1088 /// ComputeIterationCount - Compute the number of times the specified loop 1089 /// will iterate. 1090 SCEVHandle ComputeIterationCount(const Loop *L); 1091 1092 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1093 /// constant number of times (the condition evolves only from constants), 1094 /// try to evaluate a few iterations of the loop until we get the exit 1095 /// condition gets a value of ExitWhen (true or false). If we cannot 1096 /// evaluate the trip count of the loop, return UnknownValue. 1097 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1098 bool ExitWhen); 1099 1100 /// HowFarToZero - Return the number of times a backedge comparing the 1101 /// specified value to zero will execute. If not computable, return 1102 /// UnknownValue 1103 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1104 1105 /// HowFarToNonZero - Return the number of times a backedge checking the 1106 /// specified value for nonzero will execute. If not computable, return 1107 /// UnknownValue 1108 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1109 1110 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1111 /// in the header of its containing loop, we know the loop executes a 1112 /// constant number of times, and the PHI node is just a recurrence 1113 /// involving constants, fold it. 1114 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1115 const Loop *L); 1116 }; 1117} 1118 1119//===----------------------------------------------------------------------===// 1120// Basic SCEV Analysis and PHI Idiom Recognition Code 1121// 1122 1123/// deleteInstructionFromRecords - This method should be called by the 1124/// client before it removes an instruction from the program, to make sure 1125/// that no dangling references are left around. 1126void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1127 Scalars.erase(I); 1128 if (PHINode *PN = dyn_cast<PHINode>(I)) 1129 ConstantEvolutionLoopExitValue.erase(PN); 1130} 1131 1132 1133/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1134/// expression and create a new one. 1135SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1136 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1137 1138 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1139 if (I != Scalars.end()) return I->second; 1140 SCEVHandle S = createSCEV(V); 1141 Scalars.insert(std::make_pair(V, S)); 1142 return S; 1143} 1144 1145 1146/// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of 1147/// entries in the scalar map that refer to the "symbolic" PHI value instead of 1148/// the recurrence value. After we resolve the PHI we must loop over all of the 1149/// using instructions that have scalar map entries and update them. 1150void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I, 1151 PHINode *PN, 1152 std::set<Instruction*> &UpdatedInsts) { 1153 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1154 if (SI == Scalars.end()) return; // This scalar wasn't previous processed. 1155 if (UpdatedInsts.insert(I).second) { 1156 Scalars.erase(SI); // Remove the old entry 1157 getSCEV(I); // Calculate the new entry 1158 1159 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1160 UI != E; ++UI) 1161 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts); 1162 } 1163} 1164 1165 1166/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1167/// a loop header, making it a potential recurrence, or it doesn't. 1168/// 1169SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1170 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1171 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1172 if (L->getHeader() == PN->getParent()) { 1173 // If it lives in the loop header, it has two incoming values, one 1174 // from outside the loop, and one from inside. 1175 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1176 unsigned BackEdge = IncomingEdge^1; 1177 1178 // While we are analyzing this PHI node, handle its value symbolically. 1179 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1180 assert(Scalars.find(PN) == Scalars.end() && 1181 "PHI node already processed?"); 1182 Scalars.insert(std::make_pair(PN, SymbolicName)); 1183 1184 // Using this symbolic name for the PHI, analyze the value coming around 1185 // the back-edge. 1186 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1187 1188 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1189 // has a special value for the first iteration of the loop. 1190 1191 // If the value coming around the backedge is an add with the symbolic 1192 // value we just inserted, then we found a simple induction variable! 1193 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1194 // If there is a single occurrence of the symbolic value, replace it 1195 // with a recurrence. 1196 unsigned FoundIndex = Add->getNumOperands(); 1197 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1198 if (Add->getOperand(i) == SymbolicName) 1199 if (FoundIndex == e) { 1200 FoundIndex = i; 1201 break; 1202 } 1203 1204 if (FoundIndex != Add->getNumOperands()) { 1205 // Create an add with everything but the specified operand. 1206 std::vector<SCEVHandle> Ops; 1207 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1208 if (i != FoundIndex) 1209 Ops.push_back(Add->getOperand(i)); 1210 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1211 1212 // This is not a valid addrec if the step amount is varying each 1213 // loop iteration, but is not itself an addrec in this loop. 1214 if (Accum->isLoopInvariant(L) || 1215 (isa<SCEVAddRecExpr>(Accum) && 1216 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1217 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1218 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1219 1220 // Okay, for the entire analysis of this edge we assumed the PHI 1221 // to be symbolic. We now need to go back and update all of the 1222 // entries for the scalars that use the PHI (except for the PHI 1223 // itself) to use the new analyzed value instead of the "symbolic" 1224 // value. 1225 Scalars.find(PN)->second = PHISCEV; // Update the PHI value 1226 std::set<Instruction*> UpdatedInsts; 1227 UpdatedInsts.insert(PN); 1228 for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end(); 1229 UI != E; ++UI) 1230 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, 1231 UpdatedInsts); 1232 return PHISCEV; 1233 } 1234 } 1235 } 1236 1237 return SymbolicName; 1238 } 1239 1240 // If it's not a loop phi, we can't handle it yet. 1241 return SCEVUnknown::get(PN); 1242} 1243 1244/// createNodeForCast - Handle the various forms of casts that we support. 1245/// 1246SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) { 1247 const Type *SrcTy = CI->getOperand(0)->getType(); 1248 const Type *DestTy = CI->getType(); 1249 1250 // If this is a noop cast (ie, conversion from int to uint), ignore it. 1251 if (SrcTy->isLosslesslyConvertibleTo(DestTy)) 1252 return getSCEV(CI->getOperand(0)); 1253 1254 if (SrcTy->isInteger() && DestTy->isInteger()) { 1255 // Otherwise, if this is a truncating integer cast, we can represent this 1256 // cast. 1257 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1258 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)), 1259 CI->getType()->getUnsignedVersion()); 1260 if (SrcTy->isUnsigned() && 1261 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1262 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)), 1263 CI->getType()->getUnsignedVersion()); 1264 } 1265 1266 // If this is an sign or zero extending cast and we can prove that the value 1267 // will never overflow, we could do similar transformations. 1268 1269 // Otherwise, we can't handle this cast! 1270 return SCEVUnknown::get(CI); 1271} 1272 1273 1274/// createSCEV - We know that there is no SCEV for the specified value. 1275/// Analyze the expression. 1276/// 1277SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1278 if (Instruction *I = dyn_cast<Instruction>(V)) { 1279 switch (I->getOpcode()) { 1280 case Instruction::Add: 1281 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1282 getSCEV(I->getOperand(1))); 1283 case Instruction::Mul: 1284 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1285 getSCEV(I->getOperand(1))); 1286 case Instruction::Div: 1287 if (V->getType()->isInteger() && V->getType()->isUnsigned()) 1288 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), 1289 getSCEV(I->getOperand(1))); 1290 break; 1291 1292 case Instruction::Sub: 1293 return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1))); 1294 1295 case Instruction::Shl: 1296 // Turn shift left of a constant amount into a multiply. 1297 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1298 Constant *X = ConstantInt::get(V->getType(), 1); 1299 X = ConstantExpr::getShl(X, SA); 1300 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1301 } 1302 break; 1303 1304 case Instruction::Shr: 1305 if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1))) 1306 if (V->getType()->isUnsigned()) { 1307 Constant *X = ConstantInt::get(V->getType(), 1); 1308 X = ConstantExpr::getShl(X, SA); 1309 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1310 } 1311 break; 1312 1313 case Instruction::Cast: 1314 return createNodeForCast(cast<CastInst>(I)); 1315 1316 case Instruction::PHI: 1317 return createNodeForPHI(cast<PHINode>(I)); 1318 1319 default: // We cannot analyze this expression. 1320 break; 1321 } 1322 } 1323 1324 return SCEVUnknown::get(V); 1325} 1326 1327 1328 1329//===----------------------------------------------------------------------===// 1330// Iteration Count Computation Code 1331// 1332 1333/// getIterationCount - If the specified loop has a predictable iteration 1334/// count, return it. Note that it is not valid to call this method on a 1335/// loop without a loop-invariant iteration count. 1336SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1337 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1338 if (I == IterationCounts.end()) { 1339 SCEVHandle ItCount = ComputeIterationCount(L); 1340 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1341 if (ItCount != UnknownValue) { 1342 assert(ItCount->isLoopInvariant(L) && 1343 "Computed trip count isn't loop invariant for loop!"); 1344 ++NumTripCountsComputed; 1345 } else if (isa<PHINode>(L->getHeader()->begin())) { 1346 // Only count loops that have phi nodes as not being computable. 1347 ++NumTripCountsNotComputed; 1348 } 1349 } 1350 return I->second; 1351} 1352 1353/// ComputeIterationCount - Compute the number of times the specified loop 1354/// will iterate. 1355SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1356 // If the loop has a non-one exit block count, we can't analyze it. 1357 std::vector<BasicBlock*> ExitBlocks; 1358 L->getExitBlocks(ExitBlocks); 1359 if (ExitBlocks.size() != 1) return UnknownValue; 1360 1361 // Okay, there is one exit block. Try to find the condition that causes the 1362 // loop to be exited. 1363 BasicBlock *ExitBlock = ExitBlocks[0]; 1364 1365 BasicBlock *ExitingBlock = 0; 1366 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1367 PI != E; ++PI) 1368 if (L->contains(*PI)) { 1369 if (ExitingBlock == 0) 1370 ExitingBlock = *PI; 1371 else 1372 return UnknownValue; // More than one block exiting! 1373 } 1374 assert(ExitingBlock && "No exits from loop, something is broken!"); 1375 1376 // Okay, we've computed the exiting block. See what condition causes us to 1377 // exit. 1378 // 1379 // FIXME: we should be able to handle switch instructions (with a single exit) 1380 // FIXME: We should handle cast of int to bool as well 1381 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1382 if (ExitBr == 0) return UnknownValue; 1383 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1384 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1385 if (ExitCond == 0) // Not a setcc 1386 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1387 ExitBr->getSuccessor(0) == ExitBlock); 1388 1389 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1390 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1391 1392 // Try to evaluate any dependencies out of the loop. 1393 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1394 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1395 Tmp = getSCEVAtScope(RHS, L); 1396 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1397 1398 // If the condition was exit on true, convert the condition to exit on false. 1399 Instruction::BinaryOps Cond; 1400 if (ExitBr->getSuccessor(1) == ExitBlock) 1401 Cond = ExitCond->getOpcode(); 1402 else 1403 Cond = ExitCond->getInverseCondition(); 1404 1405 // At this point, we would like to compute how many iterations of the loop the 1406 // predicate will return true for these inputs. 1407 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1408 // If there is a constant, force it into the RHS. 1409 std::swap(LHS, RHS); 1410 Cond = SetCondInst::getSwappedCondition(Cond); 1411 } 1412 1413 // FIXME: think about handling pointer comparisons! i.e.: 1414 // while (P != P+100) ++P; 1415 1416 // If we have a comparison of a chrec against a constant, try to use value 1417 // ranges to answer this query. 1418 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1419 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1420 if (AddRec->getLoop() == L) { 1421 // Form the comparison range using the constant of the correct type so 1422 // that the ConstantRange class knows to do a signed or unsigned 1423 // comparison. 1424 ConstantInt *CompVal = RHSC->getValue(); 1425 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1426 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy)); 1427 if (CompVal) { 1428 // Form the constant range. 1429 ConstantRange CompRange(Cond, CompVal); 1430 1431 // Now that we have it, if it's signed, convert it to an unsigned 1432 // range. 1433 if (CompRange.getLower()->getType()->isSigned()) { 1434 const Type *NewTy = RHSC->getValue()->getType(); 1435 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy); 1436 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy); 1437 CompRange = ConstantRange(NewL, NewU); 1438 } 1439 1440 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1441 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1442 } 1443 } 1444 1445 switch (Cond) { 1446 case Instruction::SetNE: // while (X != Y) 1447 // Convert to: while (X-Y != 0) 1448 if (LHS->getType()->isInteger()) { 1449 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 1450 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1451 } 1452 break; 1453 case Instruction::SetEQ: 1454 // Convert to: while (X-Y == 0) // while (X == Y) 1455 if (LHS->getType()->isInteger()) { 1456 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 1457 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1458 } 1459 break; 1460 default: 1461#if 0 1462 std::cerr << "ComputeIterationCount "; 1463 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1464 std::cerr << "[unsigned] "; 1465 std::cerr << *LHS << " " 1466 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1467#endif 1468 break; 1469 } 1470 1471 return ComputeIterationCountExhaustively(L, ExitCond, 1472 ExitBr->getSuccessor(0) == ExitBlock); 1473} 1474 1475/// CanConstantFold - Return true if we can constant fold an instruction of the 1476/// specified type, assuming that all operands were constants. 1477static bool CanConstantFold(const Instruction *I) { 1478 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1479 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1480 return true; 1481 1482 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1483 if (const Function *F = CI->getCalledFunction()) 1484 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1485 return false; 1486} 1487 1488/// ConstantFold - Constant fold an instruction of the specified type with the 1489/// specified constant operands. This function may modify the operands vector. 1490static Constant *ConstantFold(const Instruction *I, 1491 std::vector<Constant*> &Operands) { 1492 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1493 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1494 1495 switch (I->getOpcode()) { 1496 case Instruction::Cast: 1497 return ConstantExpr::getCast(Operands[0], I->getType()); 1498 case Instruction::Select: 1499 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1500 case Instruction::Call: 1501 if (ConstantPointerRef *CPR = dyn_cast<ConstantPointerRef>(Operands[0])) { 1502 Operands.erase(Operands.begin()); 1503 return ConstantFoldCall(cast<Function>(CPR->getValue()), Operands); 1504 } 1505 1506 return 0; 1507 case Instruction::GetElementPtr: 1508 Constant *Base = Operands[0]; 1509 Operands.erase(Operands.begin()); 1510 return ConstantExpr::getGetElementPtr(Base, Operands); 1511 } 1512 return 0; 1513} 1514 1515 1516/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1517/// in the loop that V is derived from. We allow arbitrary operations along the 1518/// way, but the operands of an operation must either be constants or a value 1519/// derived from a constant PHI. If this expression does not fit with these 1520/// constraints, return null. 1521static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1522 // If this is not an instruction, or if this is an instruction outside of the 1523 // loop, it can't be derived from a loop PHI. 1524 Instruction *I = dyn_cast<Instruction>(V); 1525 if (I == 0 || !L->contains(I->getParent())) return 0; 1526 1527 if (PHINode *PN = dyn_cast<PHINode>(I)) 1528 if (L->getHeader() == I->getParent()) 1529 return PN; 1530 else 1531 // We don't currently keep track of the control flow needed to evaluate 1532 // PHIs, so we cannot handle PHIs inside of loops. 1533 return 0; 1534 1535 // If we won't be able to constant fold this expression even if the operands 1536 // are constants, return early. 1537 if (!CanConstantFold(I)) return 0; 1538 1539 // Otherwise, we can evaluate this instruction if all of its operands are 1540 // constant or derived from a PHI node themselves. 1541 PHINode *PHI = 0; 1542 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1543 if (!(isa<Constant>(I->getOperand(Op)) || 1544 isa<GlobalValue>(I->getOperand(Op)))) { 1545 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1546 if (P == 0) return 0; // Not evolving from PHI 1547 if (PHI == 0) 1548 PHI = P; 1549 else if (PHI != P) 1550 return 0; // Evolving from multiple different PHIs. 1551 } 1552 1553 // This is a expression evolving from a constant PHI! 1554 return PHI; 1555} 1556 1557/// EvaluateExpression - Given an expression that passes the 1558/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1559/// in the loop has the value PHIVal. If we can't fold this expression for some 1560/// reason, return null. 1561static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1562 if (isa<PHINode>(V)) return PHIVal; 1563 if (Constant *C = dyn_cast<Constant>(V)) return C; 1564 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1565 return ConstantPointerRef::get(GV); 1566 Instruction *I = cast<Instruction>(V); 1567 1568 std::vector<Constant*> Operands; 1569 Operands.resize(I->getNumOperands()); 1570 1571 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1572 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1573 if (Operands[i] == 0) return 0; 1574 } 1575 1576 return ConstantFold(I, Operands); 1577} 1578 1579/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1580/// in the header of its containing loop, we know the loop executes a 1581/// constant number of times, and the PHI node is just a recurrence 1582/// involving constants, fold it. 1583Constant *ScalarEvolutionsImpl:: 1584getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1585 std::map<PHINode*, Constant*>::iterator I = 1586 ConstantEvolutionLoopExitValue.find(PN); 1587 if (I != ConstantEvolutionLoopExitValue.end()) 1588 return I->second; 1589 1590 if (Its > MaxBruteForceIterations) 1591 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1592 1593 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1594 1595 // Since the loop is canonicalized, the PHI node must have two entries. One 1596 // entry must be a constant (coming in from outside of the loop), and the 1597 // second must be derived from the same PHI. 1598 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1599 Constant *StartCST = 1600 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1601 if (StartCST == 0) 1602 return RetVal = 0; // Must be a constant. 1603 1604 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1605 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1606 if (PN2 != PN) 1607 return RetVal = 0; // Not derived from same PHI. 1608 1609 // Execute the loop symbolically to determine the exit value. 1610 unsigned IterationNum = 0; 1611 unsigned NumIterations = Its; 1612 if (NumIterations != Its) 1613 return RetVal = 0; // More than 2^32 iterations?? 1614 1615 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1616 if (IterationNum == NumIterations) 1617 return RetVal = PHIVal; // Got exit value! 1618 1619 // Compute the value of the PHI node for the next iteration. 1620 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1621 if (NextPHI == PHIVal) 1622 return RetVal = NextPHI; // Stopped evolving! 1623 if (NextPHI == 0) 1624 return 0; // Couldn't evaluate! 1625 PHIVal = NextPHI; 1626 } 1627} 1628 1629/// ComputeIterationCountExhaustively - If the trip is known to execute a 1630/// constant number of times (the condition evolves only from constants), 1631/// try to evaluate a few iterations of the loop until we get the exit 1632/// condition gets a value of ExitWhen (true or false). If we cannot 1633/// evaluate the trip count of the loop, return UnknownValue. 1634SCEVHandle ScalarEvolutionsImpl:: 1635ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1636 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1637 if (PN == 0) return UnknownValue; 1638 1639 // Since the loop is canonicalized, the PHI node must have two entries. One 1640 // entry must be a constant (coming in from outside of the loop), and the 1641 // second must be derived from the same PHI. 1642 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1643 Constant *StartCST = 1644 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1645 if (StartCST == 0) return UnknownValue; // Must be a constant. 1646 1647 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1648 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1649 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1650 1651 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1652 // the loop symbolically to determine when the condition gets a value of 1653 // "ExitWhen". 1654 unsigned IterationNum = 0; 1655 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1656 for (Constant *PHIVal = StartCST; 1657 IterationNum != MaxIterations; ++IterationNum) { 1658 ConstantBool *CondVal = 1659 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1660 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1661 1662 if (CondVal->getValue() == ExitWhen) { 1663 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1664 ++NumBruteForceTripCountsComputed; 1665 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum)); 1666 } 1667 1668 // Compute the value of the PHI node for the next iteration. 1669 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1670 if (NextPHI == 0 || NextPHI == PHIVal) 1671 return UnknownValue; // Couldn't evaluate or not making progress... 1672 PHIVal = NextPHI; 1673 } 1674 1675 // Too many iterations were needed to evaluate. 1676 return UnknownValue; 1677} 1678 1679/// getSCEVAtScope - Compute the value of the specified expression within the 1680/// indicated loop (which may be null to indicate in no loop). If the 1681/// expression cannot be evaluated, return UnknownValue. 1682SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1683 // FIXME: this should be turned into a virtual method on SCEV! 1684 1685 if (isa<SCEVConstant>(V)) return V; 1686 1687 // If this instruction is evolves from a constant-evolving PHI, compute the 1688 // exit value from the loop without using SCEVs. 1689 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1690 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1691 const Loop *LI = this->LI[I->getParent()]; 1692 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1693 if (PHINode *PN = dyn_cast<PHINode>(I)) 1694 if (PN->getParent() == LI->getHeader()) { 1695 // Okay, there is no closed form solution for the PHI node. Check 1696 // to see if the loop that contains it has a known iteration count. 1697 // If so, we may be able to force computation of the exit value. 1698 SCEVHandle IterationCount = getIterationCount(LI); 1699 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1700 // Okay, we know how many times the containing loop executes. If 1701 // this is a constant evolving PHI node, get the final value at 1702 // the specified iteration number. 1703 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1704 ICC->getValue()->getRawValue(), 1705 LI); 1706 if (RV) return SCEVUnknown::get(RV); 1707 } 1708 } 1709 1710 // Okay, this is a some expression that we cannot symbolically evaluate 1711 // into a SCEV. Check to see if it's possible to symbolically evaluate 1712 // the arguments into constants, and if see, try to constant propagate the 1713 // result. This is particularly useful for computing loop exit values. 1714 if (CanConstantFold(I)) { 1715 std::vector<Constant*> Operands; 1716 Operands.reserve(I->getNumOperands()); 1717 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1718 Value *Op = I->getOperand(i); 1719 if (Constant *C = dyn_cast<Constant>(Op)) { 1720 Operands.push_back(C); 1721 } else if (GlobalValue *GV = dyn_cast<GlobalValue>(Op)) { 1722 Operands.push_back(ConstantPointerRef::get(GV)); 1723 } else { 1724 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1725 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1726 Operands.push_back(ConstantExpr::getCast(SC->getValue(), 1727 Op->getType())); 1728 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1729 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1730 Operands.push_back(ConstantExpr::getCast(C, Op->getType())); 1731 else 1732 return V; 1733 } else { 1734 return V; 1735 } 1736 } 1737 } 1738 return SCEVUnknown::get(ConstantFold(I, Operands)); 1739 } 1740 } 1741 1742 // This is some other type of SCEVUnknown, just return it. 1743 return V; 1744 } 1745 1746 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1747 // Avoid performing the look-up in the common case where the specified 1748 // expression has no loop-variant portions. 1749 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1750 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1751 if (OpAtScope != Comm->getOperand(i)) { 1752 if (OpAtScope == UnknownValue) return UnknownValue; 1753 // Okay, at least one of these operands is loop variant but might be 1754 // foldable. Build a new instance of the folded commutative expression. 1755 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 1756 NewOps.push_back(OpAtScope); 1757 1758 for (++i; i != e; ++i) { 1759 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1760 if (OpAtScope == UnknownValue) return UnknownValue; 1761 NewOps.push_back(OpAtScope); 1762 } 1763 if (isa<SCEVAddExpr>(Comm)) 1764 return SCEVAddExpr::get(NewOps); 1765 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 1766 return SCEVMulExpr::get(NewOps); 1767 } 1768 } 1769 // If we got here, all operands are loop invariant. 1770 return Comm; 1771 } 1772 1773 if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) { 1774 SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L); 1775 if (LHS == UnknownValue) return LHS; 1776 SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L); 1777 if (RHS == UnknownValue) return RHS; 1778 if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS()) 1779 return UDiv; // must be loop invariant 1780 return SCEVUDivExpr::get(LHS, RHS); 1781 } 1782 1783 // If this is a loop recurrence for a loop that does not contain L, then we 1784 // are dealing with the final value computed by the loop. 1785 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 1786 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 1787 // To evaluate this recurrence, we need to know how many times the AddRec 1788 // loop iterates. Compute this now. 1789 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 1790 if (IterationCount == UnknownValue) return UnknownValue; 1791 IterationCount = getTruncateOrZeroExtend(IterationCount, 1792 AddRec->getType()); 1793 1794 // If the value is affine, simplify the expression evaluation to just 1795 // Start + Step*IterationCount. 1796 if (AddRec->isAffine()) 1797 return SCEVAddExpr::get(AddRec->getStart(), 1798 SCEVMulExpr::get(IterationCount, 1799 AddRec->getOperand(1))); 1800 1801 // Otherwise, evaluate it the hard way. 1802 return AddRec->evaluateAtIteration(IterationCount); 1803 } 1804 return UnknownValue; 1805 } 1806 1807 //assert(0 && "Unknown SCEV type!"); 1808 return UnknownValue; 1809} 1810 1811 1812/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 1813/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 1814/// might be the same) or two SCEVCouldNotCompute objects. 1815/// 1816static std::pair<SCEVHandle,SCEVHandle> 1817SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 1818 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 1819 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 1820 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 1821 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 1822 1823 // We currently can only solve this if the coefficients are constants. 1824 if (!L || !M || !N) { 1825 SCEV *CNC = new SCEVCouldNotCompute(); 1826 return std::make_pair(CNC, CNC); 1827 } 1828 1829 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2); 1830 1831 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 1832 Constant *C = L->getValue(); 1833 // The B coefficient is M-N/2 1834 Constant *B = ConstantExpr::getSub(M->getValue(), 1835 ConstantExpr::getDiv(N->getValue(), 1836 Two)); 1837 // The A coefficient is N/2 1838 Constant *A = ConstantExpr::getDiv(N->getValue(), Two); 1839 1840 // Compute the B^2-4ac term. 1841 Constant *SqrtTerm = 1842 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 1843 ConstantExpr::getMul(A, C)); 1844 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 1845 1846 // Compute floor(sqrt(B^2-4ac)) 1847 ConstantUInt *SqrtVal = 1848 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm, 1849 SqrtTerm->getType()->getUnsignedVersion())); 1850 uint64_t SqrtValV = SqrtVal->getValue(); 1851 uint64_t SqrtValV2 = (uint64_t)sqrt(SqrtValV); 1852 // The square root might not be precise for arbitrary 64-bit integer 1853 // values. Do some sanity checks to ensure it's correct. 1854 if (SqrtValV2*SqrtValV2 > SqrtValV || 1855 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 1856 SCEV *CNC = new SCEVCouldNotCompute(); 1857 return std::make_pair(CNC, CNC); 1858 } 1859 1860 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2); 1861 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType()); 1862 1863 Constant *NegB = ConstantExpr::getNeg(B); 1864 Constant *TwoA = ConstantExpr::getMul(A, Two); 1865 1866 // The divisions must be performed as signed divisions. 1867 const Type *SignedTy = NegB->getType()->getSignedVersion(); 1868 NegB = ConstantExpr::getCast(NegB, SignedTy); 1869 TwoA = ConstantExpr::getCast(TwoA, SignedTy); 1870 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy); 1871 1872 Constant *Solution1 = 1873 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 1874 Constant *Solution2 = 1875 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 1876 return std::make_pair(SCEVUnknown::get(Solution1), 1877 SCEVUnknown::get(Solution2)); 1878} 1879 1880/// HowFarToZero - Return the number of times a backedge comparing the specified 1881/// value to zero will execute. If not computable, return UnknownValue 1882SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 1883 // If the value is a constant 1884 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 1885 // If the value is already zero, the branch will execute zero times. 1886 if (C->getValue()->isNullValue()) return C; 1887 return UnknownValue; // Otherwise it will loop infinitely. 1888 } 1889 1890 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 1891 if (!AddRec || AddRec->getLoop() != L) 1892 return UnknownValue; 1893 1894 if (AddRec->isAffine()) { 1895 // If this is an affine expression the execution count of this branch is 1896 // equal to: 1897 // 1898 // (0 - Start/Step) iff Start % Step == 0 1899 // 1900 // Get the initial value for the loop. 1901 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 1902 SCEVHandle Step = AddRec->getOperand(1); 1903 1904 Step = getSCEVAtScope(Step, L->getParentLoop()); 1905 1906 // Figure out if Start % Step == 0. 1907 // FIXME: We should add DivExpr and RemExpr operations to our AST. 1908 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 1909 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 1910 return getNegativeSCEV(Start); // 0 - Start/1 == -Start 1911 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 1912 return Start; // 0 - Start/-1 == Start 1913 1914 // Check to see if Start is divisible by SC with no remainder. 1915 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 1916 ConstantInt *StartCC = StartC->getValue(); 1917 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 1918 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue()); 1919 if (Rem->isNullValue()) { 1920 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue()); 1921 return SCEVUnknown::get(Result); 1922 } 1923 } 1924 } 1925 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 1926 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 1927 // the quadratic equation to solve it. 1928 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 1929 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 1930 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 1931 if (R1) { 1932#if 0 1933 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1 1934 << " sol#2: " << *R2 << "\n"; 1935#endif 1936 // Pick the smallest positive root value. 1937 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 1938 if (ConstantBool *CB = 1939 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 1940 R2->getValue()))) { 1941 if (CB != ConstantBool::True) 1942 std::swap(R1, R2); // R1 is the minimum root now. 1943 1944 // We can only use this value if the chrec ends up with an exact zero 1945 // value at this index. When solving for "X*X != 5", for example, we 1946 // should not accept a root of 2. 1947 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 1948 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 1949 if (EvalVal->getValue()->isNullValue()) 1950 return R1; // We found a quadratic root! 1951 } 1952 } 1953 } 1954 1955 return UnknownValue; 1956} 1957 1958/// HowFarToNonZero - Return the number of times a backedge checking the 1959/// specified value for nonzero will execute. If not computable, return 1960/// UnknownValue 1961SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 1962 // Loops that look like: while (X == 0) are very strange indeed. We don't 1963 // handle them yet except for the trivial case. This could be expanded in the 1964 // future as needed. 1965 1966 // If the value is a constant, check to see if it is known to be non-zero 1967 // already. If so, the backedge will execute zero times. 1968 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 1969 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 1970 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 1971 if (NonZero == ConstantBool::True) 1972 return getSCEV(Zero); 1973 return UnknownValue; // Otherwise it will loop infinitely. 1974 } 1975 1976 // We could implement others, but I really doubt anyone writes loops like 1977 // this, and if they did, they would already be constant folded. 1978 return UnknownValue; 1979} 1980 1981static ConstantInt * 1982EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1983 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1984 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1985 assert(isa<SCEVConstant>(Val) && 1986 "Evaluation of SCEV at constant didn't fold correctly?"); 1987 return cast<SCEVConstant>(Val)->getValue(); 1988} 1989 1990 1991/// getNumIterationsInRange - Return the number of iterations of this loop that 1992/// produce values in the specified constant range. Another way of looking at 1993/// this is that it returns the first iteration number where the value is not in 1994/// the condition, thus computing the exit count. If the iteration count can't 1995/// be computed, an instance of SCEVCouldNotCompute is returned. 1996SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 1997 if (Range.isFullSet()) // Infinite loop. 1998 return new SCEVCouldNotCompute(); 1999 2000 // If the start is a non-zero constant, shift the range to simplify things. 2001 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2002 if (!SC->getValue()->isNullValue()) { 2003 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2004 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2005 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2006 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2007 return ShiftedAddRec->getNumIterationsInRange( 2008 Range.subtract(SC->getValue())); 2009 // This is strange and shouldn't happen. 2010 return new SCEVCouldNotCompute(); 2011 } 2012 2013 // The only time we can solve this is when we have all constant indices. 2014 // Otherwise, we cannot determine the overflow conditions. 2015 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2016 if (!isa<SCEVConstant>(getOperand(i))) 2017 return new SCEVCouldNotCompute(); 2018 2019 2020 // Okay at this point we know that all elements of the chrec are constants and 2021 // that the start element is zero. 2022 2023 // First check to see if the range contains zero. If not, the first 2024 // iteration exits. 2025 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2026 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 2027 2028 if (isAffine()) { 2029 // If this is an affine expression then we have this situation: 2030 // Solve {0,+,A} in Range === Ax in Range 2031 2032 // Since we know that zero is in the range, we know that the upper value of 2033 // the range must be the first possible exit value. Also note that we 2034 // already checked for a full range. 2035 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2036 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2037 ConstantInt *One = ConstantInt::get(getType(), 1); 2038 2039 // The exit value should be (Upper+A-1)/A. 2040 Constant *ExitValue = Upper; 2041 if (A != One) { 2042 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2043 ExitValue = ConstantExpr::getDiv(ExitValue, A); 2044 } 2045 assert(isa<ConstantInt>(ExitValue) && 2046 "Constant folding of integers not implemented?"); 2047 2048 // Evaluate at the exit value. If we really did fall out of the valid 2049 // range, then we computed our trip count, otherwise wrap around or other 2050 // things must have happened. 2051 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2052 if (Range.contains(Val)) 2053 return new SCEVCouldNotCompute(); // Something strange happened 2054 2055 // Ensure that the previous value is in the range. This is a sanity check. 2056 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2057 ConstantExpr::getSub(ExitValue, One))) && 2058 "Linear scev computation is off in a bad way!"); 2059 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2060 } else if (isQuadratic()) { 2061 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2062 // quadratic equation to solve it. To do this, we must frame our problem in 2063 // terms of figuring out when zero is crossed, instead of when 2064 // Range.getUpper() is crossed. 2065 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2066 NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2067 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2068 2069 // Next, solve the constructed addrec 2070 std::pair<SCEVHandle,SCEVHandle> Roots = 2071 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2072 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2073 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2074 if (R1) { 2075 // Pick the smallest positive root value. 2076 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2077 if (ConstantBool *CB = 2078 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2079 R2->getValue()))) { 2080 if (CB != ConstantBool::True) 2081 std::swap(R1, R2); // R1 is the minimum root now. 2082 2083 // Make sure the root is not off by one. The returned iteration should 2084 // not be in the range, but the previous one should be. When solving 2085 // for "X*X < 5", for example, we should not return a root of 2. 2086 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2087 R1->getValue()); 2088 if (Range.contains(R1Val)) { 2089 // The next iteration must be out of the range... 2090 Constant *NextVal = 2091 ConstantExpr::getAdd(R1->getValue(), 2092 ConstantInt::get(R1->getType(), 1)); 2093 2094 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2095 if (!Range.contains(R1Val)) 2096 return SCEVUnknown::get(NextVal); 2097 return new SCEVCouldNotCompute(); // Something strange happened 2098 } 2099 2100 // If R1 was not in the range, then it is a good return value. Make 2101 // sure that R1-1 WAS in the range though, just in case. 2102 Constant *NextVal = 2103 ConstantExpr::getSub(R1->getValue(), 2104 ConstantInt::get(R1->getType(), 1)); 2105 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2106 if (Range.contains(R1Val)) 2107 return R1; 2108 return new SCEVCouldNotCompute(); // Something strange happened 2109 } 2110 } 2111 } 2112 2113 // Fallback, if this is a general polynomial, figure out the progression 2114 // through brute force: evaluate until we find an iteration that fails the 2115 // test. This is likely to be slow, but getting an accurate trip count is 2116 // incredibly important, we will be able to simplify the exit test a lot, and 2117 // we are almost guaranteed to get a trip count in this case. 2118 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2119 ConstantInt *One = ConstantInt::get(getType(), 1); 2120 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2121 do { 2122 ++NumBruteForceEvaluations; 2123 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2124 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2125 return new SCEVCouldNotCompute(); 2126 2127 // Check to see if we found the value! 2128 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2129 return SCEVConstant::get(TestVal); 2130 2131 // Increment to test the next index. 2132 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2133 } while (TestVal != EndVal); 2134 2135 return new SCEVCouldNotCompute(); 2136} 2137 2138 2139 2140//===----------------------------------------------------------------------===// 2141// ScalarEvolution Class Implementation 2142//===----------------------------------------------------------------------===// 2143 2144bool ScalarEvolution::runOnFunction(Function &F) { 2145 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2146 return false; 2147} 2148 2149void ScalarEvolution::releaseMemory() { 2150 delete (ScalarEvolutionsImpl*)Impl; 2151 Impl = 0; 2152} 2153 2154void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2155 AU.setPreservesAll(); 2156 AU.addRequiredID(LoopSimplifyID); 2157 AU.addRequiredTransitive<LoopInfo>(); 2158} 2159 2160SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2161 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2162} 2163 2164SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2165 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2166} 2167 2168bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2169 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2170} 2171 2172SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2173 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2174} 2175 2176void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2177 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2178} 2179 2180static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2181 const Loop *L) { 2182 // Print all inner loops first 2183 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2184 PrintLoopInfo(OS, SE, *I); 2185 2186 std::cerr << "Loop " << L->getHeader()->getName() << ": "; 2187 2188 std::vector<BasicBlock*> ExitBlocks; 2189 L->getExitBlocks(ExitBlocks); 2190 if (ExitBlocks.size() != 1) 2191 std::cerr << "<multiple exits> "; 2192 2193 if (SE->hasLoopInvariantIterationCount(L)) { 2194 std::cerr << *SE->getIterationCount(L) << " iterations! "; 2195 } else { 2196 std::cerr << "Unpredictable iteration count. "; 2197 } 2198 2199 std::cerr << "\n"; 2200} 2201 2202void ScalarEvolution::print(std::ostream &OS) const { 2203 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2204 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2205 2206 OS << "Classifying expressions for: " << F.getName() << "\n"; 2207 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2208 if (I->getType()->isInteger()) { 2209 OS << *I; 2210 OS << " --> "; 2211 SCEVHandle SV = getSCEV(&*I); 2212 SV->print(OS); 2213 OS << "\t\t"; 2214 2215 if ((*I).getType()->isIntegral()) { 2216 ConstantRange Bounds = SV->getValueRange(); 2217 if (!Bounds.isFullSet()) 2218 OS << "Bounds: " << Bounds << " "; 2219 } 2220 2221 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2222 OS << "Exits: "; 2223 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2224 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2225 OS << "<<Unknown>>"; 2226 } else { 2227 OS << *ExitValue; 2228 } 2229 } 2230 2231 2232 OS << "\n"; 2233 } 2234 2235 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2236 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2237 PrintLoopInfo(OS, this, *I); 2238} 2239 2240