LLVM API Documentation
00001 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 00002 // 00003 // The LLVM Compiler Infrastructure 00004 // 00005 // This file was developed by the LLVM research group and is distributed under 00006 // the University of Illinois Open Source License. See LICENSE.TXT for details. 00007 // 00008 //===----------------------------------------------------------------------===// 00009 // 00010 // This file contains the implementation of the scalar evolution analysis 00011 // engine, which is used primarily to analyze expressions involving induction 00012 // variables in loops. 00013 // 00014 // There are several aspects to this library. First is the representation of 00015 // scalar expressions, which are represented as subclasses of the SCEV class. 00016 // These classes are used to represent certain types of subexpressions that we 00017 // can handle. These classes are reference counted, managed by the SCEVHandle 00018 // class. We only create one SCEV of a particular shape, so pointer-comparisons 00019 // for equality are legal. 00020 // 00021 // One important aspect of the SCEV objects is that they are never cyclic, even 00022 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If 00023 // the PHI node is one of the idioms that we can represent (e.g., a polynomial 00024 // recurrence) then we represent it directly as a recurrence node, otherwise we 00025 // represent it as a SCEVUnknown node. 00026 // 00027 // In addition to being able to represent expressions of various types, we also 00028 // have folders that are used to build the *canonical* representation for a 00029 // particular expression. These folders are capable of using a variety of 00030 // rewrite rules to simplify the expressions. 00031 // 00032 // Once the folders are defined, we can implement the more interesting 00033 // higher-level code, such as the code that recognizes PHI nodes of various 00034 // types, computes the execution count of a loop, etc. 00035 // 00036 // TODO: We should use these routines and value representations to implement 00037 // dependence analysis! 00038 // 00039 //===----------------------------------------------------------------------===// 00040 // 00041 // There are several good references for the techniques used in this analysis. 00042 // 00043 // Chains of recurrences -- a method to expedite the evaluation 00044 // of closed-form functions 00045 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima 00046 // 00047 // On computational properties of chains of recurrences 00048 // Eugene V. Zima 00049 // 00050 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization 00051 // Robert A. van Engelen 00052 // 00053 // Efficient Symbolic Analysis for Optimizing Compilers 00054 // Robert A. van Engelen 00055 // 00056 // Using the chains of recurrences algebra for data dependence testing and 00057 // induction variable substitution 00058 // MS Thesis, Johnie Birch 00059 // 00060 //===----------------------------------------------------------------------===// 00061 00062 #include "llvm/Analysis/ScalarEvolutionExpressions.h" 00063 #include "llvm/Constants.h" 00064 #include "llvm/DerivedTypes.h" 00065 #include "llvm/GlobalVariable.h" 00066 #include "llvm/Instructions.h" 00067 #include "llvm/Analysis/LoopInfo.h" 00068 #include "llvm/Assembly/Writer.h" 00069 #include "llvm/Transforms/Scalar.h" 00070 #include "llvm/Transforms/Utils/Local.h" 00071 #include "llvm/Support/CFG.h" 00072 #include "llvm/Support/ConstantRange.h" 00073 #include "llvm/Support/InstIterator.h" 00074 #include "llvm/Support/CommandLine.h" 00075 #include "llvm/ADT/Statistic.h" 00076 #include <cmath> 00077 #include <algorithm> 00078 using namespace llvm; 00079 00080 namespace { 00081 RegisterAnalysis<ScalarEvolution> 00082 R("scalar-evolution", "Scalar Evolution Analysis"); 00083 00084 Statistic<> 00085 NumBruteForceEvaluations("scalar-evolution", 00086 "Number of brute force evaluations needed to " 00087 "calculate high-order polynomial exit values"); 00088 Statistic<> 00089 NumArrayLenItCounts("scalar-evolution", 00090 "Number of trip counts computed with array length"); 00091 Statistic<> 00092 NumTripCountsComputed("scalar-evolution", 00093 "Number of loops with predictable loop counts"); 00094 Statistic<> 00095 NumTripCountsNotComputed("scalar-evolution", 00096 "Number of loops without predictable loop counts"); 00097 Statistic<> 00098 NumBruteForceTripCountsComputed("scalar-evolution", 00099 "Number of loops with trip counts computed by force"); 00100 00101 cl::opt<unsigned> 00102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 00103 cl::desc("Maximum number of iterations SCEV will symbolically execute a constant derived loop"), 00104 cl::init(100)); 00105 } 00106 00107 //===----------------------------------------------------------------------===// 00108 // SCEV class definitions 00109 //===----------------------------------------------------------------------===// 00110 00111 //===----------------------------------------------------------------------===// 00112 // Implementation of the SCEV class. 00113 // 00114 SCEV::~SCEV() {} 00115 void SCEV::dump() const { 00116 print(std::cerr); 00117 } 00118 00119 /// getValueRange - Return the tightest constant bounds that this value is 00120 /// known to have. This method is only valid on integer SCEV objects. 00121 ConstantRange SCEV::getValueRange() const { 00122 const Type *Ty = getType(); 00123 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 00124 Ty = Ty->getUnsignedVersion(); 00125 // Default to a full range if no better information is available. 00126 return ConstantRange(getType()); 00127 } 00128 00129 00130 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 00131 00132 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 00133 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 00134 return false; 00135 } 00136 00137 const Type *SCEVCouldNotCompute::getType() const { 00138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 00139 return 0; 00140 } 00141 00142 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 00143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 00144 return false; 00145 } 00146 00147 void SCEVCouldNotCompute::print(std::ostream &OS) const { 00148 OS << "***COULDNOTCOMPUTE***"; 00149 } 00150 00151 bool SCEVCouldNotCompute::classof(const SCEV *S) { 00152 return S->getSCEVType() == scCouldNotCompute; 00153 } 00154 00155 00156 // SCEVConstants - Only allow the creation of one SCEVConstant for any 00157 // particular value. Don't use a SCEVHandle here, or else the object will 00158 // never be deleted! 00159 static std::map<ConstantInt*, SCEVConstant*> SCEVConstants; 00160 00161 00162 SCEVConstant::~SCEVConstant() { 00163 SCEVConstants.erase(V); 00164 } 00165 00166 SCEVHandle SCEVConstant::get(ConstantInt *V) { 00167 // Make sure that SCEVConstant instances are all unsigned. 00168 if (V->getType()->isSigned()) { 00169 const Type *NewTy = V->getType()->getUnsignedVersion(); 00170 V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy)); 00171 } 00172 00173 SCEVConstant *&R = SCEVConstants[V]; 00174 if (R == 0) R = new SCEVConstant(V); 00175 return R; 00176 } 00177 00178 ConstantRange SCEVConstant::getValueRange() const { 00179 return ConstantRange(V); 00180 } 00181 00182 const Type *SCEVConstant::getType() const { return V->getType(); } 00183 00184 void SCEVConstant::print(std::ostream &OS) const { 00185 WriteAsOperand(OS, V, false); 00186 } 00187 00188 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 00189 // particular input. Don't use a SCEVHandle here, or else the object will 00190 // never be deleted! 00191 static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates; 00192 00193 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 00194 : SCEV(scTruncate), Op(op), Ty(ty) { 00195 assert(Op->getType()->isInteger() && Ty->isInteger() && 00196 Ty->isUnsigned() && 00197 "Cannot truncate non-integer value!"); 00198 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 00199 "This is not a truncating conversion!"); 00200 } 00201 00202 SCEVTruncateExpr::~SCEVTruncateExpr() { 00203 SCEVTruncates.erase(std::make_pair(Op, Ty)); 00204 } 00205 00206 ConstantRange SCEVTruncateExpr::getValueRange() const { 00207 return getOperand()->getValueRange().truncate(getType()); 00208 } 00209 00210 void SCEVTruncateExpr::print(std::ostream &OS) const { 00211 OS << "(truncate " << *Op << " to " << *Ty << ")"; 00212 } 00213 00214 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 00215 // particular input. Don't use a SCEVHandle here, or else the object will never 00216 // be deleted! 00217 static std::map<std::pair<SCEV*, const Type*>, 00218 SCEVZeroExtendExpr*> SCEVZeroExtends; 00219 00220 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 00221 : SCEV(scTruncate), Op(Op), Ty(ty) { 00222 assert(Op->getType()->isInteger() && Ty->isInteger() && 00223 Ty->isUnsigned() && 00224 "Cannot zero extend non-integer value!"); 00225 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 00226 "This is not an extending conversion!"); 00227 } 00228 00229 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 00230 SCEVZeroExtends.erase(std::make_pair(Op, Ty)); 00231 } 00232 00233 ConstantRange SCEVZeroExtendExpr::getValueRange() const { 00234 return getOperand()->getValueRange().zeroExtend(getType()); 00235 } 00236 00237 void SCEVZeroExtendExpr::print(std::ostream &OS) const { 00238 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 00239 } 00240 00241 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 00242 // particular input. Don't use a SCEVHandle here, or else the object will never 00243 // be deleted! 00244 static std::map<std::pair<unsigned, std::vector<SCEV*> >, 00245 SCEVCommutativeExpr*> SCEVCommExprs; 00246 00247 SCEVCommutativeExpr::~SCEVCommutativeExpr() { 00248 SCEVCommExprs.erase(std::make_pair(getSCEVType(), 00249 std::vector<SCEV*>(Operands.begin(), 00250 Operands.end()))); 00251 } 00252 00253 void SCEVCommutativeExpr::print(std::ostream &OS) const { 00254 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 00255 const char *OpStr = getOperationStr(); 00256 OS << "(" << *Operands[0]; 00257 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 00258 OS << OpStr << *Operands[i]; 00259 OS << ")"; 00260 } 00261 00262 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 00263 // input. Don't use a SCEVHandle here, or else the object will never be 00264 // deleted! 00265 static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs; 00266 00267 SCEVUDivExpr::~SCEVUDivExpr() { 00268 SCEVUDivs.erase(std::make_pair(LHS, RHS)); 00269 } 00270 00271 void SCEVUDivExpr::print(std::ostream &OS) const { 00272 OS << "(" << *LHS << " /u " << *RHS << ")"; 00273 } 00274 00275 const Type *SCEVUDivExpr::getType() const { 00276 const Type *Ty = LHS->getType(); 00277 if (Ty->isSigned()) Ty = Ty->getUnsignedVersion(); 00278 return Ty; 00279 } 00280 00281 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 00282 // particular input. Don't use a SCEVHandle here, or else the object will never 00283 // be deleted! 00284 static std::map<std::pair<const Loop *, std::vector<SCEV*> >, 00285 SCEVAddRecExpr*> SCEVAddRecExprs; 00286 00287 SCEVAddRecExpr::~SCEVAddRecExpr() { 00288 SCEVAddRecExprs.erase(std::make_pair(L, 00289 std::vector<SCEV*>(Operands.begin(), 00290 Operands.end()))); 00291 } 00292 00293 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 00294 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 00295 // contain L. 00296 return !QueryLoop->contains(L->getHeader()); 00297 } 00298 00299 00300 void SCEVAddRecExpr::print(std::ostream &OS) const { 00301 OS << "{" << *Operands[0]; 00302 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 00303 OS << ",+," << *Operands[i]; 00304 OS << "}<" << L->getHeader()->getName() + ">"; 00305 } 00306 00307 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 00308 // value. Don't use a SCEVHandle here, or else the object will never be 00309 // deleted! 00310 static std::map<Value*, SCEVUnknown*> SCEVUnknowns; 00311 00312 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); } 00313 00314 bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 00315 // All non-instruction values are loop invariant. All instructions are loop 00316 // invariant if they are not contained in the specified loop. 00317 if (Instruction *I = dyn_cast<Instruction>(V)) 00318 return !L->contains(I->getParent()); 00319 return true; 00320 } 00321 00322 const Type *SCEVUnknown::getType() const { 00323 return V->getType(); 00324 } 00325 00326 void SCEVUnknown::print(std::ostream &OS) const { 00327 WriteAsOperand(OS, V, false); 00328 } 00329 00330 //===----------------------------------------------------------------------===// 00331 // SCEV Utilities 00332 //===----------------------------------------------------------------------===// 00333 00334 namespace { 00335 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 00336 /// than the complexity of the RHS. This comparator is used to canonicalize 00337 /// expressions. 00338 struct SCEVComplexityCompare { 00339 bool operator()(SCEV *LHS, SCEV *RHS) { 00340 return LHS->getSCEVType() < RHS->getSCEVType(); 00341 } 00342 }; 00343 } 00344 00345 /// GroupByComplexity - Given a list of SCEV objects, order them by their 00346 /// complexity, and group objects of the same complexity together by value. 00347 /// When this routine is finished, we know that any duplicates in the vector are 00348 /// consecutive and that complexity is monotonically increasing. 00349 /// 00350 /// Note that we go take special precautions to ensure that we get determinstic 00351 /// results from this routine. In other words, we don't want the results of 00352 /// this to depend on where the addresses of various SCEV objects happened to 00353 /// land in memory. 00354 /// 00355 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 00356 if (Ops.size() < 2) return; // Noop 00357 if (Ops.size() == 2) { 00358 // This is the common case, which also happens to be trivially simple. 00359 // Special case it. 00360 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 00361 std::swap(Ops[0], Ops[1]); 00362 return; 00363 } 00364 00365 // Do the rough sort by complexity. 00366 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 00367 00368 // Now that we are sorted by complexity, group elements of the same 00369 // complexity. Note that this is, at worst, N^2, but the vector is likely to 00370 // be extremely short in practice. Note that we take this approach because we 00371 // do not want to depend on the addresses of the objects we are grouping. 00372 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 00373 SCEV *S = Ops[i]; 00374 unsigned Complexity = S->getSCEVType(); 00375 00376 // If there are any objects of the same complexity and same value as this 00377 // one, group them. 00378 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 00379 if (Ops[j] == S) { // Found a duplicate. 00380 // Move it to immediately after i'th element. 00381 std::swap(Ops[i+1], Ops[j]); 00382 ++i; // no need to rescan it. 00383 if (i == e-2) return; // Done! 00384 } 00385 } 00386 } 00387 } 00388 00389 00390 00391 //===----------------------------------------------------------------------===// 00392 // Simple SCEV method implementations 00393 //===----------------------------------------------------------------------===// 00394 00395 /// getIntegerSCEV - Given an integer or FP type, create a constant for the 00396 /// specified signed integer value and return a SCEV for the constant. 00397 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 00398 Constant *C; 00399 if (Val == 0) 00400 C = Constant::getNullValue(Ty); 00401 else if (Ty->isFloatingPoint()) 00402 C = ConstantFP::get(Ty, Val); 00403 else if (Ty->isSigned()) 00404 C = ConstantSInt::get(Ty, Val); 00405 else { 00406 C = ConstantSInt::get(Ty->getSignedVersion(), Val); 00407 C = ConstantExpr::getCast(C, Ty); 00408 } 00409 return SCEVUnknown::get(C); 00410 } 00411 00412 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 00413 /// input value to the specified type. If the type must be extended, it is zero 00414 /// extended. 00415 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 00416 const Type *SrcTy = V->getType(); 00417 assert(SrcTy->isInteger() && Ty->isInteger() && 00418 "Cannot truncate or zero extend with non-integer arguments!"); 00419 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 00420 return V; // No conversion 00421 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 00422 return SCEVTruncateExpr::get(V, Ty); 00423 return SCEVZeroExtendExpr::get(V, Ty); 00424 } 00425 00426 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 00427 /// 00428 static SCEVHandle getNegativeSCEV(const SCEVHandle &V) { 00429 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 00430 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 00431 00432 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 00433 } 00434 00435 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 00436 /// 00437 static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 00438 // X - Y --> X + -Y 00439 return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS)); 00440 } 00441 00442 00443 /// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is 00444 /// often very small, so we try to reduce the number of N! terms we need to 00445 /// evaluate by evaluating this as (N!/(N-M)!)/M! 00446 static ConstantInt *Binomial(ConstantInt *N, unsigned M) { 00447 uint64_t NVal = N->getRawValue(); 00448 uint64_t FirstTerm = 1; 00449 for (unsigned i = 0; i != M; ++i) 00450 FirstTerm *= NVal-i; 00451 00452 unsigned MFactorial = 1; 00453 for (; M; --M) 00454 MFactorial *= M; 00455 00456 Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial); 00457 Result = ConstantExpr::getCast(Result, N->getType()); 00458 assert(isa<ConstantInt>(Result) && "Cast of integer not folded??"); 00459 return cast<ConstantInt>(Result); 00460 } 00461 00462 /// PartialFact - Compute V!/(V-NumSteps)! 00463 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 00464 // Handle this case efficiently, it is common to have constant iteration 00465 // counts while computing loop exit values. 00466 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 00467 uint64_t Val = SC->getValue()->getRawValue(); 00468 uint64_t Result = 1; 00469 for (; NumSteps; --NumSteps) 00470 Result *= Val-(NumSteps-1); 00471 Constant *Res = ConstantUInt::get(Type::ULongTy, Result); 00472 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType())); 00473 } 00474 00475 const Type *Ty = V->getType(); 00476 if (NumSteps == 0) 00477 return SCEVUnknown::getIntegerSCEV(1, Ty); 00478 00479 SCEVHandle Result = V; 00480 for (unsigned i = 1; i != NumSteps; ++i) 00481 Result = SCEVMulExpr::get(Result, getMinusSCEV(V, 00482 SCEVUnknown::getIntegerSCEV(i, Ty))); 00483 return Result; 00484 } 00485 00486 00487 /// evaluateAtIteration - Return the value of this chain of recurrences at 00488 /// the specified iteration number. We can evaluate this recurrence by 00489 /// multiplying each element in the chain by the binomial coefficient 00490 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 00491 /// 00492 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 00493 /// 00494 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 00495 /// Is the binomial equation safe using modular arithmetic?? 00496 /// 00497 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 00498 SCEVHandle Result = getStart(); 00499 int Divisor = 1; 00500 const Type *Ty = It->getType(); 00501 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 00502 SCEVHandle BC = PartialFact(It, i); 00503 Divisor *= i; 00504 SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 00505 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 00506 Result = SCEVAddExpr::get(Result, Val); 00507 } 00508 return Result; 00509 } 00510 00511 00512 //===----------------------------------------------------------------------===// 00513 // SCEV Expression folder implementations 00514 //===----------------------------------------------------------------------===// 00515 00516 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 00517 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 00518 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 00519 00520 // If the input value is a chrec scev made out of constants, truncate 00521 // all of the constants. 00522 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 00523 std::vector<SCEVHandle> Operands; 00524 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 00525 // FIXME: This should allow truncation of other expression types! 00526 if (isa<SCEVConstant>(AddRec->getOperand(i))) 00527 Operands.push_back(get(AddRec->getOperand(i), Ty)); 00528 else 00529 break; 00530 if (Operands.size() == AddRec->getNumOperands()) 00531 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 00532 } 00533 00534 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)]; 00535 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 00536 return Result; 00537 } 00538 00539 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 00540 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 00541 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 00542 00543 // FIXME: If the input value is a chrec scev, and we can prove that the value 00544 // did not overflow the old, smaller, value, we can zero extend all of the 00545 // operands (often constants). This would allow analysis of something like 00546 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 00547 00548 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)]; 00549 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 00550 return Result; 00551 } 00552 00553 // get - Get a canonical add expression, or something simpler if possible. 00554 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 00555 assert(!Ops.empty() && "Cannot get empty add!"); 00556 if (Ops.size() == 1) return Ops[0]; 00557 00558 // Sort by complexity, this groups all similar expression types together. 00559 GroupByComplexity(Ops); 00560 00561 // If there are any constants, fold them together. 00562 unsigned Idx = 0; 00563 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 00564 ++Idx; 00565 assert(Idx < Ops.size()); 00566 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 00567 // We found two constants, fold them together! 00568 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 00569 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 00570 Ops[0] = SCEVConstant::get(CI); 00571 Ops.erase(Ops.begin()+1); // Erase the folded element 00572 if (Ops.size() == 1) return Ops[0]; 00573 } else { 00574 // If we couldn't fold the expression, move to the next constant. Note 00575 // that this is impossible to happen in practice because we always 00576 // constant fold constant ints to constant ints. 00577 ++Idx; 00578 } 00579 } 00580 00581 // If we are left with a constant zero being added, strip it off. 00582 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 00583 Ops.erase(Ops.begin()); 00584 --Idx; 00585 } 00586 } 00587 00588 if (Ops.size() == 1) return Ops[0]; 00589 00590 // Okay, check to see if the same value occurs in the operand list twice. If 00591 // so, merge them together into an multiply expression. Since we sorted the 00592 // list, these values are required to be adjacent. 00593 const Type *Ty = Ops[0]->getType(); 00594 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 00595 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 00596 // Found a match, merge the two values into a multiply, and add any 00597 // remaining values to the result. 00598 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 00599 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 00600 if (Ops.size() == 2) 00601 return Mul; 00602 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 00603 Ops.push_back(Mul); 00604 return SCEVAddExpr::get(Ops); 00605 } 00606 00607 // Okay, now we know the first non-constant operand. If there are add 00608 // operands they would be next. 00609 if (Idx < Ops.size()) { 00610 bool DeletedAdd = false; 00611 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 00612 // If we have an add, expand the add operands onto the end of the operands 00613 // list. 00614 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 00615 Ops.erase(Ops.begin()+Idx); 00616 DeletedAdd = true; 00617 } 00618 00619 // If we deleted at least one add, we added operands to the end of the list, 00620 // and they are not necessarily sorted. Recurse to resort and resimplify 00621 // any operands we just aquired. 00622 if (DeletedAdd) 00623 return get(Ops); 00624 } 00625 00626 // Skip over the add expression until we get to a multiply. 00627 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 00628 ++Idx; 00629 00630 // If we are adding something to a multiply expression, make sure the 00631 // something is not already an operand of the multiply. If so, merge it into 00632 // the multiply. 00633 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 00634 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 00635 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 00636 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 00637 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 00638 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 00639 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 00640 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 00641 if (Mul->getNumOperands() != 2) { 00642 // If the multiply has more than two operands, we must get the 00643 // Y*Z term. 00644 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 00645 MulOps.erase(MulOps.begin()+MulOp); 00646 InnerMul = SCEVMulExpr::get(MulOps); 00647 } 00648 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 00649 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 00650 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 00651 if (Ops.size() == 2) return OuterMul; 00652 if (AddOp < Idx) { 00653 Ops.erase(Ops.begin()+AddOp); 00654 Ops.erase(Ops.begin()+Idx-1); 00655 } else { 00656 Ops.erase(Ops.begin()+Idx); 00657 Ops.erase(Ops.begin()+AddOp-1); 00658 } 00659 Ops.push_back(OuterMul); 00660 return SCEVAddExpr::get(Ops); 00661 } 00662 00663 // Check this multiply against other multiplies being added together. 00664 for (unsigned OtherMulIdx = Idx+1; 00665 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 00666 ++OtherMulIdx) { 00667 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 00668 // If MulOp occurs in OtherMul, we can fold the two multiplies 00669 // together. 00670 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 00671 OMulOp != e; ++OMulOp) 00672 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 00673 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 00674 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 00675 if (Mul->getNumOperands() != 2) { 00676 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 00677 MulOps.erase(MulOps.begin()+MulOp); 00678 InnerMul1 = SCEVMulExpr::get(MulOps); 00679 } 00680 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 00681 if (OtherMul->getNumOperands() != 2) { 00682 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 00683 OtherMul->op_end()); 00684 MulOps.erase(MulOps.begin()+OMulOp); 00685 InnerMul2 = SCEVMulExpr::get(MulOps); 00686 } 00687 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 00688 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 00689 if (Ops.size() == 2) return OuterMul; 00690 Ops.erase(Ops.begin()+Idx); 00691 Ops.erase(Ops.begin()+OtherMulIdx-1); 00692 Ops.push_back(OuterMul); 00693 return SCEVAddExpr::get(Ops); 00694 } 00695 } 00696 } 00697 } 00698 00699 // If there are any add recurrences in the operands list, see if any other 00700 // added values are loop invariant. If so, we can fold them into the 00701 // recurrence. 00702 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 00703 ++Idx; 00704 00705 // Scan over all recurrences, trying to fold loop invariants into them. 00706 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 00707 // Scan all of the other operands to this add and add them to the vector if 00708 // they are loop invariant w.r.t. the recurrence. 00709 std::vector<SCEVHandle> LIOps; 00710 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 00711 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 00712 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 00713 LIOps.push_back(Ops[i]); 00714 Ops.erase(Ops.begin()+i); 00715 --i; --e; 00716 } 00717 00718 // If we found some loop invariants, fold them into the recurrence. 00719 if (!LIOps.empty()) { 00720 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 00721 LIOps.push_back(AddRec->getStart()); 00722 00723 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 00724 AddRecOps[0] = SCEVAddExpr::get(LIOps); 00725 00726 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 00727 // If all of the other operands were loop invariant, we are done. 00728 if (Ops.size() == 1) return NewRec; 00729 00730 // Otherwise, add the folded AddRec by the non-liv parts. 00731 for (unsigned i = 0;; ++i) 00732 if (Ops[i] == AddRec) { 00733 Ops[i] = NewRec; 00734 break; 00735 } 00736 return SCEVAddExpr::get(Ops); 00737 } 00738 00739 // Okay, if there weren't any loop invariants to be folded, check to see if 00740 // there are multiple AddRec's with the same loop induction variable being 00741 // added together. If so, we can fold them. 00742 for (unsigned OtherIdx = Idx+1; 00743 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 00744 if (OtherIdx != Idx) { 00745 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 00746 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 00747 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 00748 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 00749 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 00750 if (i >= NewOps.size()) { 00751 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 00752 OtherAddRec->op_end()); 00753 break; 00754 } 00755 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 00756 } 00757 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 00758 00759 if (Ops.size() == 2) return NewAddRec; 00760 00761 Ops.erase(Ops.begin()+Idx); 00762 Ops.erase(Ops.begin()+OtherIdx-1); 00763 Ops.push_back(NewAddRec); 00764 return SCEVAddExpr::get(Ops); 00765 } 00766 } 00767 00768 // Otherwise couldn't fold anything into this recurrence. Move onto the 00769 // next one. 00770 } 00771 00772 // Okay, it looks like we really DO need an add expr. Check to see if we 00773 // already have one, otherwise create a new one. 00774 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 00775 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr, 00776 SCEVOps)]; 00777 if (Result == 0) Result = new SCEVAddExpr(Ops); 00778 return Result; 00779 } 00780 00781 00782 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 00783 assert(!Ops.empty() && "Cannot get empty mul!"); 00784 00785 // Sort by complexity, this groups all similar expression types together. 00786 GroupByComplexity(Ops); 00787 00788 // If there are any constants, fold them together. 00789 unsigned Idx = 0; 00790 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 00791 00792 // C1*(C2+V) -> C1*C2 + C1*V 00793 if (Ops.size() == 2) 00794 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 00795 if (Add->getNumOperands() == 2 && 00796 isa<SCEVConstant>(Add->getOperand(0))) 00797 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 00798 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 00799 00800 00801 ++Idx; 00802 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 00803 // We found two constants, fold them together! 00804 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 00805 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 00806 Ops[0] = SCEVConstant::get(CI); 00807 Ops.erase(Ops.begin()+1); // Erase the folded element 00808 if (Ops.size() == 1) return Ops[0]; 00809 } else { 00810 // If we couldn't fold the expression, move to the next constant. Note 00811 // that this is impossible to happen in practice because we always 00812 // constant fold constant ints to constant ints. 00813 ++Idx; 00814 } 00815 } 00816 00817 // If we are left with a constant one being multiplied, strip it off. 00818 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 00819 Ops.erase(Ops.begin()); 00820 --Idx; 00821 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 00822 // If we have a multiply of zero, it will always be zero. 00823 return Ops[0]; 00824 } 00825 } 00826 00827 // Skip over the add expression until we get to a multiply. 00828 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 00829 ++Idx; 00830 00831 if (Ops.size() == 1) 00832 return Ops[0]; 00833 00834 // If there are mul operands inline them all into this expression. 00835 if (Idx < Ops.size()) { 00836 bool DeletedMul = false; 00837 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 00838 // If we have an mul, expand the mul operands onto the end of the operands 00839 // list. 00840 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 00841 Ops.erase(Ops.begin()+Idx); 00842 DeletedMul = true; 00843 } 00844 00845 // If we deleted at least one mul, we added operands to the end of the list, 00846 // and they are not necessarily sorted. Recurse to resort and resimplify 00847 // any operands we just aquired. 00848 if (DeletedMul) 00849 return get(Ops); 00850 } 00851 00852 // If there are any add recurrences in the operands list, see if any other 00853 // added values are loop invariant. If so, we can fold them into the 00854 // recurrence. 00855 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 00856 ++Idx; 00857 00858 // Scan over all recurrences, trying to fold loop invariants into them. 00859 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 00860 // Scan all of the other operands to this mul and add them to the vector if 00861 // they are loop invariant w.r.t. the recurrence. 00862 std::vector<SCEVHandle> LIOps; 00863 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 00864 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 00865 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 00866 LIOps.push_back(Ops[i]); 00867 Ops.erase(Ops.begin()+i); 00868 --i; --e; 00869 } 00870 00871 // If we found some loop invariants, fold them into the recurrence. 00872 if (!LIOps.empty()) { 00873 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 00874 std::vector<SCEVHandle> NewOps; 00875 NewOps.reserve(AddRec->getNumOperands()); 00876 if (LIOps.size() == 1) { 00877 SCEV *Scale = LIOps[0]; 00878 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 00879 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 00880 } else { 00881 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 00882 std::vector<SCEVHandle> MulOps(LIOps); 00883 MulOps.push_back(AddRec->getOperand(i)); 00884 NewOps.push_back(SCEVMulExpr::get(MulOps)); 00885 } 00886 } 00887 00888 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 00889 00890 // If all of the other operands were loop invariant, we are done. 00891 if (Ops.size() == 1) return NewRec; 00892 00893 // Otherwise, multiply the folded AddRec by the non-liv parts. 00894 for (unsigned i = 0;; ++i) 00895 if (Ops[i] == AddRec) { 00896 Ops[i] = NewRec; 00897 break; 00898 } 00899 return SCEVMulExpr::get(Ops); 00900 } 00901 00902 // Okay, if there weren't any loop invariants to be folded, check to see if 00903 // there are multiple AddRec's with the same loop induction variable being 00904 // multiplied together. If so, we can fold them. 00905 for (unsigned OtherIdx = Idx+1; 00906 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 00907 if (OtherIdx != Idx) { 00908 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 00909 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 00910 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 00911 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 00912 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 00913 G->getStart()); 00914 SCEVHandle B = F->getStepRecurrence(); 00915 SCEVHandle D = G->getStepRecurrence(); 00916 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 00917 SCEVMulExpr::get(G, B), 00918 SCEVMulExpr::get(B, D)); 00919 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 00920 F->getLoop()); 00921 if (Ops.size() == 2) return NewAddRec; 00922 00923 Ops.erase(Ops.begin()+Idx); 00924 Ops.erase(Ops.begin()+OtherIdx-1); 00925 Ops.push_back(NewAddRec); 00926 return SCEVMulExpr::get(Ops); 00927 } 00928 } 00929 00930 // Otherwise couldn't fold anything into this recurrence. Move onto the 00931 // next one. 00932 } 00933 00934 // Okay, it looks like we really DO need an mul expr. Check to see if we 00935 // already have one, otherwise create a new one. 00936 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 00937 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr, 00938 SCEVOps)]; 00939 if (Result == 0) 00940 Result = new SCEVMulExpr(Ops); 00941 return Result; 00942 } 00943 00944 SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 00945 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 00946 if (RHSC->getValue()->equalsInt(1)) 00947 return LHS; // X /u 1 --> x 00948 if (RHSC->getValue()->isAllOnesValue()) 00949 return getNegativeSCEV(LHS); // X /u -1 --> -x 00950 00951 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 00952 Constant *LHSCV = LHSC->getValue(); 00953 Constant *RHSCV = RHSC->getValue(); 00954 if (LHSCV->getType()->isSigned()) 00955 LHSCV = ConstantExpr::getCast(LHSCV, 00956 LHSCV->getType()->getUnsignedVersion()); 00957 if (RHSCV->getType()->isSigned()) 00958 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType()); 00959 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV)); 00960 } 00961 } 00962 00963 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 00964 00965 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)]; 00966 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 00967 return Result; 00968 } 00969 00970 00971 /// SCEVAddRecExpr::get - Get a add recurrence expression for the 00972 /// specified loop. Simplify the expression as much as possible. 00973 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 00974 const SCEVHandle &Step, const Loop *L) { 00975 std::vector<SCEVHandle> Operands; 00976 Operands.push_back(Start); 00977 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 00978 if (StepChrec->getLoop() == L) { 00979 Operands.insert(Operands.end(), StepChrec->op_begin(), 00980 StepChrec->op_end()); 00981 return get(Operands, L); 00982 } 00983 00984 Operands.push_back(Step); 00985 return get(Operands, L); 00986 } 00987 00988 /// SCEVAddRecExpr::get - Get a add recurrence expression for the 00989 /// specified loop. Simplify the expression as much as possible. 00990 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 00991 const Loop *L) { 00992 if (Operands.size() == 1) return Operands[0]; 00993 00994 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 00995 if (StepC->getValue()->isNullValue()) { 00996 Operands.pop_back(); 00997 return get(Operands, L); // { X,+,0 } --> X 00998 } 00999 01000 SCEVAddRecExpr *&Result = 01001 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 01002 Operands.end()))]; 01003 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 01004 return Result; 01005 } 01006 01007 SCEVHandle SCEVUnknown::get(Value *V) { 01008 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 01009 return SCEVConstant::get(CI); 01010 SCEVUnknown *&Result = SCEVUnknowns[V]; 01011 if (Result == 0) Result = new SCEVUnknown(V); 01012 return Result; 01013 } 01014 01015 01016 //===----------------------------------------------------------------------===// 01017 // ScalarEvolutionsImpl Definition and Implementation 01018 //===----------------------------------------------------------------------===// 01019 // 01020 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar 01021 /// evolution code. 01022 /// 01023 namespace { 01024 struct ScalarEvolutionsImpl { 01025 /// F - The function we are analyzing. 01026 /// 01027 Function &F; 01028 01029 /// LI - The loop information for the function we are currently analyzing. 01030 /// 01031 LoopInfo &LI; 01032 01033 /// UnknownValue - This SCEV is used to represent unknown trip counts and 01034 /// things. 01035 SCEVHandle UnknownValue; 01036 01037 /// Scalars - This is a cache of the scalars we have analyzed so far. 01038 /// 01039 std::map<Value*, SCEVHandle> Scalars; 01040 01041 /// IterationCounts - Cache the iteration count of the loops for this 01042 /// function as they are computed. 01043 std::map<const Loop*, SCEVHandle> IterationCounts; 01044 01045 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 01046 /// the PHI instructions that we attempt to compute constant evolutions for. 01047 /// This allows us to avoid potentially expensive recomputation of these 01048 /// properties. An instruction maps to null if we are unable to compute its 01049 /// exit value. 01050 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 01051 01052 public: 01053 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 01054 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 01055 01056 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 01057 /// expression and create a new one. 01058 SCEVHandle getSCEV(Value *V); 01059 01060 /// getSCEVAtScope - Compute the value of the specified expression within 01061 /// the indicated loop (which may be null to indicate in no loop). If the 01062 /// expression cannot be evaluated, return UnknownValue itself. 01063 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 01064 01065 01066 /// hasLoopInvariantIterationCount - Return true if the specified loop has 01067 /// an analyzable loop-invariant iteration count. 01068 bool hasLoopInvariantIterationCount(const Loop *L); 01069 01070 /// getIterationCount - If the specified loop has a predictable iteration 01071 /// count, return it. Note that it is not valid to call this method on a 01072 /// loop without a loop-invariant iteration count. 01073 SCEVHandle getIterationCount(const Loop *L); 01074 01075 /// deleteInstructionFromRecords - This method should be called by the 01076 /// client before it removes an instruction from the program, to make sure 01077 /// that no dangling references are left around. 01078 void deleteInstructionFromRecords(Instruction *I); 01079 01080 private: 01081 /// createSCEV - We know that there is no SCEV for the specified value. 01082 /// Analyze the expression. 01083 SCEVHandle createSCEV(Value *V); 01084 SCEVHandle createNodeForCast(CastInst *CI); 01085 01086 /// createNodeForPHI - Provide the special handling we need to analyze PHI 01087 /// SCEVs. 01088 SCEVHandle createNodeForPHI(PHINode *PN); 01089 void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN, 01090 std::set<Instruction*> &UpdatedInsts); 01091 01092 /// ComputeIterationCount - Compute the number of times the specified loop 01093 /// will iterate. 01094 SCEVHandle ComputeIterationCount(const Loop *L); 01095 01096 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 01097 /// 'setcc load X, cst', try to se if we can compute the trip count. 01098 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 01099 Constant *RHS, 01100 const Loop *L, 01101 unsigned SetCCOpcode); 01102 01103 /// ComputeIterationCountExhaustively - If the trip is known to execute a 01104 /// constant number of times (the condition evolves only from constants), 01105 /// try to evaluate a few iterations of the loop until we get the exit 01106 /// condition gets a value of ExitWhen (true or false). If we cannot 01107 /// evaluate the trip count of the loop, return UnknownValue. 01108 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 01109 bool ExitWhen); 01110 01111 /// HowFarToZero - Return the number of times a backedge comparing the 01112 /// specified value to zero will execute. If not computable, return 01113 /// UnknownValue 01114 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 01115 01116 /// HowFarToNonZero - Return the number of times a backedge checking the 01117 /// specified value for nonzero will execute. If not computable, return 01118 /// UnknownValue 01119 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 01120 01121 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 01122 /// in the header of its containing loop, we know the loop executes a 01123 /// constant number of times, and the PHI node is just a recurrence 01124 /// involving constants, fold it. 01125 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 01126 const Loop *L); 01127 }; 01128 } 01129 01130 //===----------------------------------------------------------------------===// 01131 // Basic SCEV Analysis and PHI Idiom Recognition Code 01132 // 01133 01134 /// deleteInstructionFromRecords - This method should be called by the 01135 /// client before it removes an instruction from the program, to make sure 01136 /// that no dangling references are left around. 01137 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 01138 Scalars.erase(I); 01139 if (PHINode *PN = dyn_cast<PHINode>(I)) 01140 ConstantEvolutionLoopExitValue.erase(PN); 01141 } 01142 01143 01144 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 01145 /// expression and create a new one. 01146 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 01147 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 01148 01149 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 01150 if (I != Scalars.end()) return I->second; 01151 SCEVHandle S = createSCEV(V); 01152 Scalars.insert(std::make_pair(V, S)); 01153 return S; 01154 } 01155 01156 01157 /// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of 01158 /// entries in the scalar map that refer to the "symbolic" PHI value instead of 01159 /// the recurrence value. After we resolve the PHI we must loop over all of the 01160 /// using instructions that have scalar map entries and update them. 01161 void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I, 01162 PHINode *PN, 01163 std::set<Instruction*> &UpdatedInsts) { 01164 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 01165 if (SI == Scalars.end()) return; // This scalar wasn't previous processed. 01166 if (UpdatedInsts.insert(I).second) { 01167 Scalars.erase(SI); // Remove the old entry 01168 getSCEV(I); // Calculate the new entry 01169 01170 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 01171 UI != E; ++UI) 01172 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts); 01173 } 01174 } 01175 01176 01177 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 01178 /// a loop header, making it a potential recurrence, or it doesn't. 01179 /// 01180 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 01181 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 01182 if (const Loop *L = LI.getLoopFor(PN->getParent())) 01183 if (L->getHeader() == PN->getParent()) { 01184 // If it lives in the loop header, it has two incoming values, one 01185 // from outside the loop, and one from inside. 01186 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 01187 unsigned BackEdge = IncomingEdge^1; 01188 01189 // While we are analyzing this PHI node, handle its value symbolically. 01190 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 01191 assert(Scalars.find(PN) == Scalars.end() && 01192 "PHI node already processed?"); 01193 Scalars.insert(std::make_pair(PN, SymbolicName)); 01194 01195 // Using this symbolic name for the PHI, analyze the value coming around 01196 // the back-edge. 01197 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 01198 01199 // NOTE: If BEValue is loop invariant, we know that the PHI node just 01200 // has a special value for the first iteration of the loop. 01201 01202 // If the value coming around the backedge is an add with the symbolic 01203 // value we just inserted, then we found a simple induction variable! 01204 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 01205 // If there is a single occurrence of the symbolic value, replace it 01206 // with a recurrence. 01207 unsigned FoundIndex = Add->getNumOperands(); 01208 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 01209 if (Add->getOperand(i) == SymbolicName) 01210 if (FoundIndex == e) { 01211 FoundIndex = i; 01212 break; 01213 } 01214 01215 if (FoundIndex != Add->getNumOperands()) { 01216 // Create an add with everything but the specified operand. 01217 std::vector<SCEVHandle> Ops; 01218 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 01219 if (i != FoundIndex) 01220 Ops.push_back(Add->getOperand(i)); 01221 SCEVHandle Accum = SCEVAddExpr::get(Ops); 01222 01223 // This is not a valid addrec if the step amount is varying each 01224 // loop iteration, but is not itself an addrec in this loop. 01225 if (Accum->isLoopInvariant(L) || 01226 (isa<SCEVAddRecExpr>(Accum) && 01227 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 01228 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 01229 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 01230 01231 // Okay, for the entire analysis of this edge we assumed the PHI 01232 // to be symbolic. We now need to go back and update all of the 01233 // entries for the scalars that use the PHI (except for the PHI 01234 // itself) to use the new analyzed value instead of the "symbolic" 01235 // value. 01236 Scalars.find(PN)->second = PHISCEV; // Update the PHI value 01237 std::set<Instruction*> UpdatedInsts; 01238 UpdatedInsts.insert(PN); 01239 for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end(); 01240 UI != E; ++UI) 01241 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, 01242 UpdatedInsts); 01243 return PHISCEV; 01244 } 01245 } 01246 } 01247 01248 return SymbolicName; 01249 } 01250 01251 // If it's not a loop phi, we can't handle it yet. 01252 return SCEVUnknown::get(PN); 01253 } 01254 01255 /// createNodeForCast - Handle the various forms of casts that we support. 01256 /// 01257 SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) { 01258 const Type *SrcTy = CI->getOperand(0)->getType(); 01259 const Type *DestTy = CI->getType(); 01260 01261 // If this is a noop cast (ie, conversion from int to uint), ignore it. 01262 if (SrcTy->isLosslesslyConvertibleTo(DestTy)) 01263 return getSCEV(CI->getOperand(0)); 01264 01265 if (SrcTy->isInteger() && DestTy->isInteger()) { 01266 // Otherwise, if this is a truncating integer cast, we can represent this 01267 // cast. 01268 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 01269 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)), 01270 CI->getType()->getUnsignedVersion()); 01271 if (SrcTy->isUnsigned() && 01272 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 01273 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)), 01274 CI->getType()->getUnsignedVersion()); 01275 } 01276 01277 // If this is an sign or zero extending cast and we can prove that the value 01278 // will never overflow, we could do similar transformations. 01279 01280 // Otherwise, we can't handle this cast! 01281 return SCEVUnknown::get(CI); 01282 } 01283 01284 01285 /// createSCEV - We know that there is no SCEV for the specified value. 01286 /// Analyze the expression. 01287 /// 01288 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 01289 if (Instruction *I = dyn_cast<Instruction>(V)) { 01290 switch (I->getOpcode()) { 01291 case Instruction::Add: 01292 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 01293 getSCEV(I->getOperand(1))); 01294 case Instruction::Mul: 01295 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 01296 getSCEV(I->getOperand(1))); 01297 case Instruction::Div: 01298 if (V->getType()->isInteger() && V->getType()->isUnsigned()) 01299 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), 01300 getSCEV(I->getOperand(1))); 01301 break; 01302 01303 case Instruction::Sub: 01304 return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1))); 01305 01306 case Instruction::Shl: 01307 // Turn shift left of a constant amount into a multiply. 01308 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 01309 Constant *X = ConstantInt::get(V->getType(), 1); 01310 X = ConstantExpr::getShl(X, SA); 01311 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 01312 } 01313 break; 01314 01315 case Instruction::Shr: 01316 if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1))) 01317 if (V->getType()->isUnsigned()) { 01318 Constant *X = ConstantInt::get(V->getType(), 1); 01319 X = ConstantExpr::getShl(X, SA); 01320 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 01321 } 01322 break; 01323 01324 case Instruction::Cast: 01325 return createNodeForCast(cast<CastInst>(I)); 01326 01327 case Instruction::PHI: 01328 return createNodeForPHI(cast<PHINode>(I)); 01329 01330 default: // We cannot analyze this expression. 01331 break; 01332 } 01333 } 01334 01335 return SCEVUnknown::get(V); 01336 } 01337 01338 01339 01340 //===----------------------------------------------------------------------===// 01341 // Iteration Count Computation Code 01342 // 01343 01344 /// getIterationCount - If the specified loop has a predictable iteration 01345 /// count, return it. Note that it is not valid to call this method on a 01346 /// loop without a loop-invariant iteration count. 01347 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 01348 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 01349 if (I == IterationCounts.end()) { 01350 SCEVHandle ItCount = ComputeIterationCount(L); 01351 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 01352 if (ItCount != UnknownValue) { 01353 assert(ItCount->isLoopInvariant(L) && 01354 "Computed trip count isn't loop invariant for loop!"); 01355 ++NumTripCountsComputed; 01356 } else if (isa<PHINode>(L->getHeader()->begin())) { 01357 // Only count loops that have phi nodes as not being computable. 01358 ++NumTripCountsNotComputed; 01359 } 01360 } 01361 return I->second; 01362 } 01363 01364 /// ComputeIterationCount - Compute the number of times the specified loop 01365 /// will iterate. 01366 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 01367 // If the loop has a non-one exit block count, we can't analyze it. 01368 std::vector<BasicBlock*> ExitBlocks; 01369 L->getExitBlocks(ExitBlocks); 01370 if (ExitBlocks.size() != 1) return UnknownValue; 01371 01372 // Okay, there is one exit block. Try to find the condition that causes the 01373 // loop to be exited. 01374 BasicBlock *ExitBlock = ExitBlocks[0]; 01375 01376 BasicBlock *ExitingBlock = 0; 01377 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 01378 PI != E; ++PI) 01379 if (L->contains(*PI)) { 01380 if (ExitingBlock == 0) 01381 ExitingBlock = *PI; 01382 else 01383 return UnknownValue; // More than one block exiting! 01384 } 01385 assert(ExitingBlock && "No exits from loop, something is broken!"); 01386 01387 // Okay, we've computed the exiting block. See what condition causes us to 01388 // exit. 01389 // 01390 // FIXME: we should be able to handle switch instructions (with a single exit) 01391 // FIXME: We should handle cast of int to bool as well 01392 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 01393 if (ExitBr == 0) return UnknownValue; 01394 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 01395 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 01396 if (ExitCond == 0) // Not a setcc 01397 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 01398 ExitBr->getSuccessor(0) == ExitBlock); 01399 01400 // If the condition was exit on true, convert the condition to exit on false. 01401 Instruction::BinaryOps Cond; 01402 if (ExitBr->getSuccessor(1) == ExitBlock) 01403 Cond = ExitCond->getOpcode(); 01404 else 01405 Cond = ExitCond->getInverseCondition(); 01406 01407 // Handle common loops like: for (X = "string"; *X; ++X) 01408 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 01409 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 01410 SCEVHandle ItCnt = 01411 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 01412 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 01413 } 01414 01415 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 01416 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 01417 01418 // Try to evaluate any dependencies out of the loop. 01419 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 01420 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 01421 Tmp = getSCEVAtScope(RHS, L); 01422 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 01423 01424 // At this point, we would like to compute how many iterations of the loop the 01425 // predicate will return true for these inputs. 01426 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 01427 // If there is a constant, force it into the RHS. 01428 std::swap(LHS, RHS); 01429 Cond = SetCondInst::getSwappedCondition(Cond); 01430 } 01431 01432 // FIXME: think about handling pointer comparisons! i.e.: 01433 // while (P != P+100) ++P; 01434 01435 // If we have a comparison of a chrec against a constant, try to use value 01436 // ranges to answer this query. 01437 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 01438 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 01439 if (AddRec->getLoop() == L) { 01440 // Form the comparison range using the constant of the correct type so 01441 // that the ConstantRange class knows to do a signed or unsigned 01442 // comparison. 01443 ConstantInt *CompVal = RHSC->getValue(); 01444 const Type *RealTy = ExitCond->getOperand(0)->getType(); 01445 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy)); 01446 if (CompVal) { 01447 // Form the constant range. 01448 ConstantRange CompRange(Cond, CompVal); 01449 01450 // Now that we have it, if it's signed, convert it to an unsigned 01451 // range. 01452 if (CompRange.getLower()->getType()->isSigned()) { 01453 const Type *NewTy = RHSC->getValue()->getType(); 01454 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy); 01455 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy); 01456 CompRange = ConstantRange(NewL, NewU); 01457 } 01458 01459 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 01460 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 01461 } 01462 } 01463 01464 switch (Cond) { 01465 case Instruction::SetNE: // while (X != Y) 01466 // Convert to: while (X-Y != 0) 01467 if (LHS->getType()->isInteger()) { 01468 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 01469 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 01470 } 01471 break; 01472 case Instruction::SetEQ: 01473 // Convert to: while (X-Y == 0) // while (X == Y) 01474 if (LHS->getType()->isInteger()) { 01475 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 01476 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 01477 } 01478 break; 01479 default: 01480 #if 0 01481 std::cerr << "ComputeIterationCount "; 01482 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 01483 std::cerr << "[unsigned] "; 01484 std::cerr << *LHS << " " 01485 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 01486 #endif 01487 break; 01488 } 01489 01490 return ComputeIterationCountExhaustively(L, ExitCond, 01491 ExitBr->getSuccessor(0) == ExitBlock); 01492 } 01493 01494 static ConstantInt * 01495 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 01496 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 01497 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 01498 assert(isa<SCEVConstant>(Val) && 01499 "Evaluation of SCEV at constant didn't fold correctly?"); 01500 return cast<SCEVConstant>(Val)->getValue(); 01501 } 01502 01503 /// GetAddressedElementFromGlobal - Given a global variable with an initializer 01504 /// and a GEP expression (missing the pointer index) indexing into it, return 01505 /// the addressed element of the initializer or null if the index expression is 01506 /// invalid. 01507 static Constant * 01508 GetAddressedElementFromGlobal(GlobalVariable *GV, 01509 const std::vector<ConstantInt*> &Indices) { 01510 Constant *Init = GV->getInitializer(); 01511 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 01512 uint64_t Idx = Indices[i]->getRawValue(); 01513 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 01514 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 01515 Init = cast<Constant>(CS->getOperand(Idx)); 01516 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 01517 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 01518 Init = cast<Constant>(CA->getOperand(Idx)); 01519 } else if (isa<ConstantAggregateZero>(Init)) { 01520 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 01521 assert(Idx < STy->getNumElements() && "Bad struct index!"); 01522 Init = Constant::getNullValue(STy->getElementType(Idx)); 01523 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 01524 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 01525 Init = Constant::getNullValue(ATy->getElementType()); 01526 } else { 01527 assert(0 && "Unknown constant aggregate type!"); 01528 } 01529 return 0; 01530 } else { 01531 return 0; // Unknown initializer type 01532 } 01533 } 01534 return Init; 01535 } 01536 01537 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 01538 /// 'setcc load X, cst', try to se if we can compute the trip count. 01539 SCEVHandle ScalarEvolutionsImpl:: 01540 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 01541 const Loop *L, unsigned SetCCOpcode) { 01542 if (LI->isVolatile()) return UnknownValue; 01543 01544 // Check to see if the loaded pointer is a getelementptr of a global. 01545 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 01546 if (!GEP) return UnknownValue; 01547 01548 // Make sure that it is really a constant global we are gepping, with an 01549 // initializer, and make sure the first IDX is really 0. 01550 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 01551 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 01552 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 01553 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 01554 return UnknownValue; 01555 01556 // Okay, we allow one non-constant index into the GEP instruction. 01557 Value *VarIdx = 0; 01558 std::vector<ConstantInt*> Indexes; 01559 unsigned VarIdxNum = 0; 01560 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 01561 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 01562 Indexes.push_back(CI); 01563 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 01564 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 01565 VarIdx = GEP->getOperand(i); 01566 VarIdxNum = i-2; 01567 Indexes.push_back(0); 01568 } 01569 01570 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 01571 // Check to see if X is a loop variant variable value now. 01572 SCEVHandle Idx = getSCEV(VarIdx); 01573 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 01574 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 01575 01576 // We can only recognize very limited forms of loop index expressions, in 01577 // particular, only affine AddRec's like {C1,+,C2}. 01578 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 01579 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 01580 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 01581 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 01582 return UnknownValue; 01583 01584 unsigned MaxSteps = MaxBruteForceIterations; 01585 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 01586 ConstantUInt *ItCst = 01587 ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum); 01588 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 01589 01590 // Form the GEP offset. 01591 Indexes[VarIdxNum] = Val; 01592 01593 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 01594 if (Result == 0) break; // Cannot compute! 01595 01596 // Evaluate the condition for this iteration. 01597 Result = ConstantExpr::get(SetCCOpcode, Result, RHS); 01598 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure 01599 if (Result == ConstantBool::False) { 01600 #if 0 01601 std::cerr << "\n***\n*** Computed loop count " << *ItCst 01602 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 01603 << "***\n"; 01604 #endif 01605 ++NumArrayLenItCounts; 01606 return SCEVConstant::get(ItCst); // Found terminating iteration! 01607 } 01608 } 01609 return UnknownValue; 01610 } 01611 01612 01613 /// CanConstantFold - Return true if we can constant fold an instruction of the 01614 /// specified type, assuming that all operands were constants. 01615 static bool CanConstantFold(const Instruction *I) { 01616 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 01617 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 01618 return true; 01619 01620 if (const CallInst *CI = dyn_cast<CallInst>(I)) 01621 if (const Function *F = CI->getCalledFunction()) 01622 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 01623 return false; 01624 } 01625 01626 /// ConstantFold - Constant fold an instruction of the specified type with the 01627 /// specified constant operands. This function may modify the operands vector. 01628 static Constant *ConstantFold(const Instruction *I, 01629 std::vector<Constant*> &Operands) { 01630 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 01631 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 01632 01633 switch (I->getOpcode()) { 01634 case Instruction::Cast: 01635 return ConstantExpr::getCast(Operands[0], I->getType()); 01636 case Instruction::Select: 01637 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 01638 case Instruction::Call: 01639 if (Function *GV = dyn_cast<Function>(Operands[0])) { 01640 Operands.erase(Operands.begin()); 01641 return ConstantFoldCall(cast<Function>(GV), Operands); 01642 } 01643 01644 return 0; 01645 case Instruction::GetElementPtr: 01646 Constant *Base = Operands[0]; 01647 Operands.erase(Operands.begin()); 01648 return ConstantExpr::getGetElementPtr(Base, Operands); 01649 } 01650 return 0; 01651 } 01652 01653 01654 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 01655 /// in the loop that V is derived from. We allow arbitrary operations along the 01656 /// way, but the operands of an operation must either be constants or a value 01657 /// derived from a constant PHI. If this expression does not fit with these 01658 /// constraints, return null. 01659 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 01660 // If this is not an instruction, or if this is an instruction outside of the 01661 // loop, it can't be derived from a loop PHI. 01662 Instruction *I = dyn_cast<Instruction>(V); 01663 if (I == 0 || !L->contains(I->getParent())) return 0; 01664 01665 if (PHINode *PN = dyn_cast<PHINode>(I)) 01666 if (L->getHeader() == I->getParent()) 01667 return PN; 01668 else 01669 // We don't currently keep track of the control flow needed to evaluate 01670 // PHIs, so we cannot handle PHIs inside of loops. 01671 return 0; 01672 01673 // If we won't be able to constant fold this expression even if the operands 01674 // are constants, return early. 01675 if (!CanConstantFold(I)) return 0; 01676 01677 // Otherwise, we can evaluate this instruction if all of its operands are 01678 // constant or derived from a PHI node themselves. 01679 PHINode *PHI = 0; 01680 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 01681 if (!(isa<Constant>(I->getOperand(Op)) || 01682 isa<GlobalValue>(I->getOperand(Op)))) { 01683 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 01684 if (P == 0) return 0; // Not evolving from PHI 01685 if (PHI == 0) 01686 PHI = P; 01687 else if (PHI != P) 01688 return 0; // Evolving from multiple different PHIs. 01689 } 01690 01691 // This is a expression evolving from a constant PHI! 01692 return PHI; 01693 } 01694 01695 /// EvaluateExpression - Given an expression that passes the 01696 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 01697 /// in the loop has the value PHIVal. If we can't fold this expression for some 01698 /// reason, return null. 01699 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 01700 if (isa<PHINode>(V)) return PHIVal; 01701 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 01702 return GV; 01703 if (Constant *C = dyn_cast<Constant>(V)) return C; 01704 Instruction *I = cast<Instruction>(V); 01705 01706 std::vector<Constant*> Operands; 01707 Operands.resize(I->getNumOperands()); 01708 01709 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 01710 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 01711 if (Operands[i] == 0) return 0; 01712 } 01713 01714 return ConstantFold(I, Operands); 01715 } 01716 01717 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 01718 /// in the header of its containing loop, we know the loop executes a 01719 /// constant number of times, and the PHI node is just a recurrence 01720 /// involving constants, fold it. 01721 Constant *ScalarEvolutionsImpl:: 01722 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 01723 std::map<PHINode*, Constant*>::iterator I = 01724 ConstantEvolutionLoopExitValue.find(PN); 01725 if (I != ConstantEvolutionLoopExitValue.end()) 01726 return I->second; 01727 01728 if (Its > MaxBruteForceIterations) 01729 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 01730 01731 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 01732 01733 // Since the loop is canonicalized, the PHI node must have two entries. One 01734 // entry must be a constant (coming in from outside of the loop), and the 01735 // second must be derived from the same PHI. 01736 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 01737 Constant *StartCST = 01738 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 01739 if (StartCST == 0) 01740 return RetVal = 0; // Must be a constant. 01741 01742 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 01743 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 01744 if (PN2 != PN) 01745 return RetVal = 0; // Not derived from same PHI. 01746 01747 // Execute the loop symbolically to determine the exit value. 01748 unsigned IterationNum = 0; 01749 unsigned NumIterations = Its; 01750 if (NumIterations != Its) 01751 return RetVal = 0; // More than 2^32 iterations?? 01752 01753 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 01754 if (IterationNum == NumIterations) 01755 return RetVal = PHIVal; // Got exit value! 01756 01757 // Compute the value of the PHI node for the next iteration. 01758 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 01759 if (NextPHI == PHIVal) 01760 return RetVal = NextPHI; // Stopped evolving! 01761 if (NextPHI == 0) 01762 return 0; // Couldn't evaluate! 01763 PHIVal = NextPHI; 01764 } 01765 } 01766 01767 /// ComputeIterationCountExhaustively - If the trip is known to execute a 01768 /// constant number of times (the condition evolves only from constants), 01769 /// try to evaluate a few iterations of the loop until we get the exit 01770 /// condition gets a value of ExitWhen (true or false). If we cannot 01771 /// evaluate the trip count of the loop, return UnknownValue. 01772 SCEVHandle ScalarEvolutionsImpl:: 01773 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 01774 PHINode *PN = getConstantEvolvingPHI(Cond, L); 01775 if (PN == 0) return UnknownValue; 01776 01777 // Since the loop is canonicalized, the PHI node must have two entries. One 01778 // entry must be a constant (coming in from outside of the loop), and the 01779 // second must be derived from the same PHI. 01780 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 01781 Constant *StartCST = 01782 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 01783 if (StartCST == 0) return UnknownValue; // Must be a constant. 01784 01785 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 01786 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 01787 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 01788 01789 // Okay, we find a PHI node that defines the trip count of this loop. Execute 01790 // the loop symbolically to determine when the condition gets a value of 01791 // "ExitWhen". 01792 unsigned IterationNum = 0; 01793 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 01794 for (Constant *PHIVal = StartCST; 01795 IterationNum != MaxIterations; ++IterationNum) { 01796 ConstantBool *CondVal = 01797 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 01798 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 01799 01800 if (CondVal->getValue() == ExitWhen) { 01801 ConstantEvolutionLoopExitValue[PN] = PHIVal; 01802 ++NumBruteForceTripCountsComputed; 01803 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum)); 01804 } 01805 01806 // Compute the value of the PHI node for the next iteration. 01807 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 01808 if (NextPHI == 0 || NextPHI == PHIVal) 01809 return UnknownValue; // Couldn't evaluate or not making progress... 01810 PHIVal = NextPHI; 01811 } 01812 01813 // Too many iterations were needed to evaluate. 01814 return UnknownValue; 01815 } 01816 01817 /// getSCEVAtScope - Compute the value of the specified expression within the 01818 /// indicated loop (which may be null to indicate in no loop). If the 01819 /// expression cannot be evaluated, return UnknownValue. 01820 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 01821 // FIXME: this should be turned into a virtual method on SCEV! 01822 01823 if (isa<SCEVConstant>(V)) return V; 01824 01825 // If this instruction is evolves from a constant-evolving PHI, compute the 01826 // exit value from the loop without using SCEVs. 01827 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 01828 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 01829 const Loop *LI = this->LI[I->getParent()]; 01830 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 01831 if (PHINode *PN = dyn_cast<PHINode>(I)) 01832 if (PN->getParent() == LI->getHeader()) { 01833 // Okay, there is no closed form solution for the PHI node. Check 01834 // to see if the loop that contains it has a known iteration count. 01835 // If so, we may be able to force computation of the exit value. 01836 SCEVHandle IterationCount = getIterationCount(LI); 01837 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 01838 // Okay, we know how many times the containing loop executes. If 01839 // this is a constant evolving PHI node, get the final value at 01840 // the specified iteration number. 01841 Constant *RV = getConstantEvolutionLoopExitValue(PN, 01842 ICC->getValue()->getRawValue(), 01843 LI); 01844 if (RV) return SCEVUnknown::get(RV); 01845 } 01846 } 01847 01848 // Okay, this is a some expression that we cannot symbolically evaluate 01849 // into a SCEV. Check to see if it's possible to symbolically evaluate 01850 // the arguments into constants, and if see, try to constant propagate the 01851 // result. This is particularly useful for computing loop exit values. 01852 if (CanConstantFold(I)) { 01853 std::vector<Constant*> Operands; 01854 Operands.reserve(I->getNumOperands()); 01855 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 01856 Value *Op = I->getOperand(i); 01857 if (Constant *C = dyn_cast<Constant>(Op)) { 01858 Operands.push_back(C); 01859 } else { 01860 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 01861 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 01862 Operands.push_back(ConstantExpr::getCast(SC->getValue(), 01863 Op->getType())); 01864 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 01865 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 01866 Operands.push_back(ConstantExpr::getCast(C, Op->getType())); 01867 else 01868 return V; 01869 } else { 01870 return V; 01871 } 01872 } 01873 } 01874 return SCEVUnknown::get(ConstantFold(I, Operands)); 01875 } 01876 } 01877 01878 // This is some other type of SCEVUnknown, just return it. 01879 return V; 01880 } 01881 01882 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 01883 // Avoid performing the look-up in the common case where the specified 01884 // expression has no loop-variant portions. 01885 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 01886 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 01887 if (OpAtScope != Comm->getOperand(i)) { 01888 if (OpAtScope == UnknownValue) return UnknownValue; 01889 // Okay, at least one of these operands is loop variant but might be 01890 // foldable. Build a new instance of the folded commutative expression. 01891 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 01892 NewOps.push_back(OpAtScope); 01893 01894 for (++i; i != e; ++i) { 01895 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 01896 if (OpAtScope == UnknownValue) return UnknownValue; 01897 NewOps.push_back(OpAtScope); 01898 } 01899 if (isa<SCEVAddExpr>(Comm)) 01900 return SCEVAddExpr::get(NewOps); 01901 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 01902 return SCEVMulExpr::get(NewOps); 01903 } 01904 } 01905 // If we got here, all operands are loop invariant. 01906 return Comm; 01907 } 01908 01909 if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) { 01910 SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L); 01911 if (LHS == UnknownValue) return LHS; 01912 SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L); 01913 if (RHS == UnknownValue) return RHS; 01914 if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS()) 01915 return UDiv; // must be loop invariant 01916 return SCEVUDivExpr::get(LHS, RHS); 01917 } 01918 01919 // If this is a loop recurrence for a loop that does not contain L, then we 01920 // are dealing with the final value computed by the loop. 01921 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 01922 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 01923 // To evaluate this recurrence, we need to know how many times the AddRec 01924 // loop iterates. Compute this now. 01925 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 01926 if (IterationCount == UnknownValue) return UnknownValue; 01927 IterationCount = getTruncateOrZeroExtend(IterationCount, 01928 AddRec->getType()); 01929 01930 // If the value is affine, simplify the expression evaluation to just 01931 // Start + Step*IterationCount. 01932 if (AddRec->isAffine()) 01933 return SCEVAddExpr::get(AddRec->getStart(), 01934 SCEVMulExpr::get(IterationCount, 01935 AddRec->getOperand(1))); 01936 01937 // Otherwise, evaluate it the hard way. 01938 return AddRec->evaluateAtIteration(IterationCount); 01939 } 01940 return UnknownValue; 01941 } 01942 01943 //assert(0 && "Unknown SCEV type!"); 01944 return UnknownValue; 01945 } 01946 01947 01948 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the 01949 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 01950 /// might be the same) or two SCEVCouldNotCompute objects. 01951 /// 01952 static std::pair<SCEVHandle,SCEVHandle> 01953 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 01954 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 01955 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 01956 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 01957 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 01958 01959 // We currently can only solve this if the coefficients are constants. 01960 if (!L || !M || !N) { 01961 SCEV *CNC = new SCEVCouldNotCompute(); 01962 return std::make_pair(CNC, CNC); 01963 } 01964 01965 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2); 01966 01967 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 01968 Constant *C = L->getValue(); 01969 // The B coefficient is M-N/2 01970 Constant *B = ConstantExpr::getSub(M->getValue(), 01971 ConstantExpr::getDiv(N->getValue(), 01972 Two)); 01973 // The A coefficient is N/2 01974 Constant *A = ConstantExpr::getDiv(N->getValue(), Two); 01975 01976 // Compute the B^2-4ac term. 01977 Constant *SqrtTerm = 01978 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 01979 ConstantExpr::getMul(A, C)); 01980 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 01981 01982 // Compute floor(sqrt(B^2-4ac)) 01983 ConstantUInt *SqrtVal = 01984 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm, 01985 SqrtTerm->getType()->getUnsignedVersion())); 01986 uint64_t SqrtValV = SqrtVal->getValue(); 01987 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 01988 // The square root might not be precise for arbitrary 64-bit integer 01989 // values. Do some sanity checks to ensure it's correct. 01990 if (SqrtValV2*SqrtValV2 > SqrtValV || 01991 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 01992 SCEV *CNC = new SCEVCouldNotCompute(); 01993 return std::make_pair(CNC, CNC); 01994 } 01995 01996 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2); 01997 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType()); 01998 01999 Constant *NegB = ConstantExpr::getNeg(B); 02000 Constant *TwoA = ConstantExpr::getMul(A, Two); 02001 02002 // The divisions must be performed as signed divisions. 02003 const Type *SignedTy = NegB->getType()->getSignedVersion(); 02004 NegB = ConstantExpr::getCast(NegB, SignedTy); 02005 TwoA = ConstantExpr::getCast(TwoA, SignedTy); 02006 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy); 02007 02008 Constant *Solution1 = 02009 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 02010 Constant *Solution2 = 02011 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 02012 return std::make_pair(SCEVUnknown::get(Solution1), 02013 SCEVUnknown::get(Solution2)); 02014 } 02015 02016 /// HowFarToZero - Return the number of times a backedge comparing the specified 02017 /// value to zero will execute. If not computable, return UnknownValue 02018 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 02019 // If the value is a constant 02020 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 02021 // If the value is already zero, the branch will execute zero times. 02022 if (C->getValue()->isNullValue()) return C; 02023 return UnknownValue; // Otherwise it will loop infinitely. 02024 } 02025 02026 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 02027 if (!AddRec || AddRec->getLoop() != L) 02028 return UnknownValue; 02029 02030 if (AddRec->isAffine()) { 02031 // If this is an affine expression the execution count of this branch is 02032 // equal to: 02033 // 02034 // (0 - Start/Step) iff Start % Step == 0 02035 // 02036 // Get the initial value for the loop. 02037 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 02038 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 02039 SCEVHandle Step = AddRec->getOperand(1); 02040 02041 Step = getSCEVAtScope(Step, L->getParentLoop()); 02042 02043 // Figure out if Start % Step == 0. 02044 // FIXME: We should add DivExpr and RemExpr operations to our AST. 02045 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 02046 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 02047 return getNegativeSCEV(Start); // 0 - Start/1 == -Start 02048 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 02049 return Start; // 0 - Start/-1 == Start 02050 02051 // Check to see if Start is divisible by SC with no remainder. 02052 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 02053 ConstantInt *StartCC = StartC->getValue(); 02054 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 02055 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue()); 02056 if (Rem->isNullValue()) { 02057 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue()); 02058 return SCEVUnknown::get(Result); 02059 } 02060 } 02061 } 02062 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 02063 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 02064 // the quadratic equation to solve it. 02065 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 02066 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 02067 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 02068 if (R1) { 02069 #if 0 02070 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1 02071 << " sol#2: " << *R2 << "\n"; 02072 #endif 02073 // Pick the smallest positive root value. 02074 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 02075 if (ConstantBool *CB = 02076 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 02077 R2->getValue()))) { 02078 if (CB != ConstantBool::True) 02079 std::swap(R1, R2); // R1 is the minimum root now. 02080 02081 // We can only use this value if the chrec ends up with an exact zero 02082 // value at this index. When solving for "X*X != 5", for example, we 02083 // should not accept a root of 2. 02084 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 02085 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 02086 if (EvalVal->getValue()->isNullValue()) 02087 return R1; // We found a quadratic root! 02088 } 02089 } 02090 } 02091 02092 return UnknownValue; 02093 } 02094 02095 /// HowFarToNonZero - Return the number of times a backedge checking the 02096 /// specified value for nonzero will execute. If not computable, return 02097 /// UnknownValue 02098 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 02099 // Loops that look like: while (X == 0) are very strange indeed. We don't 02100 // handle them yet except for the trivial case. This could be expanded in the 02101 // future as needed. 02102 02103 // If the value is a constant, check to see if it is known to be non-zero 02104 // already. If so, the backedge will execute zero times. 02105 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 02106 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 02107 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 02108 if (NonZero == ConstantBool::True) 02109 return getSCEV(Zero); 02110 return UnknownValue; // Otherwise it will loop infinitely. 02111 } 02112 02113 // We could implement others, but I really doubt anyone writes loops like 02114 // this, and if they did, they would already be constant folded. 02115 return UnknownValue; 02116 } 02117 02118 /// getNumIterationsInRange - Return the number of iterations of this loop that 02119 /// produce values in the specified constant range. Another way of looking at 02120 /// this is that it returns the first iteration number where the value is not in 02121 /// the condition, thus computing the exit count. If the iteration count can't 02122 /// be computed, an instance of SCEVCouldNotCompute is returned. 02123 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 02124 if (Range.isFullSet()) // Infinite loop. 02125 return new SCEVCouldNotCompute(); 02126 02127 // If the start is a non-zero constant, shift the range to simplify things. 02128 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 02129 if (!SC->getValue()->isNullValue()) { 02130 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 02131 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 02132 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 02133 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 02134 return ShiftedAddRec->getNumIterationsInRange( 02135 Range.subtract(SC->getValue())); 02136 // This is strange and shouldn't happen. 02137 return new SCEVCouldNotCompute(); 02138 } 02139 02140 // The only time we can solve this is when we have all constant indices. 02141 // Otherwise, we cannot determine the overflow conditions. 02142 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 02143 if (!isa<SCEVConstant>(getOperand(i))) 02144 return new SCEVCouldNotCompute(); 02145 02146 02147 // Okay at this point we know that all elements of the chrec are constants and 02148 // that the start element is zero. 02149 02150 // First check to see if the range contains zero. If not, the first 02151 // iteration exits. 02152 ConstantInt *Zero = ConstantInt::get(getType(), 0); 02153 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 02154 02155 if (isAffine()) { 02156 // If this is an affine expression then we have this situation: 02157 // Solve {0,+,A} in Range === Ax in Range 02158 02159 // Since we know that zero is in the range, we know that the upper value of 02160 // the range must be the first possible exit value. Also note that we 02161 // already checked for a full range. 02162 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 02163 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 02164 ConstantInt *One = ConstantInt::get(getType(), 1); 02165 02166 // The exit value should be (Upper+A-1)/A. 02167 Constant *ExitValue = Upper; 02168 if (A != One) { 02169 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 02170 ExitValue = ConstantExpr::getDiv(ExitValue, A); 02171 } 02172 assert(isa<ConstantInt>(ExitValue) && 02173 "Constant folding of integers not implemented?"); 02174 02175 // Evaluate at the exit value. If we really did fall out of the valid 02176 // range, then we computed our trip count, otherwise wrap around or other 02177 // things must have happened. 02178 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 02179 if (Range.contains(Val)) 02180 return new SCEVCouldNotCompute(); // Something strange happened 02181 02182 // Ensure that the previous value is in the range. This is a sanity check. 02183 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 02184 ConstantExpr::getSub(ExitValue, One))) && 02185 "Linear scev computation is off in a bad way!"); 02186 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 02187 } else if (isQuadratic()) { 02188 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 02189 // quadratic equation to solve it. To do this, we must frame our problem in 02190 // terms of figuring out when zero is crossed, instead of when 02191 // Range.getUpper() is crossed. 02192 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 02193 NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 02194 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 02195 02196 // Next, solve the constructed addrec 02197 std::pair<SCEVHandle,SCEVHandle> Roots = 02198 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 02199 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 02200 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 02201 if (R1) { 02202 // Pick the smallest positive root value. 02203 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 02204 if (ConstantBool *CB = 02205 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 02206 R2->getValue()))) { 02207 if (CB != ConstantBool::True) 02208 std::swap(R1, R2); // R1 is the minimum root now. 02209 02210 // Make sure the root is not off by one. The returned iteration should 02211 // not be in the range, but the previous one should be. When solving 02212 // for "X*X < 5", for example, we should not return a root of 2. 02213 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 02214 R1->getValue()); 02215 if (Range.contains(R1Val)) { 02216 // The next iteration must be out of the range... 02217 Constant *NextVal = 02218 ConstantExpr::getAdd(R1->getValue(), 02219 ConstantInt::get(R1->getType(), 1)); 02220 02221 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 02222 if (!Range.contains(R1Val)) 02223 return SCEVUnknown::get(NextVal); 02224 return new SCEVCouldNotCompute(); // Something strange happened 02225 } 02226 02227 // If R1 was not in the range, then it is a good return value. Make 02228 // sure that R1-1 WAS in the range though, just in case. 02229 Constant *NextVal = 02230 ConstantExpr::getSub(R1->getValue(), 02231 ConstantInt::get(R1->getType(), 1)); 02232 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 02233 if (Range.contains(R1Val)) 02234 return R1; 02235 return new SCEVCouldNotCompute(); // Something strange happened 02236 } 02237 } 02238 } 02239 02240 // Fallback, if this is a general polynomial, figure out the progression 02241 // through brute force: evaluate until we find an iteration that fails the 02242 // test. This is likely to be slow, but getting an accurate trip count is 02243 // incredibly important, we will be able to simplify the exit test a lot, and 02244 // we are almost guaranteed to get a trip count in this case. 02245 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 02246 ConstantInt *One = ConstantInt::get(getType(), 1); 02247 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 02248 do { 02249 ++NumBruteForceEvaluations; 02250 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 02251 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 02252 return new SCEVCouldNotCompute(); 02253 02254 // Check to see if we found the value! 02255 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 02256 return SCEVConstant::get(TestVal); 02257 02258 // Increment to test the next index. 02259 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 02260 } while (TestVal != EndVal); 02261 02262 return new SCEVCouldNotCompute(); 02263 } 02264 02265 02266 02267 //===----------------------------------------------------------------------===// 02268 // ScalarEvolution Class Implementation 02269 //===----------------------------------------------------------------------===// 02270 02271 bool ScalarEvolution::runOnFunction(Function &F) { 02272 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 02273 return false; 02274 } 02275 02276 void ScalarEvolution::releaseMemory() { 02277 delete (ScalarEvolutionsImpl*)Impl; 02278 Impl = 0; 02279 } 02280 02281 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 02282 AU.setPreservesAll(); 02283 AU.addRequiredID(LoopSimplifyID); 02284 AU.addRequiredTransitive<LoopInfo>(); 02285 } 02286 02287 SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 02288 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 02289 } 02290 02291 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 02292 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 02293 } 02294 02295 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 02296 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 02297 } 02298 02299 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 02300 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 02301 } 02302 02303 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 02304 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 02305 } 02306 02307 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 02308 const Loop *L) { 02309 // Print all inner loops first 02310 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 02311 PrintLoopInfo(OS, SE, *I); 02312 02313 std::cerr << "Loop " << L->getHeader()->getName() << ": "; 02314 02315 std::vector<BasicBlock*> ExitBlocks; 02316 L->getExitBlocks(ExitBlocks); 02317 if (ExitBlocks.size() != 1) 02318 std::cerr << "<multiple exits> "; 02319 02320 if (SE->hasLoopInvariantIterationCount(L)) { 02321 std::cerr << *SE->getIterationCount(L) << " iterations! "; 02322 } else { 02323 std::cerr << "Unpredictable iteration count. "; 02324 } 02325 02326 std::cerr << "\n"; 02327 } 02328 02329 void ScalarEvolution::print(std::ostream &OS) const { 02330 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 02331 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 02332 02333 OS << "Classifying expressions for: " << F.getName() << "\n"; 02334 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 02335 if (I->getType()->isInteger()) { 02336 OS << *I; 02337 OS << " --> "; 02338 SCEVHandle SV = getSCEV(&*I); 02339 SV->print(OS); 02340 OS << "\t\t"; 02341 02342 if ((*I).getType()->isIntegral()) { 02343 ConstantRange Bounds = SV->getValueRange(); 02344 if (!Bounds.isFullSet()) 02345 OS << "Bounds: " << Bounds << " "; 02346 } 02347 02348 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 02349 OS << "Exits: "; 02350 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 02351 if (isa<SCEVCouldNotCompute>(ExitValue)) { 02352 OS << "<<Unknown>>"; 02353 } else { 02354 OS << *ExitValue; 02355 } 02356 } 02357 02358 02359 OS << "\n"; 02360 } 02361 02362 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 02363 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 02364 PrintLoopInfo(OS, this, *I); 02365 } 02366