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ScalarEvolution.cpp

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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/ConstantFolding.h"
00068 #include "llvm/Analysis/LoopInfo.h"
00069 #include "llvm/Assembly/Writer.h"
00070 #include "llvm/Transforms/Scalar.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 <iostream>
00078 #include <algorithm>
00079 using namespace llvm;
00080 
00081 namespace {
00082   RegisterAnalysis<ScalarEvolution>
00083   R("scalar-evolution", "Scalar Evolution Analysis");
00084 
00085   Statistic<>
00086   NumBruteForceEvaluations("scalar-evolution",
00087                            "Number of brute force evaluations needed to "
00088                            "calculate high-order polynomial exit values");
00089   Statistic<>
00090   NumArrayLenItCounts("scalar-evolution",
00091                       "Number of trip counts computed with array length");
00092   Statistic<>
00093   NumTripCountsComputed("scalar-evolution",
00094                         "Number of loops with predictable loop counts");
00095   Statistic<>
00096   NumTripCountsNotComputed("scalar-evolution",
00097                            "Number of loops without predictable loop counts");
00098   Statistic<>
00099   NumBruteForceTripCountsComputed("scalar-evolution",
00100                         "Number of loops with trip counts computed by force");
00101 
00102   cl::opt<unsigned>
00103   MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
00104                           cl::desc("Maximum number of iterations SCEV will "
00105                               "symbolically execute a constant derived loop"),
00106                           cl::init(100));
00107 }
00108 
00109 //===----------------------------------------------------------------------===//
00110 //                           SCEV class definitions
00111 //===----------------------------------------------------------------------===//
00112 
00113 //===----------------------------------------------------------------------===//
00114 // Implementation of the SCEV class.
00115 //
00116 SCEV::~SCEV() {}
00117 void SCEV::dump() const {
00118   print(std::cerr);
00119 }
00120 
00121 /// getValueRange - Return the tightest constant bounds that this value is
00122 /// known to have.  This method is only valid on integer SCEV objects.
00123 ConstantRange SCEV::getValueRange() const {
00124   const Type *Ty = getType();
00125   assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
00126   Ty = Ty->getUnsignedVersion();
00127   // Default to a full range if no better information is available.
00128   return ConstantRange(getType());
00129 }
00130 
00131 
00132 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
00133 
00134 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
00135   assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
00136   return false;
00137 }
00138 
00139 const Type *SCEVCouldNotCompute::getType() const {
00140   assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
00141   return 0;
00142 }
00143 
00144 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
00145   assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
00146   return false;
00147 }
00148 
00149 SCEVHandle SCEVCouldNotCompute::
00150 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
00151                                   const SCEVHandle &Conc) const {
00152   return this;
00153 }
00154 
00155 void SCEVCouldNotCompute::print(std::ostream &OS) const {
00156   OS << "***COULDNOTCOMPUTE***";
00157 }
00158 
00159 bool SCEVCouldNotCompute::classof(const SCEV *S) {
00160   return S->getSCEVType() == scCouldNotCompute;
00161 }
00162 
00163 
00164 // SCEVConstants - Only allow the creation of one SCEVConstant for any
00165 // particular value.  Don't use a SCEVHandle here, or else the object will
00166 // never be deleted!
00167 static std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
00168 
00169 
00170 SCEVConstant::~SCEVConstant() {
00171   SCEVConstants.erase(V);
00172 }
00173 
00174 SCEVHandle SCEVConstant::get(ConstantInt *V) {
00175   // Make sure that SCEVConstant instances are all unsigned.
00176   if (V->getType()->isSigned()) {
00177     const Type *NewTy = V->getType()->getUnsignedVersion();
00178     V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
00179   }
00180 
00181   SCEVConstant *&R = SCEVConstants[V];
00182   if (R == 0) R = new SCEVConstant(V);
00183   return R;
00184 }
00185 
00186 ConstantRange SCEVConstant::getValueRange() const {
00187   return ConstantRange(V);
00188 }
00189 
00190 const Type *SCEVConstant::getType() const { return V->getType(); }
00191 
00192 void SCEVConstant::print(std::ostream &OS) const {
00193   WriteAsOperand(OS, V, false);
00194 }
00195 
00196 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
00197 // particular input.  Don't use a SCEVHandle here, or else the object will
00198 // never be deleted!
00199 static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
00200 
00201 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
00202   : SCEV(scTruncate), Op(op), Ty(ty) {
00203   assert(Op->getType()->isInteger() && Ty->isInteger() &&
00204          Ty->isUnsigned() &&
00205          "Cannot truncate non-integer value!");
00206   assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
00207          "This is not a truncating conversion!");
00208 }
00209 
00210 SCEVTruncateExpr::~SCEVTruncateExpr() {
00211   SCEVTruncates.erase(std::make_pair(Op, Ty));
00212 }
00213 
00214 ConstantRange SCEVTruncateExpr::getValueRange() const {
00215   return getOperand()->getValueRange().truncate(getType());
00216 }
00217 
00218 void SCEVTruncateExpr::print(std::ostream &OS) const {
00219   OS << "(truncate " << *Op << " to " << *Ty << ")";
00220 }
00221 
00222 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
00223 // particular input.  Don't use a SCEVHandle here, or else the object will never
00224 // be deleted!
00225 static std::map<std::pair<SCEV*, const Type*>,
00226                 SCEVZeroExtendExpr*> SCEVZeroExtends;
00227 
00228 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
00229   : SCEV(scTruncate), Op(op), Ty(ty) {
00230   assert(Op->getType()->isInteger() && Ty->isInteger() &&
00231          Ty->isUnsigned() &&
00232          "Cannot zero extend non-integer value!");
00233   assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
00234          "This is not an extending conversion!");
00235 }
00236 
00237 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
00238   SCEVZeroExtends.erase(std::make_pair(Op, Ty));
00239 }
00240 
00241 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
00242   return getOperand()->getValueRange().zeroExtend(getType());
00243 }
00244 
00245 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
00246   OS << "(zeroextend " << *Op << " to " << *Ty << ")";
00247 }
00248 
00249 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
00250 // particular input.  Don't use a SCEVHandle here, or else the object will never
00251 // be deleted!
00252 static std::map<std::pair<unsigned, std::vector<SCEV*> >,
00253                 SCEVCommutativeExpr*> SCEVCommExprs;
00254 
00255 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
00256   SCEVCommExprs.erase(std::make_pair(getSCEVType(),
00257                                      std::vector<SCEV*>(Operands.begin(),
00258                                                         Operands.end())));
00259 }
00260 
00261 void SCEVCommutativeExpr::print(std::ostream &OS) const {
00262   assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
00263   const char *OpStr = getOperationStr();
00264   OS << "(" << *Operands[0];
00265   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
00266     OS << OpStr << *Operands[i];
00267   OS << ")";
00268 }
00269 
00270 SCEVHandle SCEVCommutativeExpr::
00271 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
00272                                   const SCEVHandle &Conc) const {
00273   for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
00274     SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
00275     if (H != getOperand(i)) {
00276       std::vector<SCEVHandle> NewOps;
00277       NewOps.reserve(getNumOperands());
00278       for (unsigned j = 0; j != i; ++j)
00279         NewOps.push_back(getOperand(j));
00280       NewOps.push_back(H);
00281       for (++i; i != e; ++i)
00282         NewOps.push_back(getOperand(i)->
00283                          replaceSymbolicValuesWithConcrete(Sym, Conc));
00284 
00285       if (isa<SCEVAddExpr>(this))
00286         return SCEVAddExpr::get(NewOps);
00287       else if (isa<SCEVMulExpr>(this))
00288         return SCEVMulExpr::get(NewOps);
00289       else
00290         assert(0 && "Unknown commutative expr!");
00291     }
00292   }
00293   return this;
00294 }
00295 
00296 
00297 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
00298 // input.  Don't use a SCEVHandle here, or else the object will never be
00299 // deleted!
00300 static std::map<std::pair<SCEV*, SCEV*>, SCEVSDivExpr*> SCEVSDivs;
00301 
00302 SCEVSDivExpr::~SCEVSDivExpr() {
00303   SCEVSDivs.erase(std::make_pair(LHS, RHS));
00304 }
00305 
00306 void SCEVSDivExpr::print(std::ostream &OS) const {
00307   OS << "(" << *LHS << " /s " << *RHS << ")";
00308 }
00309 
00310 const Type *SCEVSDivExpr::getType() const {
00311   const Type *Ty = LHS->getType();
00312   if (Ty->isUnsigned()) Ty = Ty->getSignedVersion();
00313   return Ty;
00314 }
00315 
00316 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
00317 // particular input.  Don't use a SCEVHandle here, or else the object will never
00318 // be deleted!
00319 static std::map<std::pair<const Loop *, std::vector<SCEV*> >,
00320                 SCEVAddRecExpr*> SCEVAddRecExprs;
00321 
00322 SCEVAddRecExpr::~SCEVAddRecExpr() {
00323   SCEVAddRecExprs.erase(std::make_pair(L,
00324                                        std::vector<SCEV*>(Operands.begin(),
00325                                                           Operands.end())));
00326 }
00327 
00328 SCEVHandle SCEVAddRecExpr::
00329 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
00330                                   const SCEVHandle &Conc) const {
00331   for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
00332     SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
00333     if (H != getOperand(i)) {
00334       std::vector<SCEVHandle> NewOps;
00335       NewOps.reserve(getNumOperands());
00336       for (unsigned j = 0; j != i; ++j)
00337         NewOps.push_back(getOperand(j));
00338       NewOps.push_back(H);
00339       for (++i; i != e; ++i)
00340         NewOps.push_back(getOperand(i)->
00341                          replaceSymbolicValuesWithConcrete(Sym, Conc));
00342 
00343       return get(NewOps, L);
00344     }
00345   }
00346   return this;
00347 }
00348 
00349 
00350 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
00351   // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
00352   // contain L and if the start is invariant.
00353   return !QueryLoop->contains(L->getHeader()) &&
00354          getOperand(0)->isLoopInvariant(QueryLoop);
00355 }
00356 
00357 
00358 void SCEVAddRecExpr::print(std::ostream &OS) const {
00359   OS << "{" << *Operands[0];
00360   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
00361     OS << ",+," << *Operands[i];
00362   OS << "}<" << L->getHeader()->getName() + ">";
00363 }
00364 
00365 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
00366 // value.  Don't use a SCEVHandle here, or else the object will never be
00367 // deleted!
00368 static std::map<Value*, SCEVUnknown*> SCEVUnknowns;
00369 
00370 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); }
00371 
00372 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
00373   // All non-instruction values are loop invariant.  All instructions are loop
00374   // invariant if they are not contained in the specified loop.
00375   if (Instruction *I = dyn_cast<Instruction>(V))
00376     return !L->contains(I->getParent());
00377   return true;
00378 }
00379 
00380 const Type *SCEVUnknown::getType() const {
00381   return V->getType();
00382 }
00383 
00384 void SCEVUnknown::print(std::ostream &OS) const {
00385   WriteAsOperand(OS, V, false);
00386 }
00387 
00388 //===----------------------------------------------------------------------===//
00389 //                               SCEV Utilities
00390 //===----------------------------------------------------------------------===//
00391 
00392 namespace {
00393   /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
00394   /// than the complexity of the RHS.  This comparator is used to canonicalize
00395   /// expressions.
00396   struct SCEVComplexityCompare {
00397     bool operator()(SCEV *LHS, SCEV *RHS) {
00398       return LHS->getSCEVType() < RHS->getSCEVType();
00399     }
00400   };
00401 }
00402 
00403 /// GroupByComplexity - Given a list of SCEV objects, order them by their
00404 /// complexity, and group objects of the same complexity together by value.
00405 /// When this routine is finished, we know that any duplicates in the vector are
00406 /// consecutive and that complexity is monotonically increasing.
00407 ///
00408 /// Note that we go take special precautions to ensure that we get determinstic
00409 /// results from this routine.  In other words, we don't want the results of
00410 /// this to depend on where the addresses of various SCEV objects happened to
00411 /// land in memory.
00412 ///
00413 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
00414   if (Ops.size() < 2) return;  // Noop
00415   if (Ops.size() == 2) {
00416     // This is the common case, which also happens to be trivially simple.
00417     // Special case it.
00418     if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
00419       std::swap(Ops[0], Ops[1]);
00420     return;
00421   }
00422 
00423   // Do the rough sort by complexity.
00424   std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
00425 
00426   // Now that we are sorted by complexity, group elements of the same
00427   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
00428   // be extremely short in practice.  Note that we take this approach because we
00429   // do not want to depend on the addresses of the objects we are grouping.
00430   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
00431     SCEV *S = Ops[i];
00432     unsigned Complexity = S->getSCEVType();
00433 
00434     // If there are any objects of the same complexity and same value as this
00435     // one, group them.
00436     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
00437       if (Ops[j] == S) { // Found a duplicate.
00438         // Move it to immediately after i'th element.
00439         std::swap(Ops[i+1], Ops[j]);
00440         ++i;   // no need to rescan it.
00441         if (i == e-2) return;  // Done!
00442       }
00443     }
00444   }
00445 }
00446 
00447 
00448 
00449 //===----------------------------------------------------------------------===//
00450 //                      Simple SCEV method implementations
00451 //===----------------------------------------------------------------------===//
00452 
00453 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
00454 /// specified signed integer value and return a SCEV for the constant.
00455 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
00456   Constant *C;
00457   if (Val == 0)
00458     C = Constant::getNullValue(Ty);
00459   else if (Ty->isFloatingPoint())
00460     C = ConstantFP::get(Ty, Val);
00461   else if (Ty->isSigned())
00462     C = ConstantSInt::get(Ty, Val);
00463   else {
00464     C = ConstantSInt::get(Ty->getSignedVersion(), Val);
00465     C = ConstantExpr::getCast(C, Ty);
00466   }
00467   return SCEVUnknown::get(C);
00468 }
00469 
00470 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
00471 /// input value to the specified type.  If the type must be extended, it is zero
00472 /// extended.
00473 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
00474   const Type *SrcTy = V->getType();
00475   assert(SrcTy->isInteger() && Ty->isInteger() &&
00476          "Cannot truncate or zero extend with non-integer arguments!");
00477   if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
00478     return V;  // No conversion
00479   if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
00480     return SCEVTruncateExpr::get(V, Ty);
00481   return SCEVZeroExtendExpr::get(V, Ty);
00482 }
00483 
00484 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
00485 ///
00486 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
00487   if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
00488     return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
00489 
00490   return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
00491 }
00492 
00493 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
00494 ///
00495 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
00496   // X - Y --> X + -Y
00497   return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
00498 }
00499 
00500 
00501 /// PartialFact - Compute V!/(V-NumSteps)!
00502 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
00503   // Handle this case efficiently, it is common to have constant iteration
00504   // counts while computing loop exit values.
00505   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
00506     uint64_t Val = SC->getValue()->getRawValue();
00507     uint64_t Result = 1;
00508     for (; NumSteps; --NumSteps)
00509       Result *= Val-(NumSteps-1);
00510     Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
00511     return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
00512   }
00513 
00514   const Type *Ty = V->getType();
00515   if (NumSteps == 0)
00516     return SCEVUnknown::getIntegerSCEV(1, Ty);
00517 
00518   SCEVHandle Result = V;
00519   for (unsigned i = 1; i != NumSteps; ++i)
00520     Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
00521                                           SCEVUnknown::getIntegerSCEV(i, Ty)));
00522   return Result;
00523 }
00524 
00525 
00526 /// evaluateAtIteration - Return the value of this chain of recurrences at
00527 /// the specified iteration number.  We can evaluate this recurrence by
00528 /// multiplying each element in the chain by the binomial coefficient
00529 /// corresponding to it.  In other words, we can evaluate {A,+,B,+,C,+,D} as:
00530 ///
00531 ///   A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
00532 ///
00533 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
00534 /// Is the binomial equation safe using modular arithmetic??
00535 ///
00536 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
00537   SCEVHandle Result = getStart();
00538   int Divisor = 1;
00539   const Type *Ty = It->getType();
00540   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
00541     SCEVHandle BC = PartialFact(It, i);
00542     Divisor *= i;
00543     SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
00544                                        SCEVUnknown::getIntegerSCEV(Divisor,Ty));
00545     Result = SCEVAddExpr::get(Result, Val);
00546   }
00547   return Result;
00548 }
00549 
00550 
00551 //===----------------------------------------------------------------------===//
00552 //                    SCEV Expression folder implementations
00553 //===----------------------------------------------------------------------===//
00554 
00555 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
00556   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
00557     return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
00558 
00559   // If the input value is a chrec scev made out of constants, truncate
00560   // all of the constants.
00561   if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
00562     std::vector<SCEVHandle> Operands;
00563     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
00564       // FIXME: This should allow truncation of other expression types!
00565       if (isa<SCEVConstant>(AddRec->getOperand(i)))
00566         Operands.push_back(get(AddRec->getOperand(i), Ty));
00567       else
00568         break;
00569     if (Operands.size() == AddRec->getNumOperands())
00570       return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
00571   }
00572 
00573   SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
00574   if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
00575   return Result;
00576 }
00577 
00578 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
00579   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
00580     return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
00581 
00582   // FIXME: If the input value is a chrec scev, and we can prove that the value
00583   // did not overflow the old, smaller, value, we can zero extend all of the
00584   // operands (often constants).  This would allow analysis of something like
00585   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
00586 
00587   SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
00588   if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
00589   return Result;
00590 }
00591 
00592 // get - Get a canonical add expression, or something simpler if possible.
00593 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
00594   assert(!Ops.empty() && "Cannot get empty add!");
00595   if (Ops.size() == 1) return Ops[0];
00596 
00597   // Sort by complexity, this groups all similar expression types together.
00598   GroupByComplexity(Ops);
00599 
00600   // If there are any constants, fold them together.
00601   unsigned Idx = 0;
00602   if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
00603     ++Idx;
00604     assert(Idx < Ops.size());
00605     while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
00606       // We found two constants, fold them together!
00607       Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
00608       if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
00609         Ops[0] = SCEVConstant::get(CI);
00610         Ops.erase(Ops.begin()+1);  // Erase the folded element
00611         if (Ops.size() == 1) return Ops[0];
00612         LHSC = cast<SCEVConstant>(Ops[0]);
00613       } else {
00614         // If we couldn't fold the expression, move to the next constant.  Note
00615         // that this is impossible to happen in practice because we always
00616         // constant fold constant ints to constant ints.
00617         ++Idx;
00618       }
00619     }
00620 
00621     // If we are left with a constant zero being added, strip it off.
00622     if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
00623       Ops.erase(Ops.begin());
00624       --Idx;
00625     }
00626   }
00627 
00628   if (Ops.size() == 1) return Ops[0];
00629 
00630   // Okay, check to see if the same value occurs in the operand list twice.  If
00631   // so, merge them together into an multiply expression.  Since we sorted the
00632   // list, these values are required to be adjacent.
00633   const Type *Ty = Ops[0]->getType();
00634   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
00635     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
00636       // Found a match, merge the two values into a multiply, and add any
00637       // remaining values to the result.
00638       SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
00639       SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
00640       if (Ops.size() == 2)
00641         return Mul;
00642       Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
00643       Ops.push_back(Mul);
00644       return SCEVAddExpr::get(Ops);
00645     }
00646 
00647   // Okay, now we know the first non-constant operand.  If there are add
00648   // operands they would be next.
00649   if (Idx < Ops.size()) {
00650     bool DeletedAdd = false;
00651     while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
00652       // If we have an add, expand the add operands onto the end of the operands
00653       // list.
00654       Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
00655       Ops.erase(Ops.begin()+Idx);
00656       DeletedAdd = true;
00657     }
00658 
00659     // If we deleted at least one add, we added operands to the end of the list,
00660     // and they are not necessarily sorted.  Recurse to resort and resimplify
00661     // any operands we just aquired.
00662     if (DeletedAdd)
00663       return get(Ops);
00664   }
00665 
00666   // Skip over the add expression until we get to a multiply.
00667   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
00668     ++Idx;
00669 
00670   // If we are adding something to a multiply expression, make sure the
00671   // something is not already an operand of the multiply.  If so, merge it into
00672   // the multiply.
00673   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
00674     SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
00675     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
00676       SCEV *MulOpSCEV = Mul->getOperand(MulOp);
00677       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
00678         if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
00679           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
00680           SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
00681           if (Mul->getNumOperands() != 2) {
00682             // If the multiply has more than two operands, we must get the
00683             // Y*Z term.
00684             std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
00685             MulOps.erase(MulOps.begin()+MulOp);
00686             InnerMul = SCEVMulExpr::get(MulOps);
00687           }
00688           SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
00689           SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
00690           SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
00691           if (Ops.size() == 2) return OuterMul;
00692           if (AddOp < Idx) {
00693             Ops.erase(Ops.begin()+AddOp);
00694             Ops.erase(Ops.begin()+Idx-1);
00695           } else {
00696             Ops.erase(Ops.begin()+Idx);
00697             Ops.erase(Ops.begin()+AddOp-1);
00698           }
00699           Ops.push_back(OuterMul);
00700           return SCEVAddExpr::get(Ops);
00701         }
00702 
00703       // Check this multiply against other multiplies being added together.
00704       for (unsigned OtherMulIdx = Idx+1;
00705            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
00706            ++OtherMulIdx) {
00707         SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
00708         // If MulOp occurs in OtherMul, we can fold the two multiplies
00709         // together.
00710         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
00711              OMulOp != e; ++OMulOp)
00712           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
00713             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
00714             SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
00715             if (Mul->getNumOperands() != 2) {
00716               std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
00717               MulOps.erase(MulOps.begin()+MulOp);
00718               InnerMul1 = SCEVMulExpr::get(MulOps);
00719             }
00720             SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
00721             if (OtherMul->getNumOperands() != 2) {
00722               std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
00723                                              OtherMul->op_end());
00724               MulOps.erase(MulOps.begin()+OMulOp);
00725               InnerMul2 = SCEVMulExpr::get(MulOps);
00726             }
00727             SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
00728             SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
00729             if (Ops.size() == 2) return OuterMul;
00730             Ops.erase(Ops.begin()+Idx);
00731             Ops.erase(Ops.begin()+OtherMulIdx-1);
00732             Ops.push_back(OuterMul);
00733             return SCEVAddExpr::get(Ops);
00734           }
00735       }
00736     }
00737   }
00738 
00739   // If there are any add recurrences in the operands list, see if any other
00740   // added values are loop invariant.  If so, we can fold them into the
00741   // recurrence.
00742   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
00743     ++Idx;
00744 
00745   // Scan over all recurrences, trying to fold loop invariants into them.
00746   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
00747     // Scan all of the other operands to this add and add them to the vector if
00748     // they are loop invariant w.r.t. the recurrence.
00749     std::vector<SCEVHandle> LIOps;
00750     SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
00751     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
00752       if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
00753         LIOps.push_back(Ops[i]);
00754         Ops.erase(Ops.begin()+i);
00755         --i; --e;
00756       }
00757 
00758     // If we found some loop invariants, fold them into the recurrence.
00759     if (!LIOps.empty()) {
00760       //  NLI + LI + { Start,+,Step}  -->  NLI + { LI+Start,+,Step }
00761       LIOps.push_back(AddRec->getStart());
00762 
00763       std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
00764       AddRecOps[0] = SCEVAddExpr::get(LIOps);
00765 
00766       SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
00767       // If all of the other operands were loop invariant, we are done.
00768       if (Ops.size() == 1) return NewRec;
00769 
00770       // Otherwise, add the folded AddRec by the non-liv parts.
00771       for (unsigned i = 0;; ++i)
00772         if (Ops[i] == AddRec) {
00773           Ops[i] = NewRec;
00774           break;
00775         }
00776       return SCEVAddExpr::get(Ops);
00777     }
00778 
00779     // Okay, if there weren't any loop invariants to be folded, check to see if
00780     // there are multiple AddRec's with the same loop induction variable being
00781     // added together.  If so, we can fold them.
00782     for (unsigned OtherIdx = Idx+1;
00783          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
00784       if (OtherIdx != Idx) {
00785         SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
00786         if (AddRec->getLoop() == OtherAddRec->getLoop()) {
00787           // Other + {A,+,B} + {C,+,D}  -->  Other + {A+C,+,B+D}
00788           std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
00789           for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
00790             if (i >= NewOps.size()) {
00791               NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
00792                             OtherAddRec->op_end());
00793               break;
00794             }
00795             NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
00796           }
00797           SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
00798 
00799           if (Ops.size() == 2) return NewAddRec;
00800 
00801           Ops.erase(Ops.begin()+Idx);
00802           Ops.erase(Ops.begin()+OtherIdx-1);
00803           Ops.push_back(NewAddRec);
00804           return SCEVAddExpr::get(Ops);
00805         }
00806       }
00807 
00808     // Otherwise couldn't fold anything into this recurrence.  Move onto the
00809     // next one.
00810   }
00811 
00812   // Okay, it looks like we really DO need an add expr.  Check to see if we
00813   // already have one, otherwise create a new one.
00814   std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
00815   SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
00816                                                               SCEVOps)];
00817   if (Result == 0) Result = new SCEVAddExpr(Ops);
00818   return Result;
00819 }
00820 
00821 
00822 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
00823   assert(!Ops.empty() && "Cannot get empty mul!");
00824 
00825   // Sort by complexity, this groups all similar expression types together.
00826   GroupByComplexity(Ops);
00827 
00828   // If there are any constants, fold them together.
00829   unsigned Idx = 0;
00830   if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
00831 
00832     // C1*(C2+V) -> C1*C2 + C1*V
00833     if (Ops.size() == 2)
00834       if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
00835         if (Add->getNumOperands() == 2 &&
00836             isa<SCEVConstant>(Add->getOperand(0)))
00837           return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
00838                                   SCEVMulExpr::get(LHSC, Add->getOperand(1)));
00839 
00840 
00841     ++Idx;
00842     while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
00843       // We found two constants, fold them together!
00844       Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
00845       if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
00846         Ops[0] = SCEVConstant::get(CI);
00847         Ops.erase(Ops.begin()+1);  // Erase the folded element
00848         if (Ops.size() == 1) return Ops[0];
00849         LHSC = cast<SCEVConstant>(Ops[0]);
00850       } else {
00851         // If we couldn't fold the expression, move to the next constant.  Note
00852         // that this is impossible to happen in practice because we always
00853         // constant fold constant ints to constant ints.
00854         ++Idx;
00855       }
00856     }
00857 
00858     // If we are left with a constant one being multiplied, strip it off.
00859     if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
00860       Ops.erase(Ops.begin());
00861       --Idx;
00862     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
00863       // If we have a multiply of zero, it will always be zero.
00864       return Ops[0];
00865     }
00866   }
00867 
00868   // Skip over the add expression until we get to a multiply.
00869   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
00870     ++Idx;
00871 
00872   if (Ops.size() == 1)
00873     return Ops[0];
00874 
00875   // If there are mul operands inline them all into this expression.
00876   if (Idx < Ops.size()) {
00877     bool DeletedMul = false;
00878     while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
00879       // If we have an mul, expand the mul operands onto the end of the operands
00880       // list.
00881       Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
00882       Ops.erase(Ops.begin()+Idx);
00883       DeletedMul = true;
00884     }
00885 
00886     // If we deleted at least one mul, we added operands to the end of the list,
00887     // and they are not necessarily sorted.  Recurse to resort and resimplify
00888     // any operands we just aquired.
00889     if (DeletedMul)
00890       return get(Ops);
00891   }
00892 
00893   // If there are any add recurrences in the operands list, see if any other
00894   // added values are loop invariant.  If so, we can fold them into the
00895   // recurrence.
00896   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
00897     ++Idx;
00898 
00899   // Scan over all recurrences, trying to fold loop invariants into them.
00900   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
00901     // Scan all of the other operands to this mul and add them to the vector if
00902     // they are loop invariant w.r.t. the recurrence.
00903     std::vector<SCEVHandle> LIOps;
00904     SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
00905     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
00906       if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
00907         LIOps.push_back(Ops[i]);
00908         Ops.erase(Ops.begin()+i);
00909         --i; --e;
00910       }
00911 
00912     // If we found some loop invariants, fold them into the recurrence.
00913     if (!LIOps.empty()) {
00914       //  NLI * LI * { Start,+,Step}  -->  NLI * { LI*Start,+,LI*Step }
00915       std::vector<SCEVHandle> NewOps;
00916       NewOps.reserve(AddRec->getNumOperands());
00917       if (LIOps.size() == 1) {
00918         SCEV *Scale = LIOps[0];
00919         for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
00920           NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
00921       } else {
00922         for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
00923           std::vector<SCEVHandle> MulOps(LIOps);
00924           MulOps.push_back(AddRec->getOperand(i));
00925           NewOps.push_back(SCEVMulExpr::get(MulOps));
00926         }
00927       }
00928 
00929       SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
00930 
00931       // If all of the other operands were loop invariant, we are done.
00932       if (Ops.size() == 1) return NewRec;
00933 
00934       // Otherwise, multiply the folded AddRec by the non-liv parts.
00935       for (unsigned i = 0;; ++i)
00936         if (Ops[i] == AddRec) {
00937           Ops[i] = NewRec;
00938           break;
00939         }
00940       return SCEVMulExpr::get(Ops);
00941     }
00942 
00943     // Okay, if there weren't any loop invariants to be folded, check to see if
00944     // there are multiple AddRec's with the same loop induction variable being
00945     // multiplied together.  If so, we can fold them.
00946     for (unsigned OtherIdx = Idx+1;
00947          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
00948       if (OtherIdx != Idx) {
00949         SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
00950         if (AddRec->getLoop() == OtherAddRec->getLoop()) {
00951           // F * G  -->  {A,+,B} * {C,+,D}  -->  {A*C,+,F*D + G*B + B*D}
00952           SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
00953           SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
00954                                                  G->getStart());
00955           SCEVHandle B = F->getStepRecurrence();
00956           SCEVHandle D = G->getStepRecurrence();
00957           SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
00958                                                 SCEVMulExpr::get(G, B),
00959                                                 SCEVMulExpr::get(B, D));
00960           SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
00961                                                      F->getLoop());
00962           if (Ops.size() == 2) return NewAddRec;
00963 
00964           Ops.erase(Ops.begin()+Idx);
00965           Ops.erase(Ops.begin()+OtherIdx-1);
00966           Ops.push_back(NewAddRec);
00967           return SCEVMulExpr::get(Ops);
00968         }
00969       }
00970 
00971     // Otherwise couldn't fold anything into this recurrence.  Move onto the
00972     // next one.
00973   }
00974 
00975   // Okay, it looks like we really DO need an mul expr.  Check to see if we
00976   // already have one, otherwise create a new one.
00977   std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
00978   SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
00979                                                               SCEVOps)];
00980   if (Result == 0)
00981     Result = new SCEVMulExpr(Ops);
00982   return Result;
00983 }
00984 
00985 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
00986   if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
00987     if (RHSC->getValue()->equalsInt(1))
00988       return LHS;                            // X /s 1 --> x
00989     if (RHSC->getValue()->isAllOnesValue())
00990       return SCEV::getNegativeSCEV(LHS);           // X /s -1  -->  -x
00991 
00992     if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
00993       Constant *LHSCV = LHSC->getValue();
00994       Constant *RHSCV = RHSC->getValue();
00995       if (LHSCV->getType()->isUnsigned())
00996         LHSCV = ConstantExpr::getCast(LHSCV,
00997                                       LHSCV->getType()->getSignedVersion());
00998       if (RHSCV->getType()->isUnsigned())
00999         RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
01000       return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
01001     }
01002   }
01003 
01004   // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
01005 
01006   SCEVSDivExpr *&Result = SCEVSDivs[std::make_pair(LHS, RHS)];
01007   if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
01008   return Result;
01009 }
01010 
01011 
01012 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
01013 /// specified loop.  Simplify the expression as much as possible.
01014 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
01015                                const SCEVHandle &Step, const Loop *L) {
01016   std::vector<SCEVHandle> Operands;
01017   Operands.push_back(Start);
01018   if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
01019     if (StepChrec->getLoop() == L) {
01020       Operands.insert(Operands.end(), StepChrec->op_begin(),
01021                       StepChrec->op_end());
01022       return get(Operands, L);
01023     }
01024 
01025   Operands.push_back(Step);
01026   return get(Operands, L);
01027 }
01028 
01029 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
01030 /// specified loop.  Simplify the expression as much as possible.
01031 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
01032                                const Loop *L) {
01033   if (Operands.size() == 1) return Operands[0];
01034 
01035   if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
01036     if (StepC->getValue()->isNullValue()) {
01037       Operands.pop_back();
01038       return get(Operands, L);             // { X,+,0 }  -->  X
01039     }
01040 
01041   SCEVAddRecExpr *&Result =
01042     SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
01043                                                          Operands.end()))];
01044   if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
01045   return Result;
01046 }
01047 
01048 SCEVHandle SCEVUnknown::get(Value *V) {
01049   if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
01050     return SCEVConstant::get(CI);
01051   SCEVUnknown *&Result = SCEVUnknowns[V];
01052   if (Result == 0) Result = new SCEVUnknown(V);
01053   return Result;
01054 }
01055 
01056 
01057 //===----------------------------------------------------------------------===//
01058 //             ScalarEvolutionsImpl Definition and Implementation
01059 //===----------------------------------------------------------------------===//
01060 //
01061 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
01062 /// evolution code.
01063 ///
01064 namespace {
01065   struct ScalarEvolutionsImpl {
01066     /// F - The function we are analyzing.
01067     ///
01068     Function &F;
01069 
01070     /// LI - The loop information for the function we are currently analyzing.
01071     ///
01072     LoopInfo &LI;
01073 
01074     /// UnknownValue - This SCEV is used to represent unknown trip counts and
01075     /// things.
01076     SCEVHandle UnknownValue;
01077 
01078     /// Scalars - This is a cache of the scalars we have analyzed so far.
01079     ///
01080     std::map<Value*, SCEVHandle> Scalars;
01081 
01082     /// IterationCounts - Cache the iteration count of the loops for this
01083     /// function as they are computed.
01084     std::map<const Loop*, SCEVHandle> IterationCounts;
01085 
01086     /// ConstantEvolutionLoopExitValue - This map contains entries for all of
01087     /// the PHI instructions that we attempt to compute constant evolutions for.
01088     /// This allows us to avoid potentially expensive recomputation of these
01089     /// properties.  An instruction maps to null if we are unable to compute its
01090     /// exit value.
01091     std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
01092 
01093   public:
01094     ScalarEvolutionsImpl(Function &f, LoopInfo &li)
01095       : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
01096 
01097     /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
01098     /// expression and create a new one.
01099     SCEVHandle getSCEV(Value *V);
01100 
01101     /// hasSCEV - Return true if the SCEV for this value has already been
01102     /// computed.
01103     bool hasSCEV(Value *V) const {
01104       return Scalars.count(V);
01105     }
01106 
01107     /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
01108     /// the specified value.
01109     void setSCEV(Value *V, const SCEVHandle &H) {
01110       bool isNew = Scalars.insert(std::make_pair(V, H)).second;
01111       assert(isNew && "This entry already existed!");
01112     }
01113 
01114 
01115     /// getSCEVAtScope - Compute the value of the specified expression within
01116     /// the indicated loop (which may be null to indicate in no loop).  If the
01117     /// expression cannot be evaluated, return UnknownValue itself.
01118     SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
01119 
01120 
01121     /// hasLoopInvariantIterationCount - Return true if the specified loop has
01122     /// an analyzable loop-invariant iteration count.
01123     bool hasLoopInvariantIterationCount(const Loop *L);
01124 
01125     /// getIterationCount - If the specified loop has a predictable iteration
01126     /// count, return it.  Note that it is not valid to call this method on a
01127     /// loop without a loop-invariant iteration count.
01128     SCEVHandle getIterationCount(const Loop *L);
01129 
01130     /// deleteInstructionFromRecords - This method should be called by the
01131     /// client before it removes an instruction from the program, to make sure
01132     /// that no dangling references are left around.
01133     void deleteInstructionFromRecords(Instruction *I);
01134 
01135   private:
01136     /// createSCEV - We know that there is no SCEV for the specified value.
01137     /// Analyze the expression.
01138     SCEVHandle createSCEV(Value *V);
01139     SCEVHandle createNodeForCast(CastInst *CI);
01140 
01141     /// createNodeForPHI - Provide the special handling we need to analyze PHI
01142     /// SCEVs.
01143     SCEVHandle createNodeForPHI(PHINode *PN);
01144 
01145     /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
01146     /// for the specified instruction and replaces any references to the
01147     /// symbolic value SymName with the specified value.  This is used during
01148     /// PHI resolution.
01149     void ReplaceSymbolicValueWithConcrete(Instruction *I,
01150                                           const SCEVHandle &SymName,
01151                                           const SCEVHandle &NewVal);
01152 
01153     /// ComputeIterationCount - Compute the number of times the specified loop
01154     /// will iterate.
01155     SCEVHandle ComputeIterationCount(const Loop *L);
01156 
01157     /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
01158     /// 'setcc load X, cst', try to se if we can compute the trip count.
01159     SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
01160                                                         Constant *RHS,
01161                                                         const Loop *L,
01162                                                         unsigned SetCCOpcode);
01163 
01164     /// ComputeIterationCountExhaustively - If the trip is known to execute a
01165     /// constant number of times (the condition evolves only from constants),
01166     /// try to evaluate a few iterations of the loop until we get the exit
01167     /// condition gets a value of ExitWhen (true or false).  If we cannot
01168     /// evaluate the trip count of the loop, return UnknownValue.
01169     SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
01170                                                  bool ExitWhen);
01171 
01172     /// HowFarToZero - Return the number of times a backedge comparing the
01173     /// specified value to zero will execute.  If not computable, return
01174     /// UnknownValue.
01175     SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
01176 
01177     /// HowFarToNonZero - Return the number of times a backedge checking the
01178     /// specified value for nonzero will execute.  If not computable, return
01179     /// UnknownValue.
01180     SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
01181 
01182     /// HowManyLessThans - Return the number of times a backedge containing the
01183     /// specified less-than comparison will execute.  If not computable, return
01184     /// UnknownValue.
01185     SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
01186 
01187     /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
01188     /// in the header of its containing loop, we know the loop executes a
01189     /// constant number of times, and the PHI node is just a recurrence
01190     /// involving constants, fold it.
01191     Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
01192                                                 const Loop *L);
01193   };
01194 }
01195 
01196 //===----------------------------------------------------------------------===//
01197 //            Basic SCEV Analysis and PHI Idiom Recognition Code
01198 //
01199 
01200 /// deleteInstructionFromRecords - This method should be called by the
01201 /// client before it removes an instruction from the program, to make sure
01202 /// that no dangling references are left around.
01203 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
01204   Scalars.erase(I);
01205   if (PHINode *PN = dyn_cast<PHINode>(I))
01206     ConstantEvolutionLoopExitValue.erase(PN);
01207 }
01208 
01209 
01210 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
01211 /// expression and create a new one.
01212 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
01213   assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
01214 
01215   std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
01216   if (I != Scalars.end()) return I->second;
01217   SCEVHandle S = createSCEV(V);
01218   Scalars.insert(std::make_pair(V, S));
01219   return S;
01220 }
01221 
01222 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
01223 /// the specified instruction and replaces any references to the symbolic value
01224 /// SymName with the specified value.  This is used during PHI resolution.
01225 void ScalarEvolutionsImpl::
01226 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
01227                                  const SCEVHandle &NewVal) {
01228   std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
01229   if (SI == Scalars.end()) return;
01230 
01231   SCEVHandle NV =
01232     SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
01233   if (NV == SI->second) return;  // No change.
01234 
01235   SI->second = NV;       // Update the scalars map!
01236 
01237   // Any instruction values that use this instruction might also need to be
01238   // updated!
01239   for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
01240        UI != E; ++UI)
01241     ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
01242 }
01243 
01244 /// createNodeForPHI - PHI nodes have two cases.  Either the PHI node exists in
01245 /// a loop header, making it a potential recurrence, or it doesn't.
01246 ///
01247 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
01248   if (PN->getNumIncomingValues() == 2)  // The loops have been canonicalized.
01249     if (const Loop *L = LI.getLoopFor(PN->getParent()))
01250       if (L->getHeader() == PN->getParent()) {
01251         // If it lives in the loop header, it has two incoming values, one
01252         // from outside the loop, and one from inside.
01253         unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
01254         unsigned BackEdge     = IncomingEdge^1;
01255 
01256         // While we are analyzing this PHI node, handle its value symbolically.
01257         SCEVHandle SymbolicName = SCEVUnknown::get(PN);
01258         assert(Scalars.find(PN) == Scalars.end() &&
01259                "PHI node already processed?");
01260         Scalars.insert(std::make_pair(PN, SymbolicName));
01261 
01262         // Using this symbolic name for the PHI, analyze the value coming around
01263         // the back-edge.
01264         SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
01265 
01266         // NOTE: If BEValue is loop invariant, we know that the PHI node just
01267         // has a special value for the first iteration of the loop.
01268 
01269         // If the value coming around the backedge is an add with the symbolic
01270         // value we just inserted, then we found a simple induction variable!
01271         if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
01272           // If there is a single occurrence of the symbolic value, replace it
01273           // with a recurrence.
01274           unsigned FoundIndex = Add->getNumOperands();
01275           for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
01276             if (Add->getOperand(i) == SymbolicName)
01277               if (FoundIndex == e) {
01278                 FoundIndex = i;
01279                 break;
01280               }
01281 
01282           if (FoundIndex != Add->getNumOperands()) {
01283             // Create an add with everything but the specified operand.
01284             std::vector<SCEVHandle> Ops;
01285             for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
01286               if (i != FoundIndex)
01287                 Ops.push_back(Add->getOperand(i));
01288             SCEVHandle Accum = SCEVAddExpr::get(Ops);
01289 
01290             // This is not a valid addrec if the step amount is varying each
01291             // loop iteration, but is not itself an addrec in this loop.
01292             if (Accum->isLoopInvariant(L) ||
01293                 (isa<SCEVAddRecExpr>(Accum) &&
01294                  cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
01295               SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
01296               SCEVHandle PHISCEV  = SCEVAddRecExpr::get(StartVal, Accum, L);
01297 
01298               // Okay, for the entire analysis of this edge we assumed the PHI
01299               // to be symbolic.  We now need to go back and update all of the
01300               // entries for the scalars that use the PHI (except for the PHI
01301               // itself) to use the new analyzed value instead of the "symbolic"
01302               // value.
01303               ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
01304               return PHISCEV;
01305             }
01306           }
01307         }
01308 
01309         return SymbolicName;
01310       }
01311 
01312   // If it's not a loop phi, we can't handle it yet.
01313   return SCEVUnknown::get(PN);
01314 }
01315 
01316 /// createNodeForCast - Handle the various forms of casts that we support.
01317 ///
01318 SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
01319   const Type *SrcTy = CI->getOperand(0)->getType();
01320   const Type *DestTy = CI->getType();
01321 
01322   // If this is a noop cast (ie, conversion from int to uint), ignore it.
01323   if (SrcTy->isLosslesslyConvertibleTo(DestTy))
01324     return getSCEV(CI->getOperand(0));
01325 
01326   if (SrcTy->isInteger() && DestTy->isInteger()) {
01327     // Otherwise, if this is a truncating integer cast, we can represent this
01328     // cast.
01329     if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
01330       return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
01331                                    CI->getType()->getUnsignedVersion());
01332     if (SrcTy->isUnsigned() &&
01333         SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
01334       return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
01335                                      CI->getType()->getUnsignedVersion());
01336   }
01337 
01338   // If this is an sign or zero extending cast and we can prove that the value
01339   // will never overflow, we could do similar transformations.
01340 
01341   // Otherwise, we can't handle this cast!
01342   return SCEVUnknown::get(CI);
01343 }
01344 
01345 
01346 /// createSCEV - We know that there is no SCEV for the specified value.
01347 /// Analyze the expression.
01348 ///
01349 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
01350   if (Instruction *I = dyn_cast<Instruction>(V)) {
01351     switch (I->getOpcode()) {
01352     case Instruction::Add:
01353       return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
01354                               getSCEV(I->getOperand(1)));
01355     case Instruction::Mul:
01356       return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
01357                               getSCEV(I->getOperand(1)));
01358     case Instruction::Div:
01359       if (V->getType()->isInteger() && V->getType()->isSigned())
01360         return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
01361                                  getSCEV(I->getOperand(1)));
01362       break;
01363 
01364     case Instruction::Sub:
01365       return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
01366                                 getSCEV(I->getOperand(1)));
01367 
01368     case Instruction::Shl:
01369       // Turn shift left of a constant amount into a multiply.
01370       if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
01371         Constant *X = ConstantInt::get(V->getType(), 1);
01372         X = ConstantExpr::getShl(X, SA);
01373         return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
01374       }
01375       break;
01376 
01377     case Instruction::Cast:
01378       return createNodeForCast(cast<CastInst>(I));
01379 
01380     case Instruction::PHI:
01381       return createNodeForPHI(cast<PHINode>(I));
01382 
01383     default: // We cannot analyze this expression.
01384       break;
01385     }
01386   }
01387 
01388   return SCEVUnknown::get(V);
01389 }
01390 
01391 
01392 
01393 //===----------------------------------------------------------------------===//
01394 //                   Iteration Count Computation Code
01395 //
01396 
01397 /// getIterationCount - If the specified loop has a predictable iteration
01398 /// count, return it.  Note that it is not valid to call this method on a
01399 /// loop without a loop-invariant iteration count.
01400 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
01401   std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
01402   if (I == IterationCounts.end()) {
01403     SCEVHandle ItCount = ComputeIterationCount(L);
01404     I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
01405     if (ItCount != UnknownValue) {
01406       assert(ItCount->isLoopInvariant(L) &&
01407              "Computed trip count isn't loop invariant for loop!");
01408       ++NumTripCountsComputed;
01409     } else if (isa<PHINode>(L->getHeader()->begin())) {
01410       // Only count loops that have phi nodes as not being computable.
01411       ++NumTripCountsNotComputed;
01412     }
01413   }
01414   return I->second;
01415 }
01416 
01417 /// ComputeIterationCount - Compute the number of times the specified loop
01418 /// will iterate.
01419 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
01420   // If the loop has a non-one exit block count, we can't analyze it.
01421   std::vector<BasicBlock*> ExitBlocks;
01422   L->getExitBlocks(ExitBlocks);
01423   if (ExitBlocks.size() != 1) return UnknownValue;
01424 
01425   // Okay, there is one exit block.  Try to find the condition that causes the
01426   // loop to be exited.
01427   BasicBlock *ExitBlock = ExitBlocks[0];
01428 
01429   BasicBlock *ExitingBlock = 0;
01430   for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
01431        PI != E; ++PI)
01432     if (L->contains(*PI)) {
01433       if (ExitingBlock == 0)
01434         ExitingBlock = *PI;
01435       else
01436         return UnknownValue;   // More than one block exiting!
01437     }
01438   assert(ExitingBlock && "No exits from loop, something is broken!");
01439 
01440   // Okay, we've computed the exiting block.  See what condition causes us to
01441   // exit.
01442   //
01443   // FIXME: we should be able to handle switch instructions (with a single exit)
01444   // FIXME: We should handle cast of int to bool as well
01445   BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
01446   if (ExitBr == 0) return UnknownValue;
01447   assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
01448   SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
01449   if (ExitCond == 0)  // Not a setcc
01450     return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
01451                                           ExitBr->getSuccessor(0) == ExitBlock);
01452 
01453   // If the condition was exit on true, convert the condition to exit on false.
01454   Instruction::BinaryOps Cond;
01455   if (ExitBr->getSuccessor(1) == ExitBlock)
01456     Cond = ExitCond->getOpcode();
01457   else
01458     Cond = ExitCond->getInverseCondition();
01459 
01460   // Handle common loops like: for (X = "string"; *X; ++X)
01461   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
01462     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
01463       SCEVHandle ItCnt =
01464         ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
01465       if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
01466     }
01467 
01468   SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
01469   SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
01470 
01471   // Try to evaluate any dependencies out of the loop.
01472   SCEVHandle Tmp = getSCEVAtScope(LHS, L);
01473   if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
01474   Tmp = getSCEVAtScope(RHS, L);
01475   if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
01476 
01477   // At this point, we would like to compute how many iterations of the loop the
01478   // predicate will return true for these inputs.
01479   if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
01480     // If there is a constant, force it into the RHS.
01481     std::swap(LHS, RHS);
01482     Cond = SetCondInst::getSwappedCondition(Cond);
01483   }
01484 
01485   // FIXME: think about handling pointer comparisons!  i.e.:
01486   // while (P != P+100) ++P;
01487 
01488   // If we have a comparison of a chrec against a constant, try to use value
01489   // ranges to answer this query.
01490   if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
01491     if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
01492       if (AddRec->getLoop() == L) {
01493         // Form the comparison range using the constant of the correct type so
01494         // that the ConstantRange class knows to do a signed or unsigned
01495         // comparison.
01496         ConstantInt *CompVal = RHSC->getValue();
01497         const Type *RealTy = ExitCond->getOperand(0)->getType();
01498         CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
01499         if (CompVal) {
01500           // Form the constant range.
01501           ConstantRange CompRange(Cond, CompVal);
01502 
01503           // Now that we have it, if it's signed, convert it to an unsigned
01504           // range.
01505           if (CompRange.getLower()->getType()->isSigned()) {
01506             const Type *NewTy = RHSC->getValue()->getType();
01507             Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
01508             Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
01509             CompRange = ConstantRange(NewL, NewU);
01510           }
01511 
01512           SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
01513           if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
01514         }
01515       }
01516 
01517   switch (Cond) {
01518   case Instruction::SetNE:                     // while (X != Y)
01519     // Convert to: while (X-Y != 0)
01520     if (LHS->getType()->isInteger()) {
01521       SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
01522       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01523     }
01524     break;
01525   case Instruction::SetEQ:
01526     // Convert to: while (X-Y == 0)           // while (X == Y)
01527     if (LHS->getType()->isInteger()) {
01528       SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
01529       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01530     }
01531     break;
01532   case Instruction::SetLT:
01533     if (LHS->getType()->isInteger() && 
01534         ExitCond->getOperand(0)->getType()->isSigned()) {
01535       SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
01536       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01537     }
01538     break;
01539   case Instruction::SetGT:
01540     if (LHS->getType()->isInteger() &&
01541         ExitCond->getOperand(0)->getType()->isSigned()) {
01542       SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
01543       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01544     }
01545     break;
01546   default:
01547 #if 0
01548     std::cerr << "ComputeIterationCount ";
01549     if (ExitCond->getOperand(0)->getType()->isUnsigned())
01550       std::cerr << "[unsigned] ";
01551     std::cerr << *LHS << "   "
01552               << Instruction::getOpcodeName(Cond) << "   " << *RHS << "\n";
01553 #endif
01554     break;
01555   }
01556 
01557   return ComputeIterationCountExhaustively(L, ExitCond,
01558                                          ExitBr->getSuccessor(0) == ExitBlock);
01559 }
01560 
01561 static ConstantInt *
01562 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
01563   SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
01564   SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
01565   assert(isa<SCEVConstant>(Val) &&
01566          "Evaluation of SCEV at constant didn't fold correctly?");
01567   return cast<SCEVConstant>(Val)->getValue();
01568 }
01569 
01570 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
01571 /// and a GEP expression (missing the pointer index) indexing into it, return
01572 /// the addressed element of the initializer or null if the index expression is
01573 /// invalid.
01574 static Constant *
01575 GetAddressedElementFromGlobal(GlobalVariable *GV,
01576                               const std::vector<ConstantInt*> &Indices) {
01577   Constant *Init = GV->getInitializer();
01578   for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
01579     uint64_t Idx = Indices[i]->getRawValue();
01580     if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
01581       assert(Idx < CS->getNumOperands() && "Bad struct index!");
01582       Init = cast<Constant>(CS->getOperand(Idx));
01583     } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
01584       if (Idx >= CA->getNumOperands()) return 0;  // Bogus program
01585       Init = cast<Constant>(CA->getOperand(Idx));
01586     } else if (isa<ConstantAggregateZero>(Init)) {
01587       if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
01588         assert(Idx < STy->getNumElements() && "Bad struct index!");
01589         Init = Constant::getNullValue(STy->getElementType(Idx));
01590       } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
01591         if (Idx >= ATy->getNumElements()) return 0;  // Bogus program
01592         Init = Constant::getNullValue(ATy->getElementType());
01593       } else {
01594         assert(0 && "Unknown constant aggregate type!");
01595       }
01596       return 0;
01597     } else {
01598       return 0; // Unknown initializer type
01599     }
01600   }
01601   return Init;
01602 }
01603 
01604 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
01605 /// 'setcc load X, cst', try to se if we can compute the trip count.
01606 SCEVHandle ScalarEvolutionsImpl::
01607 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
01608                                          const Loop *L, unsigned SetCCOpcode) {
01609   if (LI->isVolatile()) return UnknownValue;
01610 
01611   // Check to see if the loaded pointer is a getelementptr of a global.
01612   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
01613   if (!GEP) return UnknownValue;
01614 
01615   // Make sure that it is really a constant global we are gepping, with an
01616   // initializer, and make sure the first IDX is really 0.
01617   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
01618   if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
01619       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
01620       !cast<Constant>(GEP->getOperand(1))->isNullValue())
01621     return UnknownValue;
01622 
01623   // Okay, we allow one non-constant index into the GEP instruction.
01624   Value *VarIdx = 0;
01625   std::vector<ConstantInt*> Indexes;
01626   unsigned VarIdxNum = 0;
01627   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
01628     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
01629       Indexes.push_back(CI);
01630     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
01631       if (VarIdx) return UnknownValue;  // Multiple non-constant idx's.
01632       VarIdx = GEP->getOperand(i);
01633       VarIdxNum = i-2;
01634       Indexes.push_back(0);
01635     }
01636 
01637   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
01638   // Check to see if X is a loop variant variable value now.
01639   SCEVHandle Idx = getSCEV(VarIdx);
01640   SCEVHandle Tmp = getSCEVAtScope(Idx, L);
01641   if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
01642 
01643   // We can only recognize very limited forms of loop index expressions, in
01644   // particular, only affine AddRec's like {C1,+,C2}.
01645   SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
01646   if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
01647       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
01648       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
01649     return UnknownValue;
01650 
01651   unsigned MaxSteps = MaxBruteForceIterations;
01652   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
01653     ConstantUInt *ItCst =
01654       ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum);
01655     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
01656 
01657     // Form the GEP offset.
01658     Indexes[VarIdxNum] = Val;
01659 
01660     Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
01661     if (Result == 0) break;  // Cannot compute!
01662 
01663     // Evaluate the condition for this iteration.
01664     Result = ConstantExpr::get(SetCCOpcode, Result, RHS);
01665     if (!isa<ConstantBool>(Result)) break;  // Couldn't decide for sure
01666     if (Result == ConstantBool::False) {
01667 #if 0
01668       std::cerr << "\n***\n*** Computed loop count " << *ItCst
01669                 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
01670                 << "***\n";
01671 #endif
01672       ++NumArrayLenItCounts;
01673       return SCEVConstant::get(ItCst);   // Found terminating iteration!
01674     }
01675   }
01676   return UnknownValue;
01677 }
01678 
01679 
01680 /// CanConstantFold - Return true if we can constant fold an instruction of the
01681 /// specified type, assuming that all operands were constants.
01682 static bool CanConstantFold(const Instruction *I) {
01683   if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) ||
01684       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
01685     return true;
01686 
01687   if (const CallInst *CI = dyn_cast<CallInst>(I))
01688     if (const Function *F = CI->getCalledFunction())
01689       return canConstantFoldCallTo((Function*)F);  // FIXME: elim cast
01690   return false;
01691 }
01692 
01693 /// ConstantFold - Constant fold an instruction of the specified type with the
01694 /// specified constant operands.  This function may modify the operands vector.
01695 static Constant *ConstantFold(const Instruction *I,
01696                               std::vector<Constant*> &Operands) {
01697   if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
01698     return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
01699 
01700   switch (I->getOpcode()) {
01701   case Instruction::Cast:
01702     return ConstantExpr::getCast(Operands[0], I->getType());
01703   case Instruction::Select:
01704     return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
01705   case Instruction::Call:
01706     if (Function *GV = dyn_cast<Function>(Operands[0])) {
01707       Operands.erase(Operands.begin());
01708       return ConstantFoldCall(cast<Function>(GV), Operands);
01709     }
01710 
01711     return 0;
01712   case Instruction::GetElementPtr:
01713     Constant *Base = Operands[0];
01714     Operands.erase(Operands.begin());
01715     return ConstantExpr::getGetElementPtr(Base, Operands);
01716   }
01717   return 0;
01718 }
01719 
01720 
01721 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
01722 /// in the loop that V is derived from.  We allow arbitrary operations along the
01723 /// way, but the operands of an operation must either be constants or a value
01724 /// derived from a constant PHI.  If this expression does not fit with these
01725 /// constraints, return null.
01726 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
01727   // If this is not an instruction, or if this is an instruction outside of the
01728   // loop, it can't be derived from a loop PHI.
01729   Instruction *I = dyn_cast<Instruction>(V);
01730   if (I == 0 || !L->contains(I->getParent())) return 0;
01731 
01732   if (PHINode *PN = dyn_cast<PHINode>(I))
01733     if (L->getHeader() == I->getParent())
01734       return PN;
01735     else
01736       // We don't currently keep track of the control flow needed to evaluate
01737       // PHIs, so we cannot handle PHIs inside of loops.
01738       return 0;
01739 
01740   // If we won't be able to constant fold this expression even if the operands
01741   // are constants, return early.
01742   if (!CanConstantFold(I)) return 0;
01743 
01744   // Otherwise, we can evaluate this instruction if all of its operands are
01745   // constant or derived from a PHI node themselves.
01746   PHINode *PHI = 0;
01747   for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
01748     if (!(isa<Constant>(I->getOperand(Op)) ||
01749           isa<GlobalValue>(I->getOperand(Op)))) {
01750       PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
01751       if (P == 0) return 0;  // Not evolving from PHI
01752       if (PHI == 0)
01753         PHI = P;
01754       else if (PHI != P)
01755         return 0;  // Evolving from multiple different PHIs.
01756     }
01757 
01758   // This is a expression evolving from a constant PHI!
01759   return PHI;
01760 }
01761 
01762 /// EvaluateExpression - Given an expression that passes the
01763 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
01764 /// in the loop has the value PHIVal.  If we can't fold this expression for some
01765 /// reason, return null.
01766 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
01767   if (isa<PHINode>(V)) return PHIVal;
01768   if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
01769     return GV;
01770   if (Constant *C = dyn_cast<Constant>(V)) return C;
01771   Instruction *I = cast<Instruction>(V);
01772 
01773   std::vector<Constant*> Operands;
01774   Operands.resize(I->getNumOperands());
01775 
01776   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
01777     Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
01778     if (Operands[i] == 0) return 0;
01779   }
01780 
01781   return ConstantFold(I, Operands);
01782 }
01783 
01784 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
01785 /// in the header of its containing loop, we know the loop executes a
01786 /// constant number of times, and the PHI node is just a recurrence
01787 /// involving constants, fold it.
01788 Constant *ScalarEvolutionsImpl::
01789 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
01790   std::map<PHINode*, Constant*>::iterator I =
01791     ConstantEvolutionLoopExitValue.find(PN);
01792   if (I != ConstantEvolutionLoopExitValue.end())
01793     return I->second;
01794 
01795   if (Its > MaxBruteForceIterations)
01796     return ConstantEvolutionLoopExitValue[PN] = 0;  // Not going to evaluate it.
01797 
01798   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
01799 
01800   // Since the loop is canonicalized, the PHI node must have two entries.  One
01801   // entry must be a constant (coming in from outside of the loop), and the
01802   // second must be derived from the same PHI.
01803   bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
01804   Constant *StartCST =
01805     dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
01806   if (StartCST == 0)
01807     return RetVal = 0;  // Must be a constant.
01808 
01809   Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
01810   PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
01811   if (PN2 != PN)
01812     return RetVal = 0;  // Not derived from same PHI.
01813 
01814   // Execute the loop symbolically to determine the exit value.
01815   unsigned IterationNum = 0;
01816   unsigned NumIterations = Its;
01817   if (NumIterations != Its)
01818     return RetVal = 0;  // More than 2^32 iterations??
01819 
01820   for (Constant *PHIVal = StartCST; ; ++IterationNum) {
01821     if (IterationNum == NumIterations)
01822       return RetVal = PHIVal;  // Got exit value!
01823 
01824     // Compute the value of the PHI node for the next iteration.
01825     Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
01826     if (NextPHI == PHIVal)
01827       return RetVal = NextPHI;  // Stopped evolving!
01828     if (NextPHI == 0)
01829       return 0;        // Couldn't evaluate!
01830     PHIVal = NextPHI;
01831   }
01832 }
01833 
01834 /// ComputeIterationCountExhaustively - If the trip is known to execute a
01835 /// constant number of times (the condition evolves only from constants),
01836 /// try to evaluate a few iterations of the loop until we get the exit
01837 /// condition gets a value of ExitWhen (true or false).  If we cannot
01838 /// evaluate the trip count of the loop, return UnknownValue.
01839 SCEVHandle ScalarEvolutionsImpl::
01840 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
01841   PHINode *PN = getConstantEvolvingPHI(Cond, L);
01842   if (PN == 0) return UnknownValue;
01843 
01844   // Since the loop is canonicalized, the PHI node must have two entries.  One
01845   // entry must be a constant (coming in from outside of the loop), and the
01846   // second must be derived from the same PHI.
01847   bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
01848   Constant *StartCST =
01849     dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
01850   if (StartCST == 0) return UnknownValue;  // Must be a constant.
01851 
01852   Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
01853   PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
01854   if (PN2 != PN) return UnknownValue;  // Not derived from same PHI.
01855 
01856   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
01857   // the loop symbolically to determine when the condition gets a value of
01858   // "ExitWhen".
01859   unsigned IterationNum = 0;
01860   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
01861   for (Constant *PHIVal = StartCST;
01862        IterationNum != MaxIterations; ++IterationNum) {
01863     ConstantBool *CondVal =
01864       dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
01865     if (!CondVal) return UnknownValue;     // Couldn't symbolically evaluate.
01866 
01867     if (CondVal->getValue() == ExitWhen) {
01868       ConstantEvolutionLoopExitValue[PN] = PHIVal;
01869       ++NumBruteForceTripCountsComputed;
01870       return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum));
01871     }
01872 
01873     // Compute the value of the PHI node for the next iteration.
01874     Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
01875     if (NextPHI == 0 || NextPHI == PHIVal)
01876       return UnknownValue;  // Couldn't evaluate or not making progress...
01877     PHIVal = NextPHI;
01878   }
01879 
01880   // Too many iterations were needed to evaluate.
01881   return UnknownValue;
01882 }
01883 
01884 /// getSCEVAtScope - Compute the value of the specified expression within the
01885 /// indicated loop (which may be null to indicate in no loop).  If the
01886 /// expression cannot be evaluated, return UnknownValue.
01887 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
01888   // FIXME: this should be turned into a virtual method on SCEV!
01889 
01890   if (isa<SCEVConstant>(V)) return V;
01891 
01892   // If this instruction is evolves from a constant-evolving PHI, compute the
01893   // exit value from the loop without using SCEVs.
01894   if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
01895     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
01896       const Loop *LI = this->LI[I->getParent()];
01897       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
01898         if (PHINode *PN = dyn_cast<PHINode>(I))
01899           if (PN->getParent() == LI->getHeader()) {
01900             // Okay, there is no closed form solution for the PHI node.  Check
01901             // to see if the loop that contains it has a known iteration count.
01902             // If so, we may be able to force computation of the exit value.
01903             SCEVHandle IterationCount = getIterationCount(LI);
01904             if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
01905               // Okay, we know how many times the containing loop executes.  If
01906               // this is a constant evolving PHI node, get the final value at
01907               // the specified iteration number.
01908               Constant *RV = getConstantEvolutionLoopExitValue(PN,
01909                                                ICC->getValue()->getRawValue(),
01910                                                                LI);
01911               if (RV) return SCEVUnknown::get(RV);
01912             }
01913           }
01914 
01915       // Okay, this is a some expression that we cannot symbolically evaluate
01916       // into a SCEV.  Check to see if it's possible to symbolically evaluate
01917       // the arguments into constants, and if see, try to constant propagate the
01918       // result.  This is particularly useful for computing loop exit values.
01919       if (CanConstantFold(I)) {
01920         std::vector<Constant*> Operands;
01921         Operands.reserve(I->getNumOperands());
01922         for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
01923           Value *Op = I->getOperand(i);
01924           if (Constant *C = dyn_cast<Constant>(Op)) {
01925             Operands.push_back(C);
01926           } else {
01927             SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
01928             if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
01929               Operands.push_back(ConstantExpr::getCast(SC->getValue(),
01930                                                        Op->getType()));
01931             else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
01932               if (Constant *C = dyn_cast<Constant>(SU->getValue()))
01933                 Operands.push_back(ConstantExpr::getCast(C, Op->getType()));
01934               else
01935                 return V;
01936             } else {
01937               return V;
01938             }
01939           }
01940         }
01941         return SCEVUnknown::get(ConstantFold(I, Operands));
01942       }
01943     }
01944 
01945     // This is some other type of SCEVUnknown, just return it.
01946     return V;
01947   }
01948 
01949   if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
01950     // Avoid performing the look-up in the common case where the specified
01951     // expression has no loop-variant portions.
01952     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
01953       SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
01954       if (OpAtScope != Comm->getOperand(i)) {
01955         if (OpAtScope == UnknownValue) return UnknownValue;
01956         // Okay, at least one of these operands is loop variant but might be
01957         // foldable.  Build a new instance of the folded commutative expression.
01958         std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
01959         NewOps.push_back(OpAtScope);
01960 
01961         for (++i; i != e; ++i) {
01962           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
01963           if (OpAtScope == UnknownValue) return UnknownValue;
01964           NewOps.push_back(OpAtScope);
01965         }
01966         if (isa<SCEVAddExpr>(Comm))
01967           return SCEVAddExpr::get(NewOps);
01968         assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
01969         return SCEVMulExpr::get(NewOps);
01970       }
01971     }
01972     // If we got here, all operands are loop invariant.
01973     return Comm;
01974   }
01975 
01976   if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
01977     SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
01978     if (LHS == UnknownValue) return LHS;
01979     SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
01980     if (RHS == UnknownValue) return RHS;
01981     if (LHS == Div->getLHS() && RHS == Div->getRHS())
01982       return Div;   // must be loop invariant
01983     return SCEVSDivExpr::get(LHS, RHS);
01984   }
01985 
01986   // If this is a loop recurrence for a loop that does not contain L, then we
01987   // are dealing with the final value computed by the loop.
01988   if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
01989     if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
01990       // To evaluate this recurrence, we need to know how many times the AddRec
01991       // loop iterates.  Compute this now.
01992       SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
01993       if (IterationCount == UnknownValue) return UnknownValue;
01994       IterationCount = getTruncateOrZeroExtend(IterationCount,
01995                                                AddRec->getType());
01996 
01997       // If the value is affine, simplify the expression evaluation to just
01998       // Start + Step*IterationCount.
01999       if (AddRec->isAffine())
02000         return SCEVAddExpr::get(AddRec->getStart(),
02001                                 SCEVMulExpr::get(IterationCount,
02002                                                  AddRec->getOperand(1)));
02003 
02004       // Otherwise, evaluate it the hard way.
02005       return AddRec->evaluateAtIteration(IterationCount);
02006     }
02007     return UnknownValue;
02008   }
02009 
02010   //assert(0 && "Unknown SCEV type!");
02011   return UnknownValue;
02012 }
02013 
02014 
02015 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
02016 /// given quadratic chrec {L,+,M,+,N}.  This returns either the two roots (which
02017 /// might be the same) or two SCEVCouldNotCompute objects.
02018 ///
02019 static std::pair<SCEVHandle,SCEVHandle>
02020 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
02021   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
02022   SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
02023   SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
02024   SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
02025 
02026   // We currently can only solve this if the coefficients are constants.
02027   if (!L || !M || !N) {
02028     SCEV *CNC = new SCEVCouldNotCompute();
02029     return std::make_pair(CNC, CNC);
02030   }
02031 
02032   Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
02033 
02034   // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
02035   Constant *C = L->getValue();
02036   // The B coefficient is M-N/2
02037   Constant *B = ConstantExpr::getSub(M->getValue(),
02038                                      ConstantExpr::getDiv(N->getValue(),
02039                                                           Two));
02040   // The A coefficient is N/2
02041   Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
02042 
02043   // Compute the B^2-4ac term.
02044   Constant *SqrtTerm =
02045     ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
02046                          ConstantExpr::getMul(A, C));
02047   SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
02048 
02049   // Compute floor(sqrt(B^2-4ac))
02050   ConstantUInt *SqrtVal =
02051     cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
02052                                    SqrtTerm->getType()->getUnsignedVersion()));
02053   uint64_t SqrtValV = SqrtVal->getValue();
02054   uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
02055   // The square root might not be precise for arbitrary 64-bit integer
02056   // values.  Do some sanity checks to ensure it's correct.
02057   if (SqrtValV2*SqrtValV2 > SqrtValV ||
02058       (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
02059     SCEV *CNC = new SCEVCouldNotCompute();
02060     return std::make_pair(CNC, CNC);
02061   }
02062 
02063   SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
02064   SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
02065 
02066   Constant *NegB = ConstantExpr::getNeg(B);
02067   Constant *TwoA = ConstantExpr::getMul(A, Two);
02068 
02069   // The divisions must be performed as signed divisions.
02070   const Type *SignedTy = NegB->getType()->getSignedVersion();
02071   NegB = ConstantExpr::getCast(NegB, SignedTy);
02072   TwoA = ConstantExpr::getCast(TwoA, SignedTy);
02073   SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
02074 
02075   Constant *Solution1 =
02076     ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
02077   Constant *Solution2 =
02078     ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
02079   return std::make_pair(SCEVUnknown::get(Solution1),
02080                         SCEVUnknown::get(Solution2));
02081 }
02082 
02083 /// HowFarToZero - Return the number of times a backedge comparing the specified
02084 /// value to zero will execute.  If not computable, return UnknownValue
02085 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
02086   // If the value is a constant
02087   if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
02088     // If the value is already zero, the branch will execute zero times.
02089     if (C->getValue()->isNullValue()) return C;
02090     return UnknownValue;  // Otherwise it will loop infinitely.
02091   }
02092 
02093   SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
02094   if (!AddRec || AddRec->getLoop() != L)
02095     return UnknownValue;
02096 
02097   if (AddRec->isAffine()) {
02098     // If this is an affine expression the execution count of this branch is
02099     // equal to:
02100     //
02101     //     (0 - Start/Step)    iff   Start % Step == 0
02102     //
02103     // Get the initial value for the loop.
02104     SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
02105     if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
02106     SCEVHandle Step = AddRec->getOperand(1);
02107 
02108     Step = getSCEVAtScope(Step, L->getParentLoop());
02109 
02110     // Figure out if Start % Step == 0.
02111     // FIXME: We should add DivExpr and RemExpr operations to our AST.
02112     if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
02113       if (StepC->getValue()->equalsInt(1))      // N % 1 == 0
02114         return SCEV::getNegativeSCEV(Start);  // 0 - Start/1 == -Start
02115       if (StepC->getValue()->isAllOnesValue())  // N % -1 == 0
02116         return Start;                   // 0 - Start/-1 == Start
02117 
02118       // Check to see if Start is divisible by SC with no remainder.
02119       if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
02120         ConstantInt *StartCC = StartC->getValue();
02121         Constant *StartNegC = ConstantExpr::getNeg(StartCC);
02122         Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
02123         if (Rem->isNullValue()) {
02124           Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
02125           return SCEVUnknown::get(Result);
02126         }
02127       }
02128     }
02129   } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
02130     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
02131     // the quadratic equation to solve it.
02132     std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
02133     SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
02134     SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
02135     if (R1) {
02136 #if 0
02137       std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
02138                 << "  sol#2: " << *R2 << "\n";
02139 #endif
02140       // Pick the smallest positive root value.
02141       assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
02142       if (ConstantBool *CB =
02143           dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
02144                                                         R2->getValue()))) {
02145         if (CB != ConstantBool::True)
02146           std::swap(R1, R2);   // R1 is the minimum root now.
02147 
02148         // We can only use this value if the chrec ends up with an exact zero
02149         // value at this index.  When solving for "X*X != 5", for example, we
02150         // should not accept a root of 2.
02151         SCEVHandle Val = AddRec->evaluateAtIteration(R1);
02152         if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
02153           if (EvalVal->getValue()->isNullValue())
02154             return R1;  // We found a quadratic root!
02155       }
02156     }
02157   }
02158 
02159   return UnknownValue;
02160 }
02161 
02162 /// HowFarToNonZero - Return the number of times a backedge checking the
02163 /// specified value for nonzero will execute.  If not computable, return
02164 /// UnknownValue
02165 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
02166   // Loops that look like: while (X == 0) are very strange indeed.  We don't
02167   // handle them yet except for the trivial case.  This could be expanded in the
02168   // future as needed.
02169 
02170   // If the value is a constant, check to see if it is known to be non-zero
02171   // already.  If so, the backedge will execute zero times.
02172   if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
02173     Constant *Zero = Constant::getNullValue(C->getValue()->getType());
02174     Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
02175     if (NonZero == ConstantBool::True)
02176       return getSCEV(Zero);
02177     return UnknownValue;  // Otherwise it will loop infinitely.
02178   }
02179 
02180   // We could implement others, but I really doubt anyone writes loops like
02181   // this, and if they did, they would already be constant folded.
02182   return UnknownValue;
02183 }
02184 
02185 /// HowManyLessThans - Return the number of times a backedge containing the
02186 /// specified less-than comparison will execute.  If not computable, return
02187 /// UnknownValue.
02188 SCEVHandle ScalarEvolutionsImpl::
02189 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
02190   // Only handle:  "ADDREC < LoopInvariant".
02191   if (!RHS->isLoopInvariant(L)) return UnknownValue;
02192 
02193   SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
02194   if (!AddRec || AddRec->getLoop() != L)
02195     return UnknownValue;
02196 
02197   if (AddRec->isAffine()) {
02198     // FORNOW: We only support unit strides.
02199     SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
02200     if (AddRec->getOperand(1) != One)
02201       return UnknownValue;
02202 
02203     // The number of iterations for "[n,+,1] < m", is m-n.  However, we don't
02204     // know that m is >= n on input to the loop.  If it is, the condition return
02205     // true zero times.  What we really should return, for full generality, is
02206     // SMAX(0, m-n).  Since we cannot check this, we will instead check for a
02207     // canonical loop form: most do-loops will have a check that dominates the
02208     // loop, that only enters the loop if [n-1]<m.  If we can find this check,
02209     // we know that the SMAX will evaluate to m-n, because we know that m >= n.
02210 
02211     // Search for the check.
02212     BasicBlock *Preheader = L->getLoopPreheader();
02213     BasicBlock *PreheaderDest = L->getHeader();
02214     if (Preheader == 0) return UnknownValue;
02215 
02216     BranchInst *LoopEntryPredicate =
02217       dyn_cast<BranchInst>(Preheader->getTerminator());
02218     if (!LoopEntryPredicate) return UnknownValue;
02219 
02220     // This might be a critical edge broken out.  If the loop preheader ends in
02221     // an unconditional branch to the loop, check to see if the preheader has a
02222     // single predecessor, and if so, look for its terminator.
02223     while (LoopEntryPredicate->isUnconditional()) {
02224       PreheaderDest = Preheader;
02225       Preheader = Preheader->getSinglePredecessor();
02226       if (!Preheader) return UnknownValue;  // Multiple preds.
02227       
02228       LoopEntryPredicate =
02229         dyn_cast<BranchInst>(Preheader->getTerminator());
02230       if (!LoopEntryPredicate) return UnknownValue;
02231     }
02232 
02233     // Now that we found a conditional branch that dominates the loop, check to
02234     // see if it is the comparison we are looking for.
02235     SetCondInst *SCI =dyn_cast<SetCondInst>(LoopEntryPredicate->getCondition());
02236     if (!SCI) return UnknownValue;
02237     Value *PreCondLHS = SCI->getOperand(0);
02238     Value *PreCondRHS = SCI->getOperand(1);
02239     Instruction::BinaryOps Cond;
02240     if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
02241       Cond = SCI->getOpcode();
02242     else
02243       Cond = SCI->getInverseCondition();
02244     
02245     switch (Cond) {
02246     case Instruction::SetGT:
02247       std::swap(PreCondLHS, PreCondRHS);
02248       Cond = Instruction::SetLT;
02249       // Fall Through.
02250     case Instruction::SetLT:
02251       if (PreCondLHS->getType()->isInteger() &&
02252           PreCondLHS->getType()->isSigned()) { 
02253         if (RHS != getSCEV(PreCondRHS))
02254           return UnknownValue;  // Not a comparison against 'm'.
02255 
02256         if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
02257                     != getSCEV(PreCondLHS))
02258           return UnknownValue;  // Not a comparison against 'n-1'.
02259         break;
02260       } else {
02261         return UnknownValue;
02262       }
02263     default: break;
02264     }
02265 
02266     //std::cerr << "Computed Loop Trip Count as: " <<
02267     //  *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
02268     return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
02269   }
02270 
02271   return UnknownValue;
02272 }
02273 
02274 /// getNumIterationsInRange - Return the number of iterations of this loop that
02275 /// produce values in the specified constant range.  Another way of looking at
02276 /// this is that it returns the first iteration number where the value is not in
02277 /// the condition, thus computing the exit count. If the iteration count can't
02278 /// be computed, an instance of SCEVCouldNotCompute is returned.
02279 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
02280   if (Range.isFullSet())  // Infinite loop.
02281     return new SCEVCouldNotCompute();
02282 
02283   // If the start is a non-zero constant, shift the range to simplify things.
02284   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
02285     if (!SC->getValue()->isNullValue()) {
02286       std::vector<SCEVHandle> Operands(op_begin(), op_end());
02287       Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
02288       SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
02289       if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
02290         return ShiftedAddRec->getNumIterationsInRange(
02291                                               Range.subtract(SC->getValue()));
02292       // This is strange and shouldn't happen.
02293       return new SCEVCouldNotCompute();
02294     }
02295 
02296   // The only time we can solve this is when we have all constant indices.
02297   // Otherwise, we cannot determine the overflow conditions.
02298   for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
02299     if (!isa<SCEVConstant>(getOperand(i)))
02300       return new SCEVCouldNotCompute();
02301 
02302 
02303   // Okay at this point we know that all elements of the chrec are constants and
02304   // that the start element is zero.
02305 
02306   // First check to see if the range contains zero.  If not, the first
02307   // iteration exits.
02308   ConstantInt *Zero = ConstantInt::get(getType(), 0);
02309   if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
02310 
02311   if (isAffine()) {
02312     // If this is an affine expression then we have this situation:
02313     //   Solve {0,+,A} in Range  ===  Ax in Range
02314 
02315     // Since we know that zero is in the range, we know that the upper value of
02316     // the range must be the first possible exit value.  Also note that we
02317     // already checked for a full range.
02318     ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
02319     ConstantInt *A     = cast<SCEVConstant>(getOperand(1))->getValue();
02320     ConstantInt *One   = ConstantInt::get(getType(), 1);
02321 
02322     // The exit value should be (Upper+A-1)/A.
02323     Constant *ExitValue = Upper;
02324     if (A != One) {
02325       ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
02326       ExitValue = ConstantExpr::getDiv(ExitValue, A);
02327     }
02328     assert(isa<ConstantInt>(ExitValue) &&
02329            "Constant folding of integers not implemented?");
02330 
02331     // Evaluate at the exit value.  If we really did fall out of the valid
02332     // range, then we computed our trip count, otherwise wrap around or other
02333     // things must have happened.
02334     ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
02335     if (Range.contains(Val))
02336       return new SCEVCouldNotCompute();  // Something strange happened
02337 
02338     // Ensure that the previous value is in the range.  This is a sanity check.
02339     assert(Range.contains(EvaluateConstantChrecAtConstant(this,
02340                               ConstantExpr::getSub(ExitValue, One))) &&
02341            "Linear scev computation is off in a bad way!");
02342     return SCEVConstant::get(cast<ConstantInt>(ExitValue));
02343   } else if (isQuadratic()) {
02344     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
02345     // quadratic equation to solve it.  To do this, we must frame our problem in
02346     // terms of figuring out when zero is crossed, instead of when
02347     // Range.getUpper() is crossed.
02348     std::vector<SCEVHandle> NewOps(op_begin(), op_end());
02349     NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
02350     SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
02351 
02352     // Next, solve the constructed addrec
02353     std::pair<SCEVHandle,SCEVHandle> Roots =
02354       SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
02355     SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
02356     SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
02357     if (R1) {
02358       // Pick the smallest positive root value.
02359       assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
02360       if (ConstantBool *CB =
02361           dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
02362                                                         R2->getValue()))) {
02363         if (CB != ConstantBool::True)
02364           std::swap(R1, R2);   // R1 is the minimum root now.
02365 
02366         // Make sure the root is not off by one.  The returned iteration should
02367         // not be in the range, but the previous one should be.  When solving
02368         // for "X*X < 5", for example, we should not return a root of 2.
02369         ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
02370                                                              R1->getValue());
02371         if (Range.contains(R1Val)) {
02372           // The next iteration must be out of the range...
02373           Constant *NextVal =
02374             ConstantExpr::getAdd(R1->getValue(),
02375                                  ConstantInt::get(R1->getType(), 1));
02376 
02377           R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
02378           if (!Range.contains(R1Val))
02379             return SCEVUnknown::get(NextVal);
02380           return new SCEVCouldNotCompute();  // Something strange happened
02381         }
02382 
02383         // If R1 was not in the range, then it is a good return value.  Make
02384         // sure that R1-1 WAS in the range though, just in case.
02385         Constant *NextVal =
02386           ConstantExpr::getSub(R1->getValue(),
02387                                ConstantInt::get(R1->getType(), 1));
02388         R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
02389         if (Range.contains(R1Val))
02390           return R1;
02391         return new SCEVCouldNotCompute();  // Something strange happened
02392       }
02393     }
02394   }
02395 
02396   // Fallback, if this is a general polynomial, figure out the progression
02397   // through brute force: evaluate until we find an iteration that fails the
02398   // test.  This is likely to be slow, but getting an accurate trip count is
02399   // incredibly important, we will be able to simplify the exit test a lot, and
02400   // we are almost guaranteed to get a trip count in this case.
02401   ConstantInt *TestVal = ConstantInt::get(getType(), 0);
02402   ConstantInt *One     = ConstantInt::get(getType(), 1);
02403   ConstantInt *EndVal  = TestVal;  // Stop when we wrap around.
02404   do {
02405     ++NumBruteForceEvaluations;
02406     SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
02407     if (!isa<SCEVConstant>(Val))  // This shouldn't happen.
02408       return new SCEVCouldNotCompute();
02409 
02410     // Check to see if we found the value!
02411     if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
02412       return SCEVConstant::get(TestVal);
02413 
02414     // Increment to test the next index.
02415     TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
02416   } while (TestVal != EndVal);
02417 
02418   return new SCEVCouldNotCompute();
02419 }
02420 
02421 
02422 
02423 //===----------------------------------------------------------------------===//
02424 //                   ScalarEvolution Class Implementation
02425 //===----------------------------------------------------------------------===//
02426 
02427 bool ScalarEvolution::runOnFunction(Function &F) {
02428   Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
02429   return false;
02430 }
02431 
02432 void ScalarEvolution::releaseMemory() {
02433   delete (ScalarEvolutionsImpl*)Impl;
02434   Impl = 0;
02435 }
02436 
02437 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
02438   AU.setPreservesAll();
02439   AU.addRequiredTransitive<LoopInfo>();
02440 }
02441 
02442 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
02443   return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
02444 }
02445 
02446 /// hasSCEV - Return true if the SCEV for this value has already been
02447 /// computed.
02448 bool ScalarEvolution::hasSCEV(Value *V) const {
02449   return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
02450 }
02451 
02452 
02453 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
02454 /// the specified value.
02455 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
02456   ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
02457 }
02458 
02459 
02460 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
02461   return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
02462 }
02463 
02464 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
02465   return !isa<SCEVCouldNotCompute>(getIterationCount(L));
02466 }
02467 
02468 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
02469   return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
02470 }
02471 
02472 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
02473   return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
02474 }
02475 
02476 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
02477                           const Loop *L) {
02478   // Print all inner loops first
02479   for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
02480     PrintLoopInfo(OS, SE, *I);
02481 
02482   std::cerr << "Loop " << L->getHeader()->getName() << ": ";
02483 
02484   std::vector<BasicBlock*> ExitBlocks;
02485   L->getExitBlocks(ExitBlocks);
02486   if (ExitBlocks.size() != 1)
02487     std::cerr << "<multiple exits> ";
02488 
02489   if (SE->hasLoopInvariantIterationCount(L)) {
02490     std::cerr << *SE->getIterationCount(L) << " iterations! ";
02491   } else {
02492     std::cerr << "Unpredictable iteration count. ";
02493   }
02494 
02495   std::cerr << "\n";
02496 }
02497 
02498 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
02499   Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
02500   LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
02501 
02502   OS << "Classifying expressions for: " << F.getName() << "\n";
02503   for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
02504     if (I->getType()->isInteger()) {
02505       OS << *I;
02506       OS << "  --> ";
02507       SCEVHandle SV = getSCEV(&*I);
02508       SV->print(OS);
02509       OS << "\t\t";
02510 
02511       if ((*I).getType()->isIntegral()) {
02512         ConstantRange Bounds = SV->getValueRange();
02513         if (!Bounds.isFullSet())
02514           OS << "Bounds: " << Bounds << " ";
02515       }
02516 
02517       if (const Loop *L = LI.getLoopFor((*I).getParent())) {
02518         OS << "Exits: ";
02519         SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
02520         if (isa<SCEVCouldNotCompute>(ExitValue)) {
02521           OS << "<<Unknown>>";
02522         } else {
02523           OS << *ExitValue;
02524         }
02525       }
02526 
02527 
02528       OS << "\n";
02529     }
02530 
02531   OS << "Determining loop execution counts for: " << F.getName() << "\n";
02532   for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
02533     PrintLoopInfo(OS, this, *I);
02534 }
02535