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      1 //== RangeConstraintManager.cpp - Manage range constraints.------*- C++ -*--==//
      2 //
      3 //                     The LLVM Compiler Infrastructure
      4 //
      5 // This file is distributed under the University of Illinois Open Source
      6 // License. See LICENSE.TXT for details.
      7 //
      8 //===----------------------------------------------------------------------===//
      9 //
     10 //  This file defines RangeConstraintManager, a class that tracks simple
     11 //  equality and inequality constraints on symbolic values of ProgramState.
     12 //
     13 //===----------------------------------------------------------------------===//
     14 
     15 #include "SimpleConstraintManager.h"
     16 #include "clang/StaticAnalyzer/Core/PathSensitive/APSIntType.h"
     17 #include "clang/StaticAnalyzer/Core/PathSensitive/ProgramState.h"
     18 #include "clang/StaticAnalyzer/Core/PathSensitive/ProgramStateTrait.h"
     19 #include "llvm/ADT/FoldingSet.h"
     20 #include "llvm/ADT/ImmutableSet.h"
     21 #include "llvm/Support/Debug.h"
     22 #include "llvm/Support/raw_ostream.h"
     23 
     24 using namespace clang;
     25 using namespace ento;
     26 
     27 /// A Range represents the closed range [from, to].  The caller must
     28 /// guarantee that from <= to.  Note that Range is immutable, so as not
     29 /// to subvert RangeSet's immutability.
     30 namespace {
     31 class Range : public std::pair<const llvm::APSInt*,
     32                                                 const llvm::APSInt*> {
     33 public:
     34   Range(const llvm::APSInt &from, const llvm::APSInt &to)
     35     : std::pair<const llvm::APSInt*, const llvm::APSInt*>(&from, &to) {
     36     assert(from <= to);
     37   }
     38   bool Includes(const llvm::APSInt &v) const {
     39     return *first <= v && v <= *second;
     40   }
     41   const llvm::APSInt &From() const {
     42     return *first;
     43   }
     44   const llvm::APSInt &To() const {
     45     return *second;
     46   }
     47   const llvm::APSInt *getConcreteValue() const {
     48     return &From() == &To() ? &From() : nullptr;
     49   }
     50 
     51   void Profile(llvm::FoldingSetNodeID &ID) const {
     52     ID.AddPointer(&From());
     53     ID.AddPointer(&To());
     54   }
     55 };
     56 
     57 
     58 class RangeTrait : public llvm::ImutContainerInfo<Range> {
     59 public:
     60   // When comparing if one Range is less than another, we should compare
     61   // the actual APSInt values instead of their pointers.  This keeps the order
     62   // consistent (instead of comparing by pointer values) and can potentially
     63   // be used to speed up some of the operations in RangeSet.
     64   static inline bool isLess(key_type_ref lhs, key_type_ref rhs) {
     65     return *lhs.first < *rhs.first || (!(*rhs.first < *lhs.first) &&
     66                                        *lhs.second < *rhs.second);
     67   }
     68 };
     69 
     70 /// RangeSet contains a set of ranges. If the set is empty, then
     71 ///  there the value of a symbol is overly constrained and there are no
     72 ///  possible values for that symbol.
     73 class RangeSet {
     74   typedef llvm::ImmutableSet<Range, RangeTrait> PrimRangeSet;
     75   PrimRangeSet ranges; // no need to make const, since it is an
     76                        // ImmutableSet - this allows default operator=
     77                        // to work.
     78 public:
     79   typedef PrimRangeSet::Factory Factory;
     80   typedef PrimRangeSet::iterator iterator;
     81 
     82   RangeSet(PrimRangeSet RS) : ranges(RS) {}
     83 
     84   /// Create a new set with all ranges of this set and RS.
     85   /// Possible intersections are not checked here.
     86   RangeSet addRange(Factory &F, const RangeSet &RS) {
     87     PrimRangeSet Ranges(RS.ranges);
     88     for (const auto &range : ranges)
     89       Ranges = F.add(Ranges, range);
     90     return RangeSet(Ranges);
     91   }
     92 
     93   iterator begin() const { return ranges.begin(); }
     94   iterator end() const { return ranges.end(); }
     95 
     96   bool isEmpty() const { return ranges.isEmpty(); }
     97 
     98   /// Construct a new RangeSet representing '{ [from, to] }'.
     99   RangeSet(Factory &F, const llvm::APSInt &from, const llvm::APSInt &to)
    100     : ranges(F.add(F.getEmptySet(), Range(from, to))) {}
    101 
    102   /// Profile - Generates a hash profile of this RangeSet for use
    103   ///  by FoldingSet.
    104   void Profile(llvm::FoldingSetNodeID &ID) const { ranges.Profile(ID); }
    105 
    106   /// getConcreteValue - If a symbol is contrained to equal a specific integer
    107   ///  constant then this method returns that value.  Otherwise, it returns
    108   ///  NULL.
    109   const llvm::APSInt* getConcreteValue() const {
    110     return ranges.isSingleton() ? ranges.begin()->getConcreteValue() : nullptr;
    111   }
    112 
    113 private:
    114   void IntersectInRange(BasicValueFactory &BV, Factory &F,
    115                         const llvm::APSInt &Lower,
    116                         const llvm::APSInt &Upper,
    117                         PrimRangeSet &newRanges,
    118                         PrimRangeSet::iterator &i,
    119                         PrimRangeSet::iterator &e) const {
    120     // There are six cases for each range R in the set:
    121     //   1. R is entirely before the intersection range.
    122     //   2. R is entirely after the intersection range.
    123     //   3. R contains the entire intersection range.
    124     //   4. R starts before the intersection range and ends in the middle.
    125     //   5. R starts in the middle of the intersection range and ends after it.
    126     //   6. R is entirely contained in the intersection range.
    127     // These correspond to each of the conditions below.
    128     for (/* i = begin(), e = end() */; i != e; ++i) {
    129       if (i->To() < Lower) {
    130         continue;
    131       }
    132       if (i->From() > Upper) {
    133         break;
    134       }
    135 
    136       if (i->Includes(Lower)) {
    137         if (i->Includes(Upper)) {
    138           newRanges = F.add(newRanges, Range(BV.getValue(Lower),
    139                                              BV.getValue(Upper)));
    140           break;
    141         } else
    142           newRanges = F.add(newRanges, Range(BV.getValue(Lower), i->To()));
    143       } else {
    144         if (i->Includes(Upper)) {
    145           newRanges = F.add(newRanges, Range(i->From(), BV.getValue(Upper)));
    146           break;
    147         } else
    148           newRanges = F.add(newRanges, *i);
    149       }
    150     }
    151   }
    152 
    153   const llvm::APSInt &getMinValue() const {
    154     assert(!isEmpty());
    155     return ranges.begin()->From();
    156   }
    157 
    158   bool pin(llvm::APSInt &Lower, llvm::APSInt &Upper) const {
    159     // This function has nine cases, the cartesian product of range-testing
    160     // both the upper and lower bounds against the symbol's type.
    161     // Each case requires a different pinning operation.
    162     // The function returns false if the described range is entirely outside
    163     // the range of values for the associated symbol.
    164     APSIntType Type(getMinValue());
    165     APSIntType::RangeTestResultKind LowerTest = Type.testInRange(Lower, true);
    166     APSIntType::RangeTestResultKind UpperTest = Type.testInRange(Upper, true);
    167 
    168     switch (LowerTest) {
    169     case APSIntType::RTR_Below:
    170       switch (UpperTest) {
    171       case APSIntType::RTR_Below:
    172         // The entire range is outside the symbol's set of possible values.
    173         // If this is a conventionally-ordered range, the state is infeasible.
    174         if (Lower <= Upper)
    175           return false;
    176 
    177         // However, if the range wraps around, it spans all possible values.
    178         Lower = Type.getMinValue();
    179         Upper = Type.getMaxValue();
    180         break;
    181       case APSIntType::RTR_Within:
    182         // The range starts below what's possible but ends within it. Pin.
    183         Lower = Type.getMinValue();
    184         Type.apply(Upper);
    185         break;
    186       case APSIntType::RTR_Above:
    187         // The range spans all possible values for the symbol. Pin.
    188         Lower = Type.getMinValue();
    189         Upper = Type.getMaxValue();
    190         break;
    191       }
    192       break;
    193     case APSIntType::RTR_Within:
    194       switch (UpperTest) {
    195       case APSIntType::RTR_Below:
    196         // The range wraps around, but all lower values are not possible.
    197         Type.apply(Lower);
    198         Upper = Type.getMaxValue();
    199         break;
    200       case APSIntType::RTR_Within:
    201         // The range may or may not wrap around, but both limits are valid.
    202         Type.apply(Lower);
    203         Type.apply(Upper);
    204         break;
    205       case APSIntType::RTR_Above:
    206         // The range starts within what's possible but ends above it. Pin.
    207         Type.apply(Lower);
    208         Upper = Type.getMaxValue();
    209         break;
    210       }
    211       break;
    212     case APSIntType::RTR_Above:
    213       switch (UpperTest) {
    214       case APSIntType::RTR_Below:
    215         // The range wraps but is outside the symbol's set of possible values.
    216         return false;
    217       case APSIntType::RTR_Within:
    218         // The range starts above what's possible but ends within it (wrap).
    219         Lower = Type.getMinValue();
    220         Type.apply(Upper);
    221         break;
    222       case APSIntType::RTR_Above:
    223         // The entire range is outside the symbol's set of possible values.
    224         // If this is a conventionally-ordered range, the state is infeasible.
    225         if (Lower <= Upper)
    226           return false;
    227 
    228         // However, if the range wraps around, it spans all possible values.
    229         Lower = Type.getMinValue();
    230         Upper = Type.getMaxValue();
    231         break;
    232       }
    233       break;
    234     }
    235 
    236     return true;
    237   }
    238 
    239 public:
    240   // Returns a set containing the values in the receiving set, intersected with
    241   // the closed range [Lower, Upper]. Unlike the Range type, this range uses
    242   // modular arithmetic, corresponding to the common treatment of C integer
    243   // overflow. Thus, if the Lower bound is greater than the Upper bound, the
    244   // range is taken to wrap around. This is equivalent to taking the
    245   // intersection with the two ranges [Min, Upper] and [Lower, Max],
    246   // or, alternatively, /removing/ all integers between Upper and Lower.
    247   RangeSet Intersect(BasicValueFactory &BV, Factory &F,
    248                      llvm::APSInt Lower, llvm::APSInt Upper) const {
    249     if (!pin(Lower, Upper))
    250       return F.getEmptySet();
    251 
    252     PrimRangeSet newRanges = F.getEmptySet();
    253 
    254     PrimRangeSet::iterator i = begin(), e = end();
    255     if (Lower <= Upper)
    256       IntersectInRange(BV, F, Lower, Upper, newRanges, i, e);
    257     else {
    258       // The order of the next two statements is important!
    259       // IntersectInRange() does not reset the iteration state for i and e.
    260       // Therefore, the lower range most be handled first.
    261       IntersectInRange(BV, F, BV.getMinValue(Upper), Upper, newRanges, i, e);
    262       IntersectInRange(BV, F, Lower, BV.getMaxValue(Lower), newRanges, i, e);
    263     }
    264 
    265     return newRanges;
    266   }
    267 
    268   void print(raw_ostream &os) const {
    269     bool isFirst = true;
    270     os << "{ ";
    271     for (iterator i = begin(), e = end(); i != e; ++i) {
    272       if (isFirst)
    273         isFirst = false;
    274       else
    275         os << ", ";
    276 
    277       os << '[' << i->From().toString(10) << ", " << i->To().toString(10)
    278          << ']';
    279     }
    280     os << " }";
    281   }
    282 
    283   bool operator==(const RangeSet &other) const {
    284     return ranges == other.ranges;
    285   }
    286 };
    287 } // end anonymous namespace
    288 
    289 REGISTER_TRAIT_WITH_PROGRAMSTATE(ConstraintRange,
    290                                  CLANG_ENTO_PROGRAMSTATE_MAP(SymbolRef,
    291                                                              RangeSet))
    292 
    293 namespace {
    294 class RangeConstraintManager : public SimpleConstraintManager{
    295   RangeSet GetRange(ProgramStateRef state, SymbolRef sym);
    296 public:
    297   RangeConstraintManager(SubEngine *subengine, SValBuilder &SVB)
    298     : SimpleConstraintManager(subengine, SVB) {}
    299 
    300   ProgramStateRef assumeSymNE(ProgramStateRef state, SymbolRef sym,
    301                              const llvm::APSInt& Int,
    302                              const llvm::APSInt& Adjustment) override;
    303 
    304   ProgramStateRef assumeSymEQ(ProgramStateRef state, SymbolRef sym,
    305                              const llvm::APSInt& Int,
    306                              const llvm::APSInt& Adjustment) override;
    307 
    308   ProgramStateRef assumeSymLT(ProgramStateRef state, SymbolRef sym,
    309                              const llvm::APSInt& Int,
    310                              const llvm::APSInt& Adjustment) override;
    311 
    312   ProgramStateRef assumeSymGT(ProgramStateRef state, SymbolRef sym,
    313                              const llvm::APSInt& Int,
    314                              const llvm::APSInt& Adjustment) override;
    315 
    316   ProgramStateRef assumeSymGE(ProgramStateRef state, SymbolRef sym,
    317                              const llvm::APSInt& Int,
    318                              const llvm::APSInt& Adjustment) override;
    319 
    320   ProgramStateRef assumeSymLE(ProgramStateRef state, SymbolRef sym,
    321                              const llvm::APSInt& Int,
    322                              const llvm::APSInt& Adjustment) override;
    323 
    324   ProgramStateRef assumeSymbolWithinInclusiveRange(
    325         ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
    326         const llvm::APSInt &To, const llvm::APSInt &Adjustment) override;
    327 
    328   ProgramStateRef assumeSymbolOutOfInclusiveRange(
    329         ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
    330         const llvm::APSInt &To, const llvm::APSInt &Adjustment) override;
    331 
    332   const llvm::APSInt* getSymVal(ProgramStateRef St,
    333                                 SymbolRef sym) const override;
    334   ConditionTruthVal checkNull(ProgramStateRef State, SymbolRef Sym) override;
    335 
    336   ProgramStateRef removeDeadBindings(ProgramStateRef St,
    337                                      SymbolReaper& SymReaper) override;
    338 
    339   void print(ProgramStateRef St, raw_ostream &Out,
    340              const char* nl, const char *sep) override;
    341 
    342 private:
    343   RangeSet::Factory F;
    344   RangeSet getSymLTRange(ProgramStateRef St, SymbolRef Sym,
    345                          const llvm::APSInt &Int,
    346                          const llvm::APSInt &Adjustment);
    347   RangeSet getSymGTRange(ProgramStateRef St, SymbolRef Sym,
    348                          const llvm::APSInt &Int,
    349                          const llvm::APSInt &Adjustment);
    350   RangeSet getSymLERange(ProgramStateRef St, SymbolRef Sym,
    351                          const llvm::APSInt &Int,
    352                          const llvm::APSInt &Adjustment);
    353   RangeSet getSymLERange(const RangeSet &RS, const llvm::APSInt &Int,
    354                          const llvm::APSInt &Adjustment);
    355   RangeSet getSymGERange(ProgramStateRef St, SymbolRef Sym,
    356                          const llvm::APSInt &Int,
    357                          const llvm::APSInt &Adjustment);
    358 };
    359 
    360 } // end anonymous namespace
    361 
    362 std::unique_ptr<ConstraintManager>
    363 ento::CreateRangeConstraintManager(ProgramStateManager &StMgr, SubEngine *Eng) {
    364   return llvm::make_unique<RangeConstraintManager>(Eng, StMgr.getSValBuilder());
    365 }
    366 
    367 const llvm::APSInt* RangeConstraintManager::getSymVal(ProgramStateRef St,
    368                                                       SymbolRef sym) const {
    369   const ConstraintRangeTy::data_type *T = St->get<ConstraintRange>(sym);
    370   return T ? T->getConcreteValue() : nullptr;
    371 }
    372 
    373 ConditionTruthVal RangeConstraintManager::checkNull(ProgramStateRef State,
    374                                                     SymbolRef Sym) {
    375   const RangeSet *Ranges = State->get<ConstraintRange>(Sym);
    376 
    377   // If we don't have any information about this symbol, it's underconstrained.
    378   if (!Ranges)
    379     return ConditionTruthVal();
    380 
    381   // If we have a concrete value, see if it's zero.
    382   if (const llvm::APSInt *Value = Ranges->getConcreteValue())
    383     return *Value == 0;
    384 
    385   BasicValueFactory &BV = getBasicVals();
    386   APSIntType IntType = BV.getAPSIntType(Sym->getType());
    387   llvm::APSInt Zero = IntType.getZeroValue();
    388 
    389   // Check if zero is in the set of possible values.
    390   if (Ranges->Intersect(BV, F, Zero, Zero).isEmpty())
    391     return false;
    392 
    393   // Zero is a possible value, but it is not the /only/ possible value.
    394   return ConditionTruthVal();
    395 }
    396 
    397 /// Scan all symbols referenced by the constraints. If the symbol is not alive
    398 /// as marked in LSymbols, mark it as dead in DSymbols.
    399 ProgramStateRef
    400 RangeConstraintManager::removeDeadBindings(ProgramStateRef state,
    401                                            SymbolReaper& SymReaper) {
    402 
    403   ConstraintRangeTy CR = state->get<ConstraintRange>();
    404   ConstraintRangeTy::Factory& CRFactory = state->get_context<ConstraintRange>();
    405 
    406   for (ConstraintRangeTy::iterator I = CR.begin(), E = CR.end(); I != E; ++I) {
    407     SymbolRef sym = I.getKey();
    408     if (SymReaper.maybeDead(sym))
    409       CR = CRFactory.remove(CR, sym);
    410   }
    411 
    412   return state->set<ConstraintRange>(CR);
    413 }
    414 
    415 RangeSet
    416 RangeConstraintManager::GetRange(ProgramStateRef state, SymbolRef sym) {
    417   if (ConstraintRangeTy::data_type* V = state->get<ConstraintRange>(sym))
    418     return *V;
    419 
    420   // Lazily generate a new RangeSet representing all possible values for the
    421   // given symbol type.
    422   BasicValueFactory &BV = getBasicVals();
    423   QualType T = sym->getType();
    424 
    425   RangeSet Result(F, BV.getMinValue(T), BV.getMaxValue(T));
    426 
    427   // Special case: references are known to be non-zero.
    428   if (T->isReferenceType()) {
    429     APSIntType IntType = BV.getAPSIntType(T);
    430     Result = Result.Intersect(BV, F, ++IntType.getZeroValue(),
    431                                      --IntType.getZeroValue());
    432   }
    433 
    434   return Result;
    435 }
    436 
    437 //===------------------------------------------------------------------------===
    438 // assumeSymX methods: public interface for RangeConstraintManager.
    439 //===------------------------------------------------------------------------===/
    440 
    441 // The syntax for ranges below is mathematical, using [x, y] for closed ranges
    442 // and (x, y) for open ranges. These ranges are modular, corresponding with
    443 // a common treatment of C integer overflow. This means that these methods
    444 // do not have to worry about overflow; RangeSet::Intersect can handle such a
    445 // "wraparound" range.
    446 // As an example, the range [UINT_MAX-1, 3) contains five values: UINT_MAX-1,
    447 // UINT_MAX, 0, 1, and 2.
    448 
    449 ProgramStateRef
    450 RangeConstraintManager::assumeSymNE(ProgramStateRef St, SymbolRef Sym,
    451                                     const llvm::APSInt &Int,
    452                                     const llvm::APSInt &Adjustment) {
    453   // Before we do any real work, see if the value can even show up.
    454   APSIntType AdjustmentType(Adjustment);
    455   if (AdjustmentType.testInRange(Int, true) != APSIntType::RTR_Within)
    456     return St;
    457 
    458   llvm::APSInt Lower = AdjustmentType.convert(Int) - Adjustment;
    459   llvm::APSInt Upper = Lower;
    460   --Lower;
    461   ++Upper;
    462 
    463   // [Int-Adjustment+1, Int-Adjustment-1]
    464   // Notice that the lower bound is greater than the upper bound.
    465   RangeSet New = GetRange(St, Sym).Intersect(getBasicVals(), F, Upper, Lower);
    466   return New.isEmpty() ? nullptr : St->set<ConstraintRange>(Sym, New);
    467 }
    468 
    469 ProgramStateRef
    470 RangeConstraintManager::assumeSymEQ(ProgramStateRef St, SymbolRef Sym,
    471                                     const llvm::APSInt &Int,
    472                                     const llvm::APSInt &Adjustment) {
    473   // Before we do any real work, see if the value can even show up.
    474   APSIntType AdjustmentType(Adjustment);
    475   if (AdjustmentType.testInRange(Int, true) != APSIntType::RTR_Within)
    476     return nullptr;
    477 
    478   // [Int-Adjustment, Int-Adjustment]
    479   llvm::APSInt AdjInt = AdjustmentType.convert(Int) - Adjustment;
    480   RangeSet New = GetRange(St, Sym).Intersect(getBasicVals(), F, AdjInt, AdjInt);
    481   return New.isEmpty() ? nullptr : St->set<ConstraintRange>(Sym, New);
    482 }
    483 
    484 RangeSet RangeConstraintManager::getSymLTRange(ProgramStateRef St,
    485                                                SymbolRef Sym,
    486                                                const llvm::APSInt &Int,
    487                                                const llvm::APSInt &Adjustment) {
    488   // Before we do any real work, see if the value can even show up.
    489   APSIntType AdjustmentType(Adjustment);
    490   switch (AdjustmentType.testInRange(Int, true)) {
    491   case APSIntType::RTR_Below:
    492     return F.getEmptySet();
    493   case APSIntType::RTR_Within:
    494     break;
    495   case APSIntType::RTR_Above:
    496     return GetRange(St, Sym);
    497   }
    498 
    499   // Special case for Int == Min. This is always false.
    500   llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
    501   llvm::APSInt Min = AdjustmentType.getMinValue();
    502   if (ComparisonVal == Min)
    503     return F.getEmptySet();
    504 
    505   llvm::APSInt Lower = Min - Adjustment;
    506   llvm::APSInt Upper = ComparisonVal - Adjustment;
    507   --Upper;
    508 
    509   return GetRange(St, Sym).Intersect(getBasicVals(), F, Lower, Upper);
    510 }
    511 
    512 ProgramStateRef
    513 RangeConstraintManager::assumeSymLT(ProgramStateRef St, SymbolRef Sym,
    514                                     const llvm::APSInt &Int,
    515                                     const llvm::APSInt &Adjustment) {
    516   RangeSet New = getSymLTRange(St, Sym, Int, Adjustment);
    517   return New.isEmpty() ? nullptr : St->set<ConstraintRange>(Sym, New);
    518 }
    519 
    520 RangeSet
    521 RangeConstraintManager::getSymGTRange(ProgramStateRef St, SymbolRef Sym,
    522                                       const llvm::APSInt &Int,
    523                                       const llvm::APSInt &Adjustment) {
    524   // Before we do any real work, see if the value can even show up.
    525   APSIntType AdjustmentType(Adjustment);
    526   switch (AdjustmentType.testInRange(Int, true)) {
    527   case APSIntType::RTR_Below:
    528     return GetRange(St, Sym);
    529   case APSIntType::RTR_Within:
    530     break;
    531   case APSIntType::RTR_Above:
    532     return F.getEmptySet();
    533   }
    534 
    535   // Special case for Int == Max. This is always false.
    536   llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
    537   llvm::APSInt Max = AdjustmentType.getMaxValue();
    538   if (ComparisonVal == Max)
    539     return F.getEmptySet();
    540 
    541   llvm::APSInt Lower = ComparisonVal - Adjustment;
    542   llvm::APSInt Upper = Max - Adjustment;
    543   ++Lower;
    544 
    545   return GetRange(St, Sym).Intersect(getBasicVals(), F, Lower, Upper);
    546 }
    547 
    548 ProgramStateRef
    549 RangeConstraintManager::assumeSymGT(ProgramStateRef St, SymbolRef Sym,
    550                                     const llvm::APSInt &Int,
    551                                     const llvm::APSInt &Adjustment) {
    552   RangeSet New = getSymGTRange(St, Sym, Int, Adjustment);
    553   return New.isEmpty() ? nullptr : St->set<ConstraintRange>(Sym, New);
    554 }
    555 
    556 RangeSet
    557 RangeConstraintManager::getSymGERange(ProgramStateRef St, SymbolRef Sym,
    558                                       const llvm::APSInt &Int,
    559                                       const llvm::APSInt &Adjustment) {
    560   // Before we do any real work, see if the value can even show up.
    561   APSIntType AdjustmentType(Adjustment);
    562   switch (AdjustmentType.testInRange(Int, true)) {
    563   case APSIntType::RTR_Below:
    564     return GetRange(St, Sym);
    565   case APSIntType::RTR_Within:
    566     break;
    567   case APSIntType::RTR_Above:
    568     return F.getEmptySet();
    569   }
    570 
    571   // Special case for Int == Min. This is always feasible.
    572   llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
    573   llvm::APSInt Min = AdjustmentType.getMinValue();
    574   if (ComparisonVal == Min)
    575     return GetRange(St, Sym);
    576 
    577   llvm::APSInt Max = AdjustmentType.getMaxValue();
    578   llvm::APSInt Lower = ComparisonVal - Adjustment;
    579   llvm::APSInt Upper = Max - Adjustment;
    580 
    581   return GetRange(St, Sym).Intersect(getBasicVals(), F, Lower, Upper);
    582 }
    583 
    584 ProgramStateRef
    585 RangeConstraintManager::assumeSymGE(ProgramStateRef St, SymbolRef Sym,
    586                                     const llvm::APSInt &Int,
    587                                     const llvm::APSInt &Adjustment) {
    588   RangeSet New = getSymGERange(St, Sym, Int, Adjustment);
    589   return New.isEmpty() ? nullptr : St->set<ConstraintRange>(Sym, New);
    590 }
    591 
    592 RangeSet
    593 RangeConstraintManager::getSymLERange(const RangeSet &RS,
    594                                       const llvm::APSInt &Int,
    595                                       const llvm::APSInt &Adjustment) {
    596   // Before we do any real work, see if the value can even show up.
    597   APSIntType AdjustmentType(Adjustment);
    598   switch (AdjustmentType.testInRange(Int, true)) {
    599   case APSIntType::RTR_Below:
    600     return F.getEmptySet();
    601   case APSIntType::RTR_Within:
    602     break;
    603   case APSIntType::RTR_Above:
    604     return RS;
    605   }
    606 
    607   // Special case for Int == Max. This is always feasible.
    608   llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
    609   llvm::APSInt Max = AdjustmentType.getMaxValue();
    610   if (ComparisonVal == Max)
    611     return RS;
    612 
    613   llvm::APSInt Min = AdjustmentType.getMinValue();
    614   llvm::APSInt Lower = Min - Adjustment;
    615   llvm::APSInt Upper = ComparisonVal - Adjustment;
    616 
    617   return RS.Intersect(getBasicVals(), F, Lower, Upper);
    618 }
    619 
    620 RangeSet
    621 RangeConstraintManager::getSymLERange(ProgramStateRef St, SymbolRef Sym,
    622                                       const llvm::APSInt &Int,
    623                                       const llvm::APSInt &Adjustment) {
    624   // Before we do any real work, see if the value can even show up.
    625   APSIntType AdjustmentType(Adjustment);
    626   switch (AdjustmentType.testInRange(Int, true)) {
    627   case APSIntType::RTR_Below:
    628     return F.getEmptySet();
    629   case APSIntType::RTR_Within:
    630     break;
    631   case APSIntType::RTR_Above:
    632     return GetRange(St, Sym);
    633   }
    634 
    635   // Special case for Int == Max. This is always feasible.
    636   llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
    637   llvm::APSInt Max = AdjustmentType.getMaxValue();
    638   if (ComparisonVal == Max)
    639     return GetRange(St, Sym);
    640 
    641   llvm::APSInt Min = AdjustmentType.getMinValue();
    642   llvm::APSInt Lower = Min - Adjustment;
    643   llvm::APSInt Upper = ComparisonVal - Adjustment;
    644 
    645   return GetRange(St, Sym).Intersect(getBasicVals(), F, Lower, Upper);
    646 }
    647 
    648 ProgramStateRef
    649 RangeConstraintManager::assumeSymLE(ProgramStateRef St, SymbolRef Sym,
    650                                     const llvm::APSInt &Int,
    651                                     const llvm::APSInt &Adjustment) {
    652   RangeSet New = getSymLERange(St, Sym, Int, Adjustment);
    653   return New.isEmpty() ? nullptr : St->set<ConstraintRange>(Sym, New);
    654 }
    655 
    656 ProgramStateRef
    657 RangeConstraintManager::assumeSymbolWithinInclusiveRange(
    658     ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
    659     const llvm::APSInt &To, const llvm::APSInt &Adjustment) {
    660   RangeSet New = getSymGERange(State, Sym, From, Adjustment);
    661   if (New.isEmpty())
    662     return nullptr;
    663   New = getSymLERange(New, To, Adjustment);
    664   return New.isEmpty() ? nullptr : State->set<ConstraintRange>(Sym, New);
    665 }
    666 
    667 ProgramStateRef
    668 RangeConstraintManager::assumeSymbolOutOfInclusiveRange(
    669     ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
    670     const llvm::APSInt &To, const llvm::APSInt &Adjustment) {
    671   RangeSet RangeLT = getSymLTRange(State, Sym, From, Adjustment);
    672   RangeSet RangeGT = getSymGTRange(State, Sym, To, Adjustment);
    673   RangeSet New(RangeLT.addRange(F, RangeGT));
    674   return New.isEmpty() ? nullptr : State->set<ConstraintRange>(Sym, New);
    675 }
    676 
    677 //===------------------------------------------------------------------------===
    678 // Pretty-printing.
    679 //===------------------------------------------------------------------------===/
    680 
    681 void RangeConstraintManager::print(ProgramStateRef St, raw_ostream &Out,
    682                                    const char* nl, const char *sep) {
    683 
    684   ConstraintRangeTy Ranges = St->get<ConstraintRange>();
    685 
    686   if (Ranges.isEmpty()) {
    687     Out << nl << sep << "Ranges are empty." << nl;
    688     return;
    689   }
    690 
    691   Out << nl << sep << "Ranges of symbol values:";
    692   for (ConstraintRangeTy::iterator I=Ranges.begin(), E=Ranges.end(); I!=E; ++I){
    693     Out << nl << ' ' << I.getKey() << " : ";
    694     I.getData().print(Out);
    695   }
    696   Out << nl;
    697 }
    698