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