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llvm / llvm-project / clang / refs/heads/main / . / lib / StaticAnalyzer / Core / RangeConstraintManager.cpp
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//== RangeConstraintManager.cpp - Manage range constraints.------*- C++ -*--==//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file defines RangeConstraintManager, a class that tracks simple
// equality and inequality constraints on symbolic values of ProgramState.
//
//===----------------------------------------------------------------------===//
#include "clang/Basic/JsonSupport.h"
#include "clang/StaticAnalyzer/Core/PathSensitive/APSIntType.h"
#include "clang/StaticAnalyzer/Core/PathSensitive/ProgramState.h"
#include "clang/StaticAnalyzer/Core/PathSensitive/ProgramStateTrait.h"
#include "clang/StaticAnalyzer/Core/PathSensitive/RangedConstraintManager.h"
#include "clang/StaticAnalyzer/Core/PathSensitive/SValVisitor.h"
#include "llvm/ADT/FoldingSet.h"
#include "llvm/ADT/ImmutableSet.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/StringExtras.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
#include <iterator>
#include <optional>
using namespace clang;
using namespace ento;
// This class can be extended with other tables which will help to reason
// about ranges more precisely.
class OperatorRelationsTable {
static_assert(BO_LT < BO_GT && BO_GT < BO_LE && BO_LE < BO_GE &&
BO_GE < BO_EQ && BO_EQ < BO_NE,
"This class relies on operators order. Rework it otherwise.");
public:
enum TriStateKind {
False = 0,
True,
Unknown,
};
private:
// CmpOpTable holds states which represent the corresponding range for
// branching an exploded graph. We can reason about the branch if there is
// a previously known fact of the existence of a comparison expression with
// operands used in the current expression.
// E.g. assuming (x < y) is true that means (x != y) is surely true.
// if (x previous_operation y) // < | != | >
// if (x operation y) // != | > | <
// tristate // True | Unknown | False
//
// CmpOpTable represents next:
// __|< |> |<=|>=|==|!=|UnknownX2|
// < |1 |0 |* |0 |0 |* |1 |
// > |0 |1 |0 |* |0 |* |1 |
// <=|1 |0 |1 |* |1 |* |0 |
// >=|0 |1 |* |1 |1 |* |0 |
// ==|0 |0 |* |* |1 |0 |1 |
// !=|1 |1 |* |* |0 |1 |0 |
//
// Columns stands for a previous operator.
// Rows stands for a current operator.
// Each row has exactly two `Unknown` cases.
// UnknownX2 means that both `Unknown` previous operators are met in code,
// and there is a special column for that, for example:
// if (x >= y)
// if (x != y)
// if (x <= y)
// False only
static constexpr size_t CmpOpCount = BO_NE - BO_LT + 1;
const TriStateKind CmpOpTable[CmpOpCount][CmpOpCount + 1] = {
// < > <= >= == != UnknownX2
{True, False, Unknown, False, False, Unknown, True}, // <
{False, True, False, Unknown, False, Unknown, True}, // >
{True, False, True, Unknown, True, Unknown, False}, // <=
{False, True, Unknown, True, True, Unknown, False}, // >=
{False, False, Unknown, Unknown, True, False, True}, // ==
{True, True, Unknown, Unknown, False, True, False}, // !=
};
static size_t getIndexFromOp(BinaryOperatorKind OP) {
return static_cast<size_t>(OP - BO_LT);
}
public:
constexpr size_t getCmpOpCount() const { return CmpOpCount; }
static BinaryOperatorKind getOpFromIndex(size_t Index) {
return static_cast<BinaryOperatorKind>(Index + BO_LT);
}
TriStateKind getCmpOpState(BinaryOperatorKind CurrentOP,
BinaryOperatorKind QueriedOP) const {
return CmpOpTable[getIndexFromOp(CurrentOP)][getIndexFromOp(QueriedOP)];
}
TriStateKind getCmpOpStateForUnknownX2(BinaryOperatorKind CurrentOP) const {
return CmpOpTable[getIndexFromOp(CurrentOP)][CmpOpCount];
}
};
//===----------------------------------------------------------------------===//
// RangeSet implementation
//===----------------------------------------------------------------------===//
RangeSet::ContainerType RangeSet::Factory::EmptySet{};
RangeSet RangeSet::Factory::add(RangeSet LHS, RangeSet RHS) {
ContainerType Result;
Result.reserve(LHS.size() + RHS.size());
std::merge(LHS.begin(), LHS.end(), RHS.begin(), RHS.end(),
std::back_inserter(Result));
return makePersistent(std::move(Result));
}
RangeSet RangeSet::Factory::add(RangeSet Original, Range Element) {
ContainerType Result;
Result.reserve(Original.size() + 1);
const_iterator Lower = llvm::lower_bound(Original, Element);
Result.insert(Result.end(), Original.begin(), Lower);
Result.push_back(Element);
Result.insert(Result.end(), Lower, Original.end());
return makePersistent(std::move(Result));
}
RangeSet RangeSet::Factory::add(RangeSet Original, const llvm::APSInt &Point) {
return add(Original, Range(Point));
}
RangeSet RangeSet::Factory::unite(RangeSet LHS, RangeSet RHS) {
ContainerType Result = unite(*LHS.Impl, *RHS.Impl);
return makePersistent(std::move(Result));
}
RangeSet RangeSet::Factory::unite(RangeSet Original, Range R) {
ContainerType Result;
Result.push_back(R);
Result = unite(*Original.Impl, Result);
return makePersistent(std::move(Result));
}
RangeSet RangeSet::Factory::unite(RangeSet Original, llvm::APSInt Point) {
return unite(Original, Range(ValueFactory.getValue(Point)));
}
RangeSet RangeSet::Factory::unite(RangeSet Original, llvm::APSInt From,
llvm::APSInt To) {
return unite(Original,
Range(ValueFactory.getValue(From), ValueFactory.getValue(To)));
}
template <typename T>
void swapIterators(T &First, T &FirstEnd, T &Second, T &SecondEnd) {
std::swap(First, Second);
std::swap(FirstEnd, SecondEnd);
}
RangeSet::ContainerType RangeSet::Factory::unite(const ContainerType &LHS,
const ContainerType &RHS) {
if (LHS.empty())
return RHS;
if (RHS.empty())
return LHS;
using llvm::APSInt;
using iterator = ContainerType::const_iterator;
iterator First = LHS.begin();
iterator FirstEnd = LHS.end();
iterator Second = RHS.begin();
iterator SecondEnd = RHS.end();
APSIntType Ty = APSIntType(First->From());
const APSInt Min = Ty.getMinValue();
// Handle a corner case first when both range sets start from MIN.
// This helps to avoid complicated conditions below. Specifically, this
// particular check for `MIN` is not needed in the loop below every time
// when we do `Second->From() - One` operation.
if (Min == First->From() && Min == Second->From()) {
if (First->To() > Second->To()) {
// [ First ]--->
// [ Second ]----->
// MIN^
// The Second range is entirely inside the First one.
// Check if Second is the last in its RangeSet.
if (++Second == SecondEnd)
// [ First ]--[ First + 1 ]--->
// [ Second ]--------------------->
// MIN^
// The Union is equal to First's RangeSet.
return LHS;
} else {
// case 1: [ First ]----->
// case 2: [ First ]--->
// [ Second ]--->
// MIN^
// The First range is entirely inside or equal to the Second one.
// Check if First is the last in its RangeSet.
if (++First == FirstEnd)
// [ First ]----------------------->
// [ Second ]--[ Second + 1 ]---->
// MIN^
// The Union is equal to Second's RangeSet.
return RHS;
}
}
const APSInt One = Ty.getValue(1);
ContainerType Result;
// This is called when there are no ranges left in one of the ranges.
// Append the rest of the ranges from another range set to the Result
// and return with that.
const auto AppendTheRest = [&Result](iterator I, iterator E) {
Result.append(I, E);
return Result;
};
while (true) {
// We want to keep the following invariant at all times:
// ---[ First ------>
// -----[ Second --->
if (First->From() > Second->From())
swapIterators(First, FirstEnd, Second, SecondEnd);
// The Union definitely starts with First->From().
// ----------[ First ------>
// ------------[ Second --->
// ----------[ Union ------>
// UnionStart^
const llvm::APSInt &UnionStart = First->From();
// Loop where the invariant holds.
while (true) {
// Skip all enclosed ranges.
// ---[ First ]--->
// -----[ Second ]--[ Second + 1 ]--[ Second + N ]----->
while (First->To() >= Second->To()) {
// Check if Second is the last in its RangeSet.
if (++Second == SecondEnd) {
// Append the Union.
// ---[ Union ]--->
// -----[ Second ]----->
// --------[ First ]--->
// UnionEnd^
Result.emplace_back(UnionStart, First->To());
// ---[ Union ]----------------->
// --------------[ First + 1]--->
// Append all remaining ranges from the First's RangeSet.
return AppendTheRest(++First, FirstEnd);
}
}
// Check if First and Second are disjoint. It means that we find
// the end of the Union. Exit the loop and append the Union.
// ---[ First ]=------------->
// ------------=[ Second ]--->
// ----MinusOne^
if (First->To() < Second->From() - One)
break;
// First is entirely inside the Union. Go next.
// ---[ Union ----------->
// ---- [ First ]-------->
// -------[ Second ]----->
// Check if First is the last in its RangeSet.
if (++First == FirstEnd) {
// Append the Union.
// ---[ Union ]--->
// -----[ First ]------->
// --------[ Second ]--->
// UnionEnd^
Result.emplace_back(UnionStart, Second->To());
// ---[ Union ]------------------>
// --------------[ Second + 1]--->
// Append all remaining ranges from the Second's RangeSet.
return AppendTheRest(++Second, SecondEnd);
}
// We know that we are at one of the two cases:
// case 1: --[ First ]--------->
// case 2: ----[ First ]------->
// --------[ Second ]---------->
// In both cases First starts after Second->From().
// Make sure that the loop invariant holds.
swapIterators(First, FirstEnd, Second, SecondEnd);
}
// Here First and Second are disjoint.
// Append the Union.
// ---[ Union ]--------------->
// -----------------[ Second ]--->
// ------[ First ]--------------->
// UnionEnd^
Result.emplace_back(UnionStart, First->To());
// Check if First is the last in its RangeSet.
if (++First == FirstEnd)
// ---[ Union ]--------------->
// --------------[ Second ]--->
// Append all remaining ranges from the Second's RangeSet.
return AppendTheRest(Second, SecondEnd);
}
llvm_unreachable("Normally, we should not reach here");
}
RangeSet RangeSet::Factory::getRangeSet(Range From) {
ContainerType Result;
Result.push_back(From);
return makePersistent(std::move(Result));
}
RangeSet RangeSet::Factory::makePersistent(ContainerType &&From) {
llvm::FoldingSetNodeID ID;
void *InsertPos;
From.Profile(ID);
ContainerType *Result = Cache.FindNodeOrInsertPos(ID, InsertPos);
if (!Result) {
// It is cheaper to fully construct the resulting range on stack
// and move it to the freshly allocated buffer if we don't have
// a set like this already.
Result = construct(std::move(From));
Cache.InsertNode(Result, InsertPos);
}
return Result;
}
RangeSet::ContainerType *RangeSet::Factory::construct(ContainerType &&From) {
void *Buffer = Arena.Allocate();
return new (Buffer) ContainerType(std::move(From));
}
const llvm::APSInt &RangeSet::getMinValue() const {
assert(!isEmpty());
return begin()->From();
}
const llvm::APSInt &RangeSet::getMaxValue() const {
assert(!isEmpty());
return std::prev(end())->To();
}
bool clang::ento::RangeSet::isUnsigned() const {
assert(!isEmpty());
return begin()->From().isUnsigned();
}
uint32_t clang::ento::RangeSet::getBitWidth() const {
assert(!isEmpty());
return begin()->From().getBitWidth();
}
APSIntType clang::ento::RangeSet::getAPSIntType() const {
assert(!isEmpty());
return APSIntType(begin()->From());
}
bool RangeSet::containsImpl(llvm::APSInt &Point) const {
if (isEmpty() || !pin(Point))
return false;
Range Dummy(Point);
const_iterator It = llvm::upper_bound(*this, Dummy);
if (It == begin())
return false;
return std::prev(It)->Includes(Point);
}
bool RangeSet::pin(llvm::APSInt &Point) const {
APSIntType Type(getMinValue());
if (Type.testInRange(Point, true) != APSIntType::RTR_Within)
return false;
Type.apply(Point);
return true;
}
bool RangeSet::pin(llvm::APSInt &Lower, llvm::APSInt &Upper) const {
// This function has nine cases, the cartesian product of range-testing
// both the upper and lower bounds against the symbol's type.
// Each case requires a different pinning operation.
// The function returns false if the described range is entirely outside
// the range of values for the associated symbol.
APSIntType Type(getMinValue());
APSIntType::RangeTestResultKind LowerTest = Type.testInRange(Lower, true);
APSIntType::RangeTestResultKind UpperTest = Type.testInRange(Upper, true);
switch (LowerTest) {
case APSIntType::RTR_Below:
switch (UpperTest) {
case APSIntType::RTR_Below:
// The entire range is outside the symbol's set of possible values.
// If this is a conventionally-ordered range, the state is infeasible.
if (Lower <= Upper)
return false;
// However, if the range wraps around, it spans all possible values.
Lower = Type.getMinValue();
Upper = Type.getMaxValue();
break;
case APSIntType::RTR_Within:
// The range starts below what's possible but ends within it. Pin.
Lower = Type.getMinValue();
Type.apply(Upper);
break;
case APSIntType::RTR_Above:
// The range spans all possible values for the symbol. Pin.
Lower = Type.getMinValue();
Upper = Type.getMaxValue();
break;
}
break;
case APSIntType::RTR_Within:
switch (UpperTest) {
case APSIntType::RTR_Below:
// The range wraps around, but all lower values are not possible.
Type.apply(Lower);
Upper = Type.getMaxValue();
break;
case APSIntType::RTR_Within:
// The range may or may not wrap around, but both limits are valid.
Type.apply(Lower);
Type.apply(Upper);
break;
case APSIntType::RTR_Above:
// The range starts within what's possible but ends above it. Pin.
Type.apply(Lower);
Upper = Type.getMaxValue();
break;
}
break;
case APSIntType::RTR_Above:
switch (UpperTest) {
case APSIntType::RTR_Below:
// The range wraps but is outside the symbol's set of possible values.
return false;
case APSIntType::RTR_Within:
// The range starts above what's possible but ends within it (wrap).
Lower = Type.getMinValue();
Type.apply(Upper);
break;
case APSIntType::RTR_Above:
// The entire range is outside the symbol's set of possible values.
// If this is a conventionally-ordered range, the state is infeasible.
if (Lower <= Upper)
return false;
// However, if the range wraps around, it spans all possible values.
Lower = Type.getMinValue();
Upper = Type.getMaxValue();
break;
}
break;
}
return true;
}
RangeSet RangeSet::Factory::intersect(RangeSet What, llvm::APSInt Lower,
llvm::APSInt Upper) {
if (What.isEmpty() || !What.pin(Lower, Upper))
return getEmptySet();
ContainerType DummyContainer;
if (Lower <= Upper) {
// [Lower, Upper] is a regular range.
//
// Shortcut: check that there is even a possibility of the intersection
// by checking the two following situations:
//
// <---[ What ]---[------]------>
// Lower Upper
// -or-
// <----[------]----[ What ]---->
// Lower Upper
if (What.getMaxValue() < Lower || Upper < What.getMinValue())
return getEmptySet();
DummyContainer.push_back(
Range(ValueFactory.getValue(Lower), ValueFactory.getValue(Upper)));
} else {
// [Lower, Upper] is an inverted range, i.e. [MIN, Upper] U [Lower, MAX]
//
// Shortcut: check that there is even a possibility of the intersection
// by checking the following situation:
//
// <------]---[ What ]---[------>
// Upper Lower
if (What.getMaxValue() < Lower && Upper < What.getMinValue())
return getEmptySet();
DummyContainer.push_back(
Range(ValueFactory.getMinValue(Upper), ValueFactory.getValue(Upper)));
DummyContainer.push_back(
Range(ValueFactory.getValue(Lower), ValueFactory.getMaxValue(Lower)));
}
return intersect(*What.Impl, DummyContainer);
}
RangeSet RangeSet::Factory::intersect(const RangeSet::ContainerType &LHS,
const RangeSet::ContainerType &RHS) {
ContainerType Result;
Result.reserve(std::max(LHS.size(), RHS.size()));
const_iterator First = LHS.begin(), Second = RHS.begin(),
FirstEnd = LHS.end(), SecondEnd = RHS.end();
// If we ran out of ranges in one set, but not in the other,
// it means that those elements are definitely not in the
// intersection.
while (First != FirstEnd && Second != SecondEnd) {
// We want to keep the following invariant at all times:
//
// ----[ First ---------------------->
// --------[ Second ----------------->
if (Second->From() < First->From())
swapIterators(First, FirstEnd, Second, SecondEnd);
// Loop where the invariant holds:
do {
// Check for the following situation:
//
// ----[ First ]--------------------->
// ---------------[ Second ]--------->
//
// which means that...
if (Second->From() > First->To()) {
// ...First is not in the intersection.
//
// We should move on to the next range after First and break out of the
// loop because the invariant might not be true.
++First;
break;
}
// We have a guaranteed intersection at this point!
// And this is the current situation:
//
// ----[ First ]----------------->
// -------[ Second ------------------>
//
// Additionally, it definitely starts with Second->From().
const llvm::APSInt &IntersectionStart = Second->From();
// It is important to know which of the two ranges' ends
// is greater. That "longer" range might have some other
// intersections, while the "shorter" range might not.
if (Second->To() > First->To()) {
// Here we make a decision to keep First as the "longer"
// range.
swapIterators(First, FirstEnd, Second, SecondEnd);
}
// At this point, we have the following situation:
//
// ---- First ]-------------------->
// ---- Second ]--[ Second+1 ---------->
//
// We don't know the relationship between First->From and
// Second->From and we don't know whether Second+1 intersects
// with First.
//
// However, we know that [IntersectionStart, Second->To] is
// a part of the intersection...
Result.push_back(Range(IntersectionStart, Second->To()));
++Second;
// ...and that the invariant will hold for a valid Second+1
// because First->From <= Second->To < (Second+1)->From.
} while (Second != SecondEnd);
}
if (Result.empty())
return getEmptySet();
return makePersistent(std::move(Result));
}
RangeSet RangeSet::Factory::intersect(RangeSet LHS, RangeSet RHS) {
// Shortcut: let's see if the intersection is even possible.
if (LHS.isEmpty() || RHS.isEmpty() || LHS.getMaxValue() < RHS.getMinValue() ||
RHS.getMaxValue() < LHS.getMinValue())
return getEmptySet();
return intersect(*LHS.Impl, *RHS.Impl);
}
RangeSet RangeSet::Factory::intersect(RangeSet LHS, llvm::APSInt Point) {
if (LHS.containsImpl(Point))
return getRangeSet(ValueFactory.getValue(Point));
return getEmptySet();
}
RangeSet RangeSet::Factory::negate(RangeSet What) {
if (What.isEmpty())
return getEmptySet();
const llvm::APSInt SampleValue = What.getMinValue();
const llvm::APSInt &MIN = ValueFactory.getMinValue(SampleValue);
const llvm::APSInt &MAX = ValueFactory.getMaxValue(SampleValue);
ContainerType Result;
Result.reserve(What.size() + (SampleValue == MIN));
// Handle a special case for MIN value.
const_iterator It = What.begin();
const_iterator End = What.end();
const llvm::APSInt &From = It->From();
const llvm::APSInt &To = It->To();
if (From == MIN) {
// If the range [From, To] is [MIN, MAX], then result is also [MIN, MAX].
if (To == MAX) {
return What;
}
const_iterator Last = std::prev(End);
// Try to find and unite the following ranges:
// [MIN, MIN] & [MIN + 1, N] => [MIN, N].
if (Last->To() == MAX) {
// It means that in the original range we have ranges
// [MIN, A], ... , [B, MAX]
// And the result should be [MIN, -B], ..., [-A, MAX]
Result.emplace_back(MIN, ValueFactory.getValue(-Last->From()));
// We already negated Last, so we can skip it.
End = Last;
} else {
// Add a separate range for the lowest value.
Result.emplace_back(MIN, MIN);
}
// Skip adding the second range in case when [From, To] are [MIN, MIN].
if (To != MIN) {
Result.emplace_back(ValueFactory.getValue(-To), MAX);
}
// Skip the first range in the loop.
++It;
}
// Negate all other ranges.
for (; It != End; ++It) {
// Negate int values.
const llvm::APSInt &NewFrom = ValueFactory.getValue(-It->To());
const llvm::APSInt &NewTo = ValueFactory.getValue(-It->From());
// Add a negated range.
Result.emplace_back(NewFrom, NewTo);
}
llvm::sort(Result);
return makePersistent(std::move(Result));
}
// Convert range set to the given integral type using truncation and promotion.
// This works similar to APSIntType::apply function but for the range set.
RangeSet RangeSet::Factory::castTo(RangeSet What, APSIntType Ty) {
// Set is empty or NOOP (aka cast to the same type).
if (What.isEmpty() || What.getAPSIntType() == Ty)
return What;
const bool IsConversion = What.isUnsigned() != Ty.isUnsigned();
const bool IsTruncation = What.getBitWidth() > Ty.getBitWidth();
const bool IsPromotion = What.getBitWidth() < Ty.getBitWidth();
if (IsTruncation)
return makePersistent(truncateTo(What, Ty));
// Here we handle 2 cases:
// - IsConversion && !IsPromotion.
// In this case we handle changing a sign with same bitwidth: char -> uchar,
// uint -> int. Here we convert negatives to positives and positives which
// is out of range to negatives. We use convertTo function for that.
// - IsConversion && IsPromotion && !What.isUnsigned().
// In this case we handle changing a sign from signeds to unsigneds with
// higher bitwidth: char -> uint, int-> uint64. The point is that we also
// need convert negatives to positives and use convertTo function as well.
// For example, we don't need such a convertion when converting unsigned to
// signed with higher bitwidth, because all the values of unsigned is valid
// for the such signed.
if (IsConversion && (!IsPromotion || !What.isUnsigned()))
return makePersistent(convertTo(What, Ty));
assert(IsPromotion && "Only promotion operation from unsigneds left.");
return makePersistent(promoteTo(What, Ty));
}
RangeSet RangeSet::Factory::castTo(RangeSet What, QualType T) {
assert(T->isIntegralOrEnumerationType() && "T shall be an integral type.");
return castTo(What, ValueFactory.getAPSIntType(T));
}
RangeSet::ContainerType RangeSet::Factory::truncateTo(RangeSet What,
APSIntType Ty) {
using llvm::APInt;
using llvm::APSInt;
ContainerType Result;
ContainerType Dummy;
// CastRangeSize is an amount of all possible values of cast type.
// Example: `char` has 256 values; `short` has 65536 values.
// But in fact we use `amount of values` - 1, because
// we can't keep `amount of values of UINT64` inside uint64_t.
// E.g. 256 is an amount of all possible values of `char` and we can't keep
// it inside `char`.
// And it's OK, it's enough to do correct calculations.
uint64_t CastRangeSize = APInt::getMaxValue(Ty.getBitWidth()).getZExtValue();
for (const Range &R : What) {
// Get bounds of the given range.
APSInt FromInt = R.From();
APSInt ToInt = R.To();
// CurrentRangeSize is an amount of all possible values of the current
// range minus one.
uint64_t CurrentRangeSize = (ToInt - FromInt).getZExtValue();
// This is an optimization for a specific case when this Range covers
// the whole range of the target type.
Dummy.clear();
if (CurrentRangeSize >= CastRangeSize) {
Dummy.emplace_back(ValueFactory.getMinValue(Ty),
ValueFactory.getMaxValue(Ty));
Result = std::move(Dummy);
break;
}
// Cast the bounds.
Ty.apply(FromInt);
Ty.apply(ToInt);
const APSInt &PersistentFrom = ValueFactory.getValue(FromInt);
const APSInt &PersistentTo = ValueFactory.getValue(ToInt);
if (FromInt > ToInt) {
Dummy.emplace_back(ValueFactory.getMinValue(Ty), PersistentTo);
Dummy.emplace_back(PersistentFrom, ValueFactory.getMaxValue(Ty));
} else
Dummy.emplace_back(PersistentFrom, PersistentTo);
// Every range retrieved after truncation potentialy has garbage values.
// So, we have to unite every next range with the previouses.
Result = unite(Result, Dummy);
}
return Result;
}
// Divide the convertion into two phases (presented as loops here).
// First phase(loop) works when casted values go in ascending order.
// E.g. char{1,3,5,127} -> uint{1,3,5,127}
// Interrupt the first phase and go to second one when casted values start
// go in descending order. That means that we crossed over the middle of
// the type value set (aka 0 for signeds and MAX/2+1 for unsigneds).
// For instance:
// 1: uchar{1,3,5,128,255} -> char{1,3,5,-128,-1}
// Here we put {1,3,5} to one array and {-128, -1} to another
// 2: char{-128,-127,-1,0,1,2} -> uchar{128,129,255,0,1,3}
// Here we put {128,129,255} to one array and {0,1,3} to another.
// After that we unite both arrays.
// NOTE: We don't just concatenate the arrays, because they may have
// adjacent ranges, e.g.:
// 1: char(-128, 127) -> uchar -> arr1(128, 255), arr2(0, 127) ->
// unite -> uchar(0, 255)
// 2: uchar(0, 1)U(254, 255) -> char -> arr1(0, 1), arr2(-2, -1) ->
// unite -> uchar(-2, 1)
RangeSet::ContainerType RangeSet::Factory::convertTo(RangeSet What,
APSIntType Ty) {
using llvm::APInt;
using llvm::APSInt;
using Bounds = std::pair<const APSInt &, const APSInt &>;
ContainerType AscendArray;
ContainerType DescendArray;
auto CastRange = [Ty, &VF = ValueFactory](const Range &R) -> Bounds {
// Get bounds of the given range.
APSInt FromInt = R.From();
APSInt ToInt = R.To();
// Cast the bounds.
Ty.apply(FromInt);
Ty.apply(ToInt);
return {VF.getValue(FromInt), VF.getValue(ToInt)};
};
// Phase 1. Fill the first array.
APSInt LastConvertedInt = Ty.getMinValue();
const auto *It = What.begin();
const auto *E = What.end();
while (It != E) {
Bounds NewBounds = CastRange(*(It++));
// If values stop going acsending order, go to the second phase(loop).
if (NewBounds.first < LastConvertedInt) {
DescendArray.emplace_back(NewBounds.first, NewBounds.second);
break;
}
// If the range contains a midpoint, then split the range.
// E.g. char(-5, 5) -> uchar(251, 5)
// Here we shall add a range (251, 255) to the first array and (0, 5) to the
// second one.
if (NewBounds.first > NewBounds.second) {
DescendArray.emplace_back(ValueFactory.getMinValue(Ty), NewBounds.second);
AscendArray.emplace_back(NewBounds.first, ValueFactory.getMaxValue(Ty));
} else
// Values are going acsending order.
AscendArray.emplace_back(NewBounds.first, NewBounds.second);
LastConvertedInt = NewBounds.first;
}
// Phase 2. Fill the second array.
while (It != E) {
Bounds NewBounds = CastRange(*(It++));
DescendArray.emplace_back(NewBounds.first, NewBounds.second);
}
// Unite both arrays.
return unite(AscendArray, DescendArray);
}
/// Promotion from unsigneds to signeds/unsigneds left.
RangeSet::ContainerType RangeSet::Factory::promoteTo(RangeSet What,
APSIntType Ty) {
ContainerType Result;
// We definitely know the size of the result set.
Result.reserve(What.size());
// Each unsigned value fits every larger type without any changes,
// whether the larger type is signed or unsigned. So just promote and push
// back each range one by one.
for (const Range &R : What) {
// Get bounds of the given range.
llvm::APSInt FromInt = R.From();
llvm::APSInt ToInt = R.To();
// Cast the bounds.
Ty.apply(FromInt);
Ty.apply(ToInt);
Result.emplace_back(ValueFactory.getValue(FromInt),
ValueFactory.getValue(ToInt));
}
return Result;
}
RangeSet RangeSet::Factory::deletePoint(RangeSet From,
const llvm::APSInt &Point) {
if (!From.contains(Point))
return From;
llvm::APSInt Upper = Point;
llvm::APSInt Lower = Point;
++Upper;
--Lower;
// Notice that the lower bound is greater than the upper bound.
return intersect(From, Upper, Lower);
}
LLVM_DUMP_METHOD void Range::dump(raw_ostream &OS) const {
OS << '[' << toString(From(), 10) << ", " << toString(To(), 10) << ']';
}
LLVM_DUMP_METHOD void Range::dump() const { dump(llvm::errs()); }
LLVM_DUMP_METHOD void RangeSet::dump(raw_ostream &OS) const {
OS << "{ ";
llvm::interleaveComma(*this, OS, [&OS](const Range &R) { R.dump(OS); });
OS << " }";
}
LLVM_DUMP_METHOD void RangeSet::dump() const { dump(llvm::errs()); }
REGISTER_SET_FACTORY_WITH_PROGRAMSTATE(SymbolSet, SymbolRef)
namespace {
class EquivalenceClass;
} // end anonymous namespace
REGISTER_MAP_WITH_PROGRAMSTATE(ClassMap, SymbolRef, EquivalenceClass)
REGISTER_MAP_WITH_PROGRAMSTATE(ClassMembers, EquivalenceClass, SymbolSet)
REGISTER_MAP_WITH_PROGRAMSTATE(ConstraintRange, EquivalenceClass, RangeSet)
REGISTER_SET_FACTORY_WITH_PROGRAMSTATE(ClassSet, EquivalenceClass)
REGISTER_MAP_WITH_PROGRAMSTATE(DisequalityMap, EquivalenceClass, ClassSet)
namespace {
/// This class encapsulates a set of symbols equal to each other.
///
/// The main idea of the approach requiring such classes is in narrowing
/// and sharing constraints between symbols within the class. Also we can
/// conclude that there is no practical need in storing constraints for
/// every member of the class separately.
///
/// Main terminology:
///
/// * "Equivalence class" is an object of this class, which can be efficiently
/// compared to other classes. It represents the whole class without
/// storing the actual in it. The members of the class however can be
/// retrieved from the state.
///
/// * "Class members" are the symbols corresponding to the class. This means
/// that A == B for every member symbols A and B from the class. Members of
/// each class are stored in the state.
///
/// * "Trivial class" is a class that has and ever had only one same symbol.
///
/// * "Merge operation" merges two classes into one. It is the main operation
/// to produce non-trivial classes.
/// If, at some point, we can assume that two symbols from two distinct
/// classes are equal, we can merge these classes.
class EquivalenceClass : public llvm::FoldingSetNode {
public:
/// Find equivalence class for the given symbol in the given state.
[[nodiscard]] static inline EquivalenceClass find(ProgramStateRef State,
SymbolRef Sym);
/// Merge classes for the given symbols and return a new state.
[[nodiscard]] static inline ProgramStateRef merge(RangeSet::Factory &F,
ProgramStateRef State,
SymbolRef First,
SymbolRef Second);
// Merge this class with the given class and return a new state.
[[nodiscard]] inline ProgramStateRef
merge(RangeSet::Factory &F, ProgramStateRef State, EquivalenceClass Other);
/// Return a set of class members for the given state.
[[nodiscard]] inline SymbolSet getClassMembers(ProgramStateRef State) const;
/// Return true if the current class is trivial in the given state.
/// A class is trivial if and only if there is not any member relations stored
/// to it in State/ClassMembers.
/// An equivalence class with one member might seem as it does not hold any
/// meaningful information, i.e. that is a tautology. However, during the
/// removal of dead symbols we do not remove classes with one member for
/// resource and performance reasons. Consequently, a class with one member is
/// not necessarily trivial. It could happen that we have a class with two
/// members and then during the removal of dead symbols we remove one of its
/// members. In this case, the class is still non-trivial (it still has the
/// mappings in ClassMembers), even though it has only one member.
[[nodiscard]] inline bool isTrivial(ProgramStateRef State) const;
/// Return true if the current class is trivial and its only member is dead.
[[nodiscard]] inline bool isTriviallyDead(ProgramStateRef State,
SymbolReaper &Reaper) const;
[[nodiscard]] static inline ProgramStateRef
markDisequal(RangeSet::Factory &F, ProgramStateRef State, SymbolRef First,
SymbolRef Second);
[[nodiscard]] static inline ProgramStateRef
markDisequal(RangeSet::Factory &F, ProgramStateRef State,
EquivalenceClass First, EquivalenceClass Second);
[[nodiscard]] inline ProgramStateRef
markDisequal(RangeSet::Factory &F, ProgramStateRef State,
EquivalenceClass Other) const;
[[nodiscard]] static inline ClassSet getDisequalClasses(ProgramStateRef State,
SymbolRef Sym);
[[nodiscard]] inline ClassSet getDisequalClasses(ProgramStateRef State) const;
[[nodiscard]] inline ClassSet
getDisequalClasses(DisequalityMapTy Map, ClassSet::Factory &Factory) const;
[[nodiscard]] static inline std::optional<bool>
areEqual(ProgramStateRef State, EquivalenceClass First,
EquivalenceClass Second);
[[nodiscard]] static inline std::optional<bool>
areEqual(ProgramStateRef State, SymbolRef First, SymbolRef Second);
/// Remove one member from the class.
[[nodiscard]] ProgramStateRef removeMember(ProgramStateRef State,
const SymbolRef Old);
/// Iterate over all symbols and try to simplify them.
[[nodiscard]] static inline ProgramStateRef simplify(SValBuilder &SVB,
RangeSet::Factory &F,
ProgramStateRef State,
EquivalenceClass Class);
void dumpToStream(ProgramStateRef State, raw_ostream &os) const;
LLVM_DUMP_METHOD void dump(ProgramStateRef State) const {
dumpToStream(State, llvm::errs());
}
/// Check equivalence data for consistency.
[[nodiscard]] LLVM_ATTRIBUTE_UNUSED static bool
isClassDataConsistent(ProgramStateRef State);
[[nodiscard]] QualType getType() const {
return getRepresentativeSymbol()->getType();
}
EquivalenceClass() = delete;
EquivalenceClass(const EquivalenceClass &) = default;
EquivalenceClass &operator=(const EquivalenceClass &) = delete;
EquivalenceClass(EquivalenceClass &&) = default;
EquivalenceClass &operator=(EquivalenceClass &&) = delete;
bool operator==(const EquivalenceClass &Other) const {
return ID == Other.ID;
}
bool operator<(const EquivalenceClass &Other) const { return ID < Other.ID; }
bool operator!=(const EquivalenceClass &Other) const {
return !operator==(Other);
}
static void Profile(llvm::FoldingSetNodeID &ID, uintptr_t CID) {
ID.AddInteger(CID);
}
void Profile(llvm::FoldingSetNodeID &ID) const { Profile(ID, this->ID); }
private:
/* implicit */ EquivalenceClass(SymbolRef Sym)
: ID(reinterpret_cast<uintptr_t>(Sym)) {}
/// This function is intended to be used ONLY within the class.
/// The fact that ID is a pointer to a symbol is an implementation detail
/// and should stay that way.
/// In the current implementation, we use it to retrieve the only member
/// of the trivial class.
SymbolRef getRepresentativeSymbol() const {
return reinterpret_cast<SymbolRef>(ID);
}
static inline SymbolSet::Factory &getMembersFactory(ProgramStateRef State);
inline ProgramStateRef mergeImpl(RangeSet::Factory &F, ProgramStateRef State,
SymbolSet Members, EquivalenceClass Other,
SymbolSet OtherMembers);
static inline bool
addToDisequalityInfo(DisequalityMapTy &Info, ConstraintRangeTy &Constraints,
RangeSet::Factory &F, ProgramStateRef State,
EquivalenceClass First, EquivalenceClass Second);
/// This is a unique identifier of the class.
uintptr_t ID;
};
//===----------------------------------------------------------------------===//
// Constraint functions
//===----------------------------------------------------------------------===//
[[nodiscard]] LLVM_ATTRIBUTE_UNUSED bool
areFeasible(ConstraintRangeTy Constraints) {
return llvm::none_of(
Constraints,
[](const std::pair<EquivalenceClass, RangeSet> &ClassConstraint) {
return ClassConstraint.second.isEmpty();
});
}
[[nodiscard]] inline const RangeSet *getConstraint(ProgramStateRef State,
EquivalenceClass Class) {
return State->get<ConstraintRange>(Class);
}
[[nodiscard]] inline const RangeSet *getConstraint(ProgramStateRef State,
SymbolRef Sym) {
return getConstraint(State, EquivalenceClass::find(State, Sym));
}
[[nodiscard]] ProgramStateRef setConstraint(ProgramStateRef State,
EquivalenceClass Class,
RangeSet Constraint) {
return State->set<ConstraintRange>(Class, Constraint);
}
[[nodiscard]] ProgramStateRef setConstraints(ProgramStateRef State,
ConstraintRangeTy Constraints) {
return State->set<ConstraintRange>(Constraints);
}
//===----------------------------------------------------------------------===//
// Equality/diseqiality abstraction
//===----------------------------------------------------------------------===//
/// A small helper function for detecting symbolic (dis)equality.
///
/// Equality check can have different forms (like a == b or a - b) and this
/// class encapsulates those away if the only thing the user wants to check -
/// whether it's equality/diseqiality or not.
///
/// \returns true if assuming this Sym to be true means equality of operands
/// false if it means disequality of operands
/// std::nullopt otherwise
std::optional<bool> meansEquality(const SymSymExpr *Sym) {
switch (Sym->getOpcode()) {
case BO_Sub:
// This case is: A - B != 0 -> disequality check.
return false;
case BO_EQ:
// This case is: A == B != 0 -> equality check.
return true;
case BO_NE:
// This case is: A != B != 0 -> diseqiality check.
return false;
default:
return std::nullopt;
}
}
//===----------------------------------------------------------------------===//
// Intersection functions
//===----------------------------------------------------------------------===//
template <class SecondTy, class... RestTy>
[[nodiscard]] inline RangeSet intersect(RangeSet::Factory &F, RangeSet Head,
SecondTy Second, RestTy... Tail);
template <class... RangeTy> struct IntersectionTraits;
template <class... TailTy> struct IntersectionTraits<RangeSet, TailTy...> {
// Found RangeSet, no need to check any further
using Type = RangeSet;
};
template <> struct IntersectionTraits<> {
// We ran out of types, and we didn't find any RangeSet, so the result should
// be optional.
using Type = std::optional<RangeSet>;
};
template <class OptionalOrPointer, class... TailTy>
struct IntersectionTraits<OptionalOrPointer, TailTy...> {
// If current type is Optional or a raw pointer, we should keep looking.
using Type = typename IntersectionTraits<TailTy...>::Type;
};
template <class EndTy>
[[nodiscard]] inline EndTy intersect(RangeSet::Factory &F, EndTy End) {
// If the list contains only RangeSet or std::optional<RangeSet>, simply
// return that range set.
return End;
}
[[nodiscard]] LLVM_ATTRIBUTE_UNUSED inline std::optional<RangeSet>
intersect(RangeSet::Factory &F, const RangeSet *End) {
// This is an extraneous conversion from a raw pointer into
// std::optional<RangeSet>
if (End) {
return *End;
}
return std::nullopt;
}
template <class... RestTy>
[[nodiscard]] inline RangeSet intersect(RangeSet::Factory &F, RangeSet Head,
RangeSet Second, RestTy... Tail) {
// Here we call either the <RangeSet,RangeSet,...> or <RangeSet,...> version
// of the function and can be sure that the result is RangeSet.
return intersect(F, F.intersect(Head, Second), Tail...);
}
template <class SecondTy, class... RestTy>
[[nodiscard]] inline RangeSet intersect(RangeSet::Factory &F, RangeSet Head,
SecondTy Second, RestTy... Tail) {
if (Second) {
// Here we call the <RangeSet,RangeSet,...> version of the function...
return intersect(F, Head, *Second, Tail...);
}
// ...and here it is either <RangeSet,RangeSet,...> or <RangeSet,...>, which
// means that the result is definitely RangeSet.
return intersect(F, Head, Tail...);
}
/// Main generic intersect function.
/// It intersects all of the given range sets. If some of the given arguments
/// don't hold a range set (nullptr or std::nullopt), the function will skip
/// them.
///
/// Available representations for the arguments are:
/// * RangeSet
/// * std::optional<RangeSet>
/// * RangeSet *
/// Pointer to a RangeSet is automatically assumed to be nullable and will get
/// checked as well as the optional version. If this behaviour is undesired,
/// please dereference the pointer in the call.
///
/// Return type depends on the arguments' types. If we can be sure in compile
/// time that there will be a range set as a result, the returning type is
/// simply RangeSet, in other cases we have to back off to
/// std::optional<RangeSet>.
///
/// Please, prefer optional range sets to raw pointers. If the last argument is
/// a raw pointer and all previous arguments are std::nullopt, it will cost one
/// additional check to convert RangeSet * into std::optional<RangeSet>.
template <class HeadTy, class SecondTy, class... RestTy>
[[nodiscard]] inline
typename IntersectionTraits<HeadTy, SecondTy, RestTy...>::Type
intersect(RangeSet::Factory &F, HeadTy Head, SecondTy Second,
RestTy... Tail) {
if (Head) {
return intersect(F, *Head, Second, Tail...);
}
return intersect(F, Second, Tail...);
}
//===----------------------------------------------------------------------===//
// Symbolic reasoning logic
//===----------------------------------------------------------------------===//
/// A little component aggregating all of the reasoning we have about
/// the ranges of symbolic expressions.
///
/// Even when we don't know the exact values of the operands, we still
/// can get a pretty good estimate of the result's range.
class SymbolicRangeInferrer
: public SymExprVisitor<SymbolicRangeInferrer, RangeSet> {
public:
template <class SourceType>
static RangeSet inferRange(RangeSet::Factory &F, ProgramStateRef State,
SourceType Origin) {
SymbolicRangeInferrer Inferrer(F, State);
return Inferrer.infer(Origin);
}
RangeSet VisitSymExpr(SymbolRef Sym) {
if (std::optional<RangeSet> RS = getRangeForNegatedSym(Sym))
return *RS;
// If we've reached this line, the actual type of the symbolic
// expression is not supported for advanced inference.
// In this case, we simply backoff to the default "let's simply
// infer the range from the expression's type".
return infer(Sym->getType());
}
RangeSet VisitUnarySymExpr(const UnarySymExpr *USE) {
if (std::optional<RangeSet> RS = getRangeForNegatedUnarySym(USE))
return *RS;
return infer(USE->getType());
}
RangeSet VisitSymIntExpr(const SymIntExpr *Sym) {
return VisitBinaryOperator(Sym);
}
RangeSet VisitIntSymExpr(const IntSymExpr *Sym) {
return VisitBinaryOperator(Sym);
}
RangeSet VisitSymSymExpr(const SymSymExpr *SSE) {
return intersect(
RangeFactory,
// If Sym is a difference of symbols A - B, then maybe we have range
// set stored for B - A.
//
// If we have range set stored for both A - B and B - A then
// calculate the effective range set by intersecting the range set
// for A - B and the negated range set of B - A.
getRangeForNegatedSymSym(SSE),
// If Sym is a comparison expression (except <=>),
// find any other comparisons with the same operands.
// See function description.
getRangeForComparisonSymbol(SSE),
// If Sym is (dis)equality, we might have some information
// on that in our equality classes data structure.
getRangeForEqualities(SSE),
// And we should always check what we can get from the operands.
VisitBinaryOperator(SSE));
}
private:
SymbolicRangeInferrer(RangeSet::Factory &F, ProgramStateRef S)
: ValueFactory(F.getValueFactory()), RangeFactory(F), State(S) {}
/// Infer range information from the given integer constant.
///
/// It's not a real "inference", but is here for operating with
/// sub-expressions in a more polymorphic manner.
RangeSet inferAs(const llvm::APSInt &Val, QualType) {
return {RangeFactory, Val};
}
/// Infer range information from symbol in the context of the given type.
RangeSet inferAs(SymbolRef Sym, QualType DestType) {
QualType ActualType = Sym->getType();
// Check that we can reason about the symbol at all.
if (ActualType->isIntegralOrEnumerationType() ||
Loc::isLocType(ActualType)) {
return infer(Sym);
}
// Otherwise, let's simply infer from the destination type.
// We couldn't figure out nothing else about that expression.
return infer(DestType);
}
RangeSet infer(SymbolRef Sym) {
return intersect(RangeFactory,
// Of course, we should take the constraint directly
// associated with this symbol into consideration.
getConstraint(State, Sym),
// Apart from the Sym itself, we can infer quite a lot if
// we look into subexpressions of Sym.
Visit(Sym));
}
RangeSet infer(EquivalenceClass Class) {
if (const RangeSet *AssociatedConstraint = getConstraint(State, Class))
return *AssociatedConstraint;
return infer(Class.getType());
}
/// Infer range information solely from the type.
RangeSet infer(QualType T) {
// Lazily generate a new RangeSet representing all possible values for the
// given symbol type.
RangeSet Result(RangeFactory, ValueFactory.getMinValue(T),
ValueFactory.getMaxValue(T));
// References are known to be non-zero.
if (T->isReferenceType())
return assumeNonZero(Result, T);
return Result;
}
template <class BinarySymExprTy>
RangeSet VisitBinaryOperator(const BinarySymExprTy *Sym) {
// TODO #1: VisitBinaryOperator implementation might not make a good
// use of the inferred ranges. In this case, we might be calculating
// everything for nothing. This being said, we should introduce some
// sort of laziness mechanism here.
//
// TODO #2: We didn't go into the nested expressions before, so it
// might cause us spending much more time doing the inference.
// This can be a problem for deeply nested expressions that are
// involved in conditions and get tested continuously. We definitely
// need to address this issue and introduce some sort of caching
// in here.
QualType ResultType = Sym->getType();
return VisitBinaryOperator(inferAs(Sym->getLHS(), ResultType),
Sym->getOpcode(),
inferAs(Sym->getRHS(), ResultType), ResultType);
}
RangeSet VisitBinaryOperator(RangeSet LHS, BinaryOperator::Opcode Op,
RangeSet RHS, QualType T);
//===----------------------------------------------------------------------===//
// Ranges and operators
//===----------------------------------------------------------------------===//
/// Return a rough approximation of the given range set.
///
/// For the range set:
/// { [x_0, y_0], [x_1, y_1], ... , [x_N, y_N] }
/// it will return the range [x_0, y_N].
static Range fillGaps(RangeSet Origin) {
assert(!Origin.isEmpty());
return {Origin.getMinValue(), Origin.getMaxValue()};
}
/// Try to convert given range into the given type.
///
/// It will return std::nullopt only when the trivial conversion is possible.
std::optional<Range> convert(const Range &Origin, APSIntType To) {
if (To.testInRange(Origin.From(), false) != APSIntType::RTR_Within ||
To.testInRange(Origin.To(), false) != APSIntType::RTR_Within) {
return std::nullopt;
}
return Range(ValueFactory.Convert(To, Origin.From()),
ValueFactory.Convert(To, Origin.To()));
}
template <BinaryOperator::Opcode Op>
RangeSet VisitBinaryOperator(RangeSet LHS, RangeSet RHS, QualType T) {
assert(!LHS.isEmpty() && !RHS.isEmpty());
Range CoarseLHS = fillGaps(LHS);
Range CoarseRHS = fillGaps(RHS);
APSIntType ResultType = ValueFactory.getAPSIntType(T);
// We need to convert ranges to the resulting type, so we can compare values
// and combine them in a meaningful (in terms of the given operation) way.
auto ConvertedCoarseLHS = convert(CoarseLHS, ResultType);
auto ConvertedCoarseRHS = convert(CoarseRHS, ResultType);
// It is hard to reason about ranges when conversion changes
// borders of the ranges.
if (!ConvertedCoarseLHS || !ConvertedCoarseRHS) {
return infer(T);
}
return VisitBinaryOperator<Op>(*ConvertedCoarseLHS, *ConvertedCoarseRHS, T);
}
template <BinaryOperator::Opcode Op>
RangeSet VisitBinaryOperator(Range LHS, Range RHS, QualType T) {
return infer(T);
}
/// Return a symmetrical range for the given range and type.
///
/// If T is signed, return the smallest range [-x..x] that covers the original
/// range, or [-min(T), max(T)] if the aforementioned symmetric range doesn't
/// exist due to original range covering min(T)).
///
/// If T is unsigned, return the smallest range [0..x] that covers the
/// original range.
Range getSymmetricalRange(Range Origin, QualType T) {
APSIntType RangeType = ValueFactory.getAPSIntType(T);
if (RangeType.isUnsigned()) {
return Range(ValueFactory.getMinValue(RangeType), Origin.To());
}
if (Origin.From().isMinSignedValue()) {
// If mini is a minimal signed value, absolute value of it is greater
// than the maximal signed value. In order to avoid these
// complications, we simply return the whole range.
return {ValueFactory.getMinValue(RangeType),
ValueFactory.getMaxValue(RangeType)};
}
// At this point, we are sure that the type is signed and we can safely
// use unary - operator.
//
// While calculating absolute maximum, we can use the following formula
// because of these reasons:
// * If From >= 0 then To >= From and To >= -From.
// AbsMax == To == max(To, -From)
// * If To <= 0 then -From >= -To and -From >= From.
// AbsMax == -From == max(-From, To)
// * Otherwise, From <= 0, To >= 0, and
// AbsMax == max(abs(From), abs(To))
llvm::APSInt AbsMax = std::max(-Origin.From(), Origin.To());
// Intersection is guaranteed to be non-empty.
return {ValueFactory.getValue(-AbsMax), ValueFactory.getValue(AbsMax)};
}
/// Return a range set subtracting zero from \p Domain.
RangeSet assumeNonZero(RangeSet Domain, QualType T) {
APSIntType IntType = ValueFactory.getAPSIntType(T);
return RangeFactory.deletePoint(Domain, IntType.getZeroValue());
}
template <typename ProduceNegatedSymFunc>
std::optional<RangeSet> getRangeForNegatedExpr(ProduceNegatedSymFunc F,
QualType T) {
// Do not negate if the type cannot be meaningfully negated.
if (!T->isUnsignedIntegerOrEnumerationType() &&
!T->isSignedIntegerOrEnumerationType())
return std::nullopt;
if (SymbolRef NegatedSym = F())
if (const RangeSet *NegatedRange = getConstraint(State, NegatedSym))
return RangeFactory.negate(*NegatedRange);
return std::nullopt;
}
std::optional<RangeSet> getRangeForNegatedUnarySym(const UnarySymExpr *USE) {
// Just get the operand when we negate a symbol that is already negated.
// -(-a) == a
return getRangeForNegatedExpr(
[USE]() -> SymbolRef {
if (USE->getOpcode() == UO_Minus)
return USE->getOperand();
return nullptr;
},
USE->getType());
}
std::optional<RangeSet> getRangeForNegatedSymSym(const SymSymExpr *SSE) {
return getRangeForNegatedExpr(
[SSE, State = this->State]() -> SymbolRef {
if (SSE->getOpcode() == BO_Sub)
return State->getSymbolManager().getSymSymExpr(
SSE->getRHS(), BO_Sub, SSE->getLHS(), SSE->getType());
return nullptr;
},
SSE->getType());
}
std::optional<RangeSet> getRangeForNegatedSym(SymbolRef Sym) {
return getRangeForNegatedExpr(
[Sym, State = this->State]() {
return State->getSymbolManager().getUnarySymExpr(Sym, UO_Minus,
Sym->getType());
},
Sym->getType());
}
// Returns ranges only for binary comparison operators (except <=>)
// when left and right operands are symbolic values.
// Finds any other comparisons with the same operands.
// Then do logical calculations and refuse impossible branches.
// E.g. (x < y) and (x > y) at the same time are impossible.
// E.g. (x >= y) and (x != y) at the same time makes (x > y) true only.
// E.g. (x == y) and (y == x) are just reversed but the same.
// It covers all possible combinations (see CmpOpTable description).
// Note that `x` and `y` can also stand for subexpressions,
// not only for actual symbols.
std::optional<RangeSet> getRangeForComparisonSymbol(const SymSymExpr *SSE) {
const BinaryOperatorKind CurrentOP = SSE->getOpcode();
// We currently do not support <=> (C++20).
if (!BinaryOperator::isComparisonOp(CurrentOP) || (CurrentOP == BO_Cmp))
return std::nullopt;
static const OperatorRelationsTable CmpOpTable{};
const SymExpr *LHS = SSE->getLHS();
const SymExpr *RHS = SSE->getRHS();
QualType T = SSE->getType();
SymbolManager &SymMgr = State->getSymbolManager();
// We use this variable to store the last queried operator (`QueriedOP`)
// for which the `getCmpOpState` returned with `Unknown`. If there are two
// different OPs that returned `Unknown` then we have to query the special
// `UnknownX2` column. We assume that `getCmpOpState(CurrentOP, CurrentOP)`
// never returns `Unknown`, so `CurrentOP` is a good initial value.
BinaryOperatorKind LastQueriedOpToUnknown = CurrentOP;
// Loop goes through all of the columns exept the last one ('UnknownX2').
// We treat `UnknownX2` column separately at the end of the loop body.
for (size_t i = 0; i < CmpOpTable.getCmpOpCount(); ++i) {
// Let's find an expression e.g. (x < y).
BinaryOperatorKind QueriedOP = OperatorRelationsTable::getOpFromIndex(i);
const SymSymExpr *SymSym = SymMgr.getSymSymExpr(LHS, QueriedOP, RHS, T);
const RangeSet *QueriedRangeSet = getConstraint(State, SymSym);
// If ranges were not previously found,
// try to find a reversed expression (y > x).
if (!QueriedRangeSet) {
const BinaryOperatorKind ROP =
BinaryOperator::reverseComparisonOp(QueriedOP);
SymSym = SymMgr.getSymSymExpr(RHS, ROP, LHS, T);
QueriedRangeSet = getConstraint(State, SymSym);
}
if (!QueriedRangeSet || QueriedRangeSet->isEmpty())
continue;
const llvm::APSInt *ConcreteValue = QueriedRangeSet->getConcreteValue();
const bool isInFalseBranch =
ConcreteValue ? (*ConcreteValue == 0) : false;
// If it is a false branch, we shall be guided by opposite operator,
// because the table is made assuming we are in the true branch.
// E.g. when (x <= y) is false, then (x > y) is true.
if (isInFalseBranch)
QueriedOP = BinaryOperator::negateComparisonOp(QueriedOP);
OperatorRelationsTable::TriStateKind BranchState =
CmpOpTable.getCmpOpState(CurrentOP, QueriedOP);
if (BranchState == OperatorRelationsTable::Unknown) {
if (LastQueriedOpToUnknown != CurrentOP &&
LastQueriedOpToUnknown != QueriedOP) {
// If we got the Unknown state for both different operators.
// if (x <= y) // assume true
// if (x != y) // assume true
// if (x < y) // would be also true
// Get a state from `UnknownX2` column.
BranchState = CmpOpTable.getCmpOpStateForUnknownX2(CurrentOP);
} else {
LastQueriedOpToUnknown = QueriedOP;
continue;
}
}
return (BranchState == OperatorRelationsTable::True) ? getTrueRange(T)
: getFalseRange(T);
}
return std::nullopt;
}
std::optional<RangeSet> getRangeForEqualities(const SymSymExpr *Sym) {
std::optional<bool> Equality = meansEquality(Sym);
if (!Equality)
return std::nullopt;
if (std::optional<bool> AreEqual =
EquivalenceClass::areEqual(State, Sym->getLHS(), Sym->getRHS())) {
// Here we cover two cases at once:
// * if Sym is equality and its operands are known to be equal -> true
// * if Sym is disequality and its operands are disequal -> true
if (*AreEqual == *Equality) {
return getTrueRange(Sym->getType());
}
// Opposite combinations result in false.
return getFalseRange(Sym->getType());
}
return std::nullopt;
}
RangeSet getTrueRange(QualType T) {
RangeSet TypeRange = infer(T);
return assumeNonZero(TypeRange, T);
}
RangeSet getFalseRange(QualType T) {
const llvm::APSInt &Zero = ValueFactory.getValue(0, T);
return RangeSet(RangeFactory, Zero);
}
BasicValueFactory &ValueFactory;
RangeSet::Factory &RangeFactory;
ProgramStateRef State;
};
//===----------------------------------------------------------------------===//
// Range-based reasoning about symbolic operations
//===----------------------------------------------------------------------===//
template <>
RangeSet SymbolicRangeInferrer::VisitBinaryOperator<BO_NE>(RangeSet LHS,
RangeSet RHS,
QualType T) {
assert(!LHS.isEmpty() && !RHS.isEmpty());
if (LHS.getAPSIntType() == RHS.getAPSIntType()) {
if (intersect(RangeFactory, LHS, RHS).isEmpty())
return getTrueRange(T);
} else {
// We can only lose information if we are casting smaller signed type to
// bigger unsigned type. For e.g.,
// LHS (unsigned short): [2, USHRT_MAX]
// RHS (signed short): [SHRT_MIN, 0]
//
// Casting RHS to LHS type will leave us with overlapping values
// CastedRHS : [0, 0] U [SHRT_MAX + 1, USHRT_MAX]
//
// We can avoid this by checking if signed type's maximum value is lesser
// than unsigned type's minimum value.
// If both have different signs then only we can get more information.
if (LHS.isUnsigned() != RHS.isUnsigned()) {
if (LHS.isUnsigned() && (LHS.getBitWidth() >= RHS.getBitWidth())) {
if (RHS.getMaxValue().isNegative() ||
LHS.getAPSIntType().convert(RHS.getMaxValue()) < LHS.getMinValue())
return getTrueRange(T);
} else if (RHS.isUnsigned() && (LHS.getBitWidth() <= RHS.getBitWidth())) {
if (LHS.getMaxValue().isNegative() ||
RHS.getAPSIntType().convert(LHS.getMaxValue()) < RHS.getMinValue())
return getTrueRange(T);
}
}
// Both RangeSets should be casted to bigger unsigned type.
APSIntType CastingType(std::max(LHS.getBitWidth(), RHS.getBitWidth()),
LHS.isUnsigned() || RHS.isUnsigned());
RangeSet CastedLHS = RangeFactory.castTo(LHS, CastingType);
RangeSet CastedRHS = RangeFactory.castTo(RHS, CastingType);
if (intersect(RangeFactory, CastedLHS, CastedRHS).isEmpty())
return getTrueRange(T);
}
// In all other cases, the resulting range cannot be deduced.
return infer(T);
}
template <>
RangeSet SymbolicRangeInferrer::VisitBinaryOperator<BO_Or>(Range LHS, Range RHS,
QualType T) {
APSIntType ResultType = ValueFactory.getAPSIntType(T);
llvm::APSInt Zero = ResultType.getZeroValue();
bool IsLHSPositiveOrZero = LHS.From() >= Zero;
bool IsRHSPositiveOrZero = RHS.From() >= Zero;
bool IsLHSNegative = LHS.To() < Zero;
bool IsRHSNegative = RHS.To() < Zero;
// Check if both ranges have the same sign.
if ((IsLHSPositiveOrZero && IsRHSPositiveOrZero) ||
(IsLHSNegative && IsRHSNegative)) {
// The result is definitely greater or equal than any of the operands.
const llvm::APSInt &Min = std::max(LHS.From(), RHS.From());
// We estimate maximal value for positives as the maximal value for the
// given type. For negatives, we estimate it with -1 (e.g. 0x11111111).
//
// TODO: We basically, limit the resulting range from below, but don't do
// anything with the upper bound.
//
// For positive operands, it can be done as follows: for the upper
// bound of LHS and RHS we calculate the most significant bit set.
// Let's call it the N-th bit. Then we can estimate the maximal
// number to be 2^(N+1)-1, i.e. the number with all the bits up to
// the N-th bit set.
const llvm::APSInt &Max = IsLHSNegative
? ValueFactory.getValue(--Zero)
: ValueFactory.getMaxValue(ResultType);
return {RangeFactory, ValueFactory.getValue(Min), Max};
}
// Otherwise, let's check if at least one of the operands is negative.
if (IsLHSNegative || IsRHSNegative) {
// This means that the result is definitely negative as well.
return {RangeFactory, ValueFactory.getMinValue(ResultType),
ValueFactory.getValue(--Zero)};
}
RangeSet DefaultRange = infer(T);
// It is pretty hard to reason about operands with different signs
// (and especially with possibly different signs). We simply check if it
// can be zero. In order to conclude that the result could not be zero,
// at least one of the operands should be definitely not zero itself.
if (!LHS.Includes(Zero) || !RHS.Includes(Zero)) {
return assumeNonZero(DefaultRange, T);
}
// Nothing much else to do here.
return DefaultRange;
}
template <>
RangeSet SymbolicRangeInferrer::VisitBinaryOperator<BO_And>(Range LHS,
Range RHS,
QualType T) {
APSIntType ResultType = ValueFactory.getAPSIntType(T);
llvm::APSInt Zero = ResultType.getZeroValue();
bool IsLHSPositiveOrZero = LHS.From() >= Zero;
bool IsRHSPositiveOrZero = RHS.From() >= Zero;
bool IsLHSNegative = LHS.To() < Zero;
bool IsRHSNegative = RHS.To() < Zero;
// Check if both ranges have the same sign.
if ((IsLHSPositiveOrZero && IsRHSPositiveOrZero) ||
(IsLHSNegative && IsRHSNegative)) {
// The result is definitely less or equal than any of the operands.
const llvm::APSInt &Max = std::min(LHS.To(), RHS.To());
// We conservatively estimate lower bound to be the smallest positive
// or negative value corresponding to the sign of the operands.
const llvm::APSInt &Min = IsLHSNegative
? ValueFactory.getMinValue(ResultType)
: ValueFactory.getValue(Zero);
return {RangeFactory, Min, Max};
}
// Otherwise, let's check if at least one of the operands is positive.
if (IsLHSPositiveOrZero || IsRHSPositiveOrZero) {
// This makes result definitely positive.
//
// We can also reason about a maximal value by finding the maximal
// value of the positive operand.
const llvm::APSInt &Max = IsLHSPositiveOrZero ? LHS.To() : RHS.To();
// The minimal value on the other hand is much harder to reason about.
// The only thing we know for sure is that the result is positive.
return {RangeFactory, ValueFactory.getValue(Zero),
ValueFactory.getValue(Max)};
}
// Nothing much else to do here.
return infer(T);
}
template <>
RangeSet SymbolicRangeInferrer::VisitBinaryOperator<BO_Rem>(Range LHS,
Range RHS,
QualType T) {
llvm::APSInt Zero = ValueFactory.getAPSIntType(T).getZeroValue();
Range ConservativeRange = getSymmetricalRange(RHS, T);
llvm::APSInt Max = ConservativeRange.To();
llvm::APSInt Min = ConservativeRange.From();
if (Max == Zero) {
// It's an undefined behaviour to divide by 0 and it seems like we know
// for sure that RHS is 0. Let's say that the resulting range is
// simply infeasible for that matter.
return RangeFactory.getEmptySet();
}
// At this point, our conservative range is closed. The result, however,
// couldn't be greater than the RHS' maximal absolute value. Because of
// this reason, we turn the range into open (or half-open in case of
// unsigned integers).
//
// While we operate on integer values, an open interval (a, b) can be easily
// represented by the closed interval [a + 1, b - 1]. And this is exactly
// what we do next.
//
// If we are dealing with unsigned case, we shouldn't move the lower bound.
if (Min.isSigned()) {
++Min;
}
--Max;
bool IsLHSPositiveOrZero = LHS.From() >= Zero;
bool IsRHSPositiveOrZero = RHS.From() >= Zero;
// Remainder operator results with negative operands is implementation
// defined. Positive cases are much easier to reason about though.
if (IsLHSPositiveOrZero && IsRHSPositiveOrZero) {
// If maximal value of LHS is less than maximal value of RHS,
// the result won't get greater than LHS.To().
Max = std::min(LHS.To(), Max);
// We want to check if it is a situation similar to the following:
//
// <------------|---[ LHS ]--------[ RHS ]----->
// -INF 0 +INF
//
// In this situation, we can conclude that (LHS / RHS) == 0 and
// (LHS % RHS) == LHS.
Min = LHS.To() < RHS.From() ? LHS.From() : Zero;
}
// Nevertheless, the symmetrical range for RHS is a conservative estimate
// for any sign of either LHS, or RHS.
return {RangeFactory, ValueFactory.getValue(Min), ValueFactory.getValue(Max)};
}
RangeSet SymbolicRangeInferrer::VisitBinaryOperator(RangeSet LHS,
BinaryOperator::Opcode Op,
RangeSet RHS, QualType T) {
// We should propagate information about unfeasbility of one of the
// operands to the resulting range.
if (LHS.isEmpty() || RHS.isEmpty()) {
return RangeFactory.getEmptySet();
}
switch (Op) {
case BO_NE:
return VisitBinaryOperator<BO_NE>(LHS, RHS, T);
case BO_Or:
return VisitBinaryOperator<BO_Or>(LHS, RHS, T);
case BO_And:
return VisitBinaryOperator<BO_And>(LHS, RHS, T);
case BO_Rem:
return VisitBinaryOperator<BO_Rem>(LHS, RHS, T);
default:
return infer(T);
}
}
//===----------------------------------------------------------------------===//
// Constraint manager implementation details
//===----------------------------------------------------------------------===//
class RangeConstraintManager : public RangedConstraintManager {
public:
RangeConstraintManager(ExprEngine *EE, SValBuilder &SVB)
: RangedConstraintManager(EE, SVB), F(getBasicVals()) {}
//===------------------------------------------------------------------===//
// Implementation for interface from ConstraintManager.
//===------------------------------------------------------------------===//
bool haveEqualConstraints(ProgramStateRef S1,
ProgramStateRef S2) const override {
// NOTE: ClassMembers are as simple as back pointers for ClassMap,
// so comparing constraint ranges and class maps should be
// sufficient.
return S1->get<ConstraintRange>() == S2->get<ConstraintRange>() &&
S1->get<ClassMap>() == S2->get<ClassMap>();
}
bool canReasonAbout(SVal X) const override;
ConditionTruthVal checkNull(ProgramStateRef State, SymbolRef Sym) override;
const llvm::APSInt *getSymVal(ProgramStateRef State,
SymbolRef Sym) const override;
const llvm::APSInt *getSymMinVal(ProgramStateRef State,
SymbolRef Sym) const override;
const llvm::APSInt *getSymMaxVal(ProgramStateRef State,
SymbolRef Sym) const override;
ProgramStateRef removeDeadBindings(ProgramStateRef State,
SymbolReaper &SymReaper) override;
void printJson(raw_ostream &Out, ProgramStateRef State, const char *NL = "\n",
unsigned int Space = 0, bool IsDot = false) const override;
void printValue(raw_ostream &Out, ProgramStateRef State,
SymbolRef Sym) override;
void printConstraints(raw_ostream &Out, ProgramStateRef State,
const char *NL = "\n", unsigned int Space = 0,
bool IsDot = false) const;
void printEquivalenceClasses(raw_ostream &Out, ProgramStateRef State,
const char *NL = "\n", unsigned int Space = 0,
bool IsDot = false) const;
void printDisequalities(raw_ostream &Out, ProgramStateRef State,
const char *NL = "\n", unsigned int Space = 0,
bool IsDot = false) const;
//===------------------------------------------------------------------===//
// Implementation for interface from RangedConstraintManager.
//===------------------------------------------------------------------===//
ProgramStateRef assumeSymNE(ProgramStateRef State, SymbolRef Sym,
const llvm::APSInt &V,
const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymEQ(ProgramStateRef State, SymbolRef Sym,
const llvm::APSInt &V,
const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymLT(ProgramStateRef State, SymbolRef Sym,
const llvm::APSInt &V,
const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymGT(ProgramStateRef State, SymbolRef Sym,
const llvm::APSInt &V,
const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymLE(ProgramStateRef State, SymbolRef Sym,
const llvm::APSInt &V,
const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymGE(ProgramStateRef State, SymbolRef Sym,
const llvm::APSInt &V,
const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymWithinInclusiveRange(
ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
const llvm::APSInt &To, const llvm::APSInt &Adjustment) override;
ProgramStateRef assumeSymOutsideInclusiveRange(
ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
const llvm::APSInt &To, const llvm::APSInt &Adjustment) override;
private:
RangeSet::Factory F;
RangeSet getRange(ProgramStateRef State, SymbolRef Sym);
RangeSet getRange(ProgramStateRef State, EquivalenceClass Class);
ProgramStateRef setRange(ProgramStateRef State, SymbolRef Sym,
RangeSet Range);
ProgramStateRef setRange(ProgramStateRef State, EquivalenceClass Class,
RangeSet Range);
RangeSet getSymLTRange(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment);
RangeSet getSymGTRange(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment);
RangeSet getSymLERange(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment);
RangeSet getSymLERange(llvm::function_ref<RangeSet()> RS,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment);
RangeSet getSymGERange(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment);
};
//===----------------------------------------------------------------------===//
// Constraint assignment logic
//===----------------------------------------------------------------------===//
/// ConstraintAssignorBase is a small utility class that unifies visitor
/// for ranges with a visitor for constraints (rangeset/range/constant).
///
/// It is designed to have one derived class, but generally it can have more.
/// Derived class can control which types we handle by defining methods of the
/// following form:
///
/// bool handle${SYMBOL}To${CONSTRAINT}(const SYMBOL *Sym,
/// CONSTRAINT Constraint);
///
/// where SYMBOL is the type of the symbol (e.g. SymSymExpr, SymbolCast, etc.)
/// CONSTRAINT is the type of constraint (RangeSet/Range/Const)
/// return value signifies whether we should try other handle methods
/// (i.e. false would mean to stop right after calling this method)
template <class Derived> class ConstraintAssignorBase {
public:
using Const = const llvm::APSInt &;
#define DISPATCH(CLASS) return assign##CLASS##Impl(cast<CLASS>(Sym), Constraint)
#define ASSIGN(CLASS, TO, SYM, CONSTRAINT) \
if (!static_cast<Derived *>(this)->assign##CLASS##To##TO(SYM, CONSTRAINT)) \
return false
void assign(SymbolRef Sym, RangeSet Constraint) {
assignImpl(Sym, Constraint);
}
bool assignImpl(SymbolRef Sym, RangeSet Constraint) {
switch (Sym->getKind()) {
#define SYMBOL(Id, Parent) \
case SymExpr::Id##Kind: \
DISPATCH(Id);
#include "clang/StaticAnalyzer/Core/PathSensitive/Symbols.def"
}
llvm_unreachable("Unknown SymExpr kind!");
}
#define DEFAULT_ASSIGN(Id) \
bool assign##Id##To##RangeSet(const Id *Sym, RangeSet Constraint) { \
return true; \
} \
bool assign##Id##To##Range(const Id *Sym, Range Constraint) { return true; } \
bool assign##Id##To##Const(const Id *Sym, Const Constraint) { return true; }
// When we dispatch for constraint types, we first try to check
// if the new constraint is the constant and try the corresponding
// assignor methods. If it didn't interrupt, we can proceed to the
// range, and finally to the range set.
#define CONSTRAINT_DISPATCH(Id) \
if (const llvm::APSInt *Const = Constraint.getConcreteValue()) { \
ASSIGN(Id, Const, Sym, *Const); \
} \
if (Constraint.size() == 1) { \
ASSIGN(Id, Range, Sym, *Constraint.begin()); \
} \
ASSIGN(Id, RangeSet, Sym, Constraint)
// Our internal assign method first tries to call assignor methods for all
// constraint types that apply. And if not interrupted, continues with its
// parent class.
#define SYMBOL(Id, Parent) \
bool assign##Id##Impl(const Id *Sym, RangeSet Constraint) { \
CONSTRAINT_DISPATCH(Id); \
DISPATCH(Parent); \
} \
DEFAULT_ASSIGN(Id)
#define ABSTRACT_SYMBOL(Id, Parent) SYMBOL(Id, Parent)
#include "clang/StaticAnalyzer/Core/PathSensitive/Symbols.def"
// Default implementations for the top class that doesn't have parents.
bool assignSymExprImpl(const SymExpr *Sym, RangeSet Constraint) {
CONSTRAINT_DISPATCH(SymExpr);
return true;
}
DEFAULT_ASSIGN(SymExpr);
#undef DISPATCH
#undef CONSTRAINT_DISPATCH
#undef DEFAULT_ASSIGN
#undef ASSIGN
};
/// A little component aggregating all of the reasoning we have about
/// assigning new constraints to symbols.
///
/// The main purpose of this class is to associate constraints to symbols,
/// and impose additional constraints on other symbols, when we can imply
/// them.
///
/// It has a nice symmetry with SymbolicRangeInferrer. When the latter
/// can provide more precise ranges by looking into the operands of the
/// expression in question, ConstraintAssignor looks into the operands
/// to see if we can imply more from the new constraint.
class ConstraintAssignor : public ConstraintAssignorBase<ConstraintAssignor> {
public:
template <class ClassOrSymbol>
[[nodiscard]] static ProgramStateRef
assign(ProgramStateRef State, SValBuilder &Builder, RangeSet::Factory &F,
ClassOrSymbol CoS, RangeSet NewConstraint) {
if (!State || NewConstraint.isEmpty())
return nullptr;
ConstraintAssignor Assignor{State, Builder, F};
return Assignor.assign(CoS, NewConstraint);
}
/// Handle expressions like: a % b != 0.
template <typename SymT>
bool handleRemainderOp(const SymT *Sym, RangeSet Constraint) {
if (Sym->getOpcode() != BO_Rem)
return true;
// a % b != 0 implies that a != 0.
if (!Constraint.containsZero()) {
SVal SymSVal = Builder.makeSymbolVal(Sym->getLHS());
if (auto NonLocSymSVal = SymSVal.getAs<nonloc::SymbolVal>()) {
State = State->assume(*NonLocSymSVal, true);
if (!State)
return false;
}
}
return true;
}
inline bool assignSymExprToConst(const SymExpr *Sym, Const Constraint);
inline bool assignSymIntExprToRangeSet(const SymIntExpr *Sym,
RangeSet Constraint) {
return handleRemainderOp(Sym, Constraint);
}
inline bool assignSymSymExprToRangeSet(const SymSymExpr *Sym,
RangeSet Constraint);
private:
ConstraintAssignor(ProgramStateRef State, SValBuilder &Builder,
RangeSet::Factory &F)
: State(State), Builder(Builder), RangeFactory(F) {}
using Base = ConstraintAssignorBase<ConstraintAssignor>;
/// Base method for handling new constraints for symbols.
[[nodiscard]] ProgramStateRef assign(SymbolRef Sym, RangeSet NewConstraint) {
// All constraints are actually associated with equivalence classes, and
// that's what we are going to do first.
State = assign(EquivalenceClass::find(State, Sym), NewConstraint);
if (!State)
return nullptr;
// And after that we can check what other things we can get from this
// constraint.
Base::assign(Sym, NewConstraint);
return State;
}
/// Base method for handling new constraints for classes.
[[nodiscard]] ProgramStateRef assign(EquivalenceClass Class,
RangeSet NewConstraint) {
// There is a chance that we might need to update constraints for the
// classes that are known to be disequal to Class.
//
// In order for this to be even possible, the new constraint should
// be simply a constant because we can't reason about range disequalities.
if (const llvm::APSInt *Point = NewConstraint.getConcreteValue()) {
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
ConstraintRangeTy::Factory &CF = State->get_context<ConstraintRange>();
// Add new constraint.
Constraints = CF.add(Constraints, Class, NewConstraint);
for (EquivalenceClass DisequalClass : Class.getDisequalClasses(State)) {
RangeSet UpdatedConstraint = SymbolicRangeInferrer::inferRange(
RangeFactory, State, DisequalClass);
UpdatedConstraint = RangeFactory.deletePoint(UpdatedConstraint, *Point);
// If we end up with at least one of the disequal classes to be
// constrained with an empty range-set, the state is infeasible.
if (UpdatedConstraint.isEmpty())
return nullptr;
Constraints = CF.add(Constraints, DisequalClass, UpdatedConstraint);
}
assert(areFeasible(Constraints) && "Constraint manager shouldn't produce "
"a state with infeasible constraints");
return setConstraints(State, Constraints);
}
return setConstraint(State, Class, NewConstraint);
}
ProgramStateRef trackDisequality(ProgramStateRef State, SymbolRef LHS,
SymbolRef RHS) {
return EquivalenceClass::markDisequal(RangeFactory, State, LHS, RHS);
}
ProgramStateRef trackEquality(ProgramStateRef State, SymbolRef LHS,
SymbolRef RHS) {
return EquivalenceClass::merge(RangeFactory, State, LHS, RHS);
}
[[nodiscard]] std::optional<bool> interpreteAsBool(RangeSet Constraint) {
assert(!Constraint.isEmpty() && "Empty ranges shouldn't get here");
if (Constraint.getConcreteValue())
return !Constraint.getConcreteValue()->isZero();
if (!Constraint.containsZero())
return true;
return std::nullopt;
}
ProgramStateRef State;
SValBuilder &Builder;
RangeSet::Factory &RangeFactory;
};
bool ConstraintAssignor::assignSymExprToConst(const SymExpr *Sym,
const llvm::APSInt &Constraint) {
llvm::SmallSet<EquivalenceClass, 4> SimplifiedClasses;
// Iterate over all equivalence classes and try to simplify them.
ClassMembersTy Members = State->get<ClassMembers>();
for (std::pair<EquivalenceClass, SymbolSet> ClassToSymbolSet : Members) {
EquivalenceClass Class = ClassToSymbolSet.first;
State = EquivalenceClass::simplify(Builder, RangeFactory, State, Class);
if (!State)
return false;
SimplifiedClasses.insert(Class);
}
// Trivial equivalence classes (those that have only one symbol member) are
// not stored in the State. Thus, we must skim through the constraints as
// well. And we try to simplify symbols in the constraints.
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
for (std::pair<EquivalenceClass, RangeSet> ClassConstraint : Constraints) {
EquivalenceClass Class = ClassConstraint.first;
if (SimplifiedClasses.count(Class)) // Already simplified.
continue;
State = EquivalenceClass::simplify(Builder, RangeFactory, State, Class);
if (!State)
return false;
}
// We may have trivial equivalence classes in the disequality info as
// well, and we need to simplify them.
DisequalityMapTy DisequalityInfo = State->get<DisequalityMap>();
for (std::pair<EquivalenceClass, ClassSet> DisequalityEntry :
DisequalityInfo) {
EquivalenceClass Class = DisequalityEntry.first;
ClassSet DisequalClasses = DisequalityEntry.second;
State = EquivalenceClass::simplify(Builder, RangeFactory, State, Class);
if (!State)
return false;
}
return true;
}
bool ConstraintAssignor::assignSymSymExprToRangeSet(const SymSymExpr *Sym,
RangeSet Constraint) {
if (!handleRemainderOp(Sym, Constraint))
return false;
std::optional<bool> ConstraintAsBool = interpreteAsBool(Constraint);
if (!ConstraintAsBool)
return true;
if (std::optional<bool> Equality = meansEquality(Sym)) {
// Here we cover two cases:
// * if Sym is equality and the new constraint is true -> Sym's operands
// should be marked as equal
// * if Sym is disequality and the new constraint is false -> Sym's
// operands should be also marked as equal
if (*Equality == *ConstraintAsBool) {
State = trackEquality(State, Sym->getLHS(), Sym->getRHS());
} else {
// Other combinations leave as with disequal operands.
State = trackDisequality(State, Sym->getLHS(), Sym->getRHS());
}
if (!State)
return false;
}
return true;
}
} // end anonymous namespace
std::unique_ptr<ConstraintManager>
ento::CreateRangeConstraintManager(ProgramStateManager &StMgr,
ExprEngine *Eng) {
return std::make_unique<RangeConstraintManager>(Eng, StMgr.getSValBuilder());
}
ConstraintMap ento::getConstraintMap(ProgramStateRef State) {
ConstraintMap::Factory &F = State->get_context<ConstraintMap>();
ConstraintMap Result = F.getEmptyMap();
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
for (std::pair<EquivalenceClass, RangeSet> ClassConstraint : Constraints) {
EquivalenceClass Class = ClassConstraint.first;
SymbolSet ClassMembers = Class.getClassMembers(State);
assert(!ClassMembers.isEmpty() &&
"Class must always have at least one member!");
SymbolRef Representative = *ClassMembers.begin();
Result = F.add(Result, Representative, ClassConstraint.second);
}
return Result;
}
//===----------------------------------------------------------------------===//
// EqualityClass implementation details
//===----------------------------------------------------------------------===//
LLVM_DUMP_METHOD void EquivalenceClass::dumpToStream(ProgramStateRef State,
raw_ostream &os) const {
SymbolSet ClassMembers = getClassMembers(State);
for (const SymbolRef &MemberSym : ClassMembers) {
MemberSym->dump();
os << "\n";
}
}
inline EquivalenceClass EquivalenceClass::find(ProgramStateRef State,
SymbolRef Sym) {
assert(State && "State should not be null");
assert(Sym && "Symbol should not be null");
// We store far from all Symbol -> Class mappings
if (const EquivalenceClass *NontrivialClass = State->get<ClassMap>(Sym))
return *NontrivialClass;
// This is a trivial class of Sym.
return Sym;
}
inline ProgramStateRef EquivalenceClass::merge(RangeSet::Factory &F,
ProgramStateRef State,
SymbolRef First,
SymbolRef Second) {
EquivalenceClass FirstClass = find(State, First);
EquivalenceClass SecondClass = find(State, Second);
return FirstClass.merge(F, State, SecondClass);
}
inline ProgramStateRef EquivalenceClass::merge(RangeSet::Factory &F,
ProgramStateRef State,
EquivalenceClass Other) {
// It is already the same class.
if (*this == Other)
return State;
// FIXME: As of now, we support only equivalence classes of the same type.
// This limitation is connected to the lack of explicit casts in
// our symbolic expression model.
//
// That means that for `int x` and `char y` we don't distinguish
// between these two very different cases:
// * `x == y`
// * `(char)x == y`
//
// The moment we introduce symbolic casts, this restriction can be
// lifted.
if (getType() != Other.getType())
return State;
SymbolSet Members = getClassMembers(State);
SymbolSet OtherMembers = Other.getClassMembers(State);
// We estimate the size of the class by the height of tree containing
// its members. Merging is not a trivial operation, so it's easier to
// merge the smaller class into the bigger one.
if (Members.getHeight() >= OtherMembers.getHeight()) {
return mergeImpl(F, State, Members, Other, OtherMembers);
} else {
return Other.mergeImpl(F, State, OtherMembers, *this, Members);
}
}
inline ProgramStateRef
EquivalenceClass::mergeImpl(RangeSet::Factory &RangeFactory,
ProgramStateRef State, SymbolSet MyMembers,
EquivalenceClass Other, SymbolSet OtherMembers) {
// Essentially what we try to recreate here is some kind of union-find
// data structure. It does have certain limitations due to persistence
// and the need to remove elements from classes.
//
// In this setting, EquialityClass object is the representative of the class
// or the parent element. ClassMap is a mapping of class members to their
// parent. Unlike the union-find structure, they all point directly to the
// class representative because we don't have an opportunity to actually do
// path compression when dealing with immutability. This means that we
// compress paths every time we do merges. It also means that we lose
// the main amortized complexity benefit from the original data structure.
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
ConstraintRangeTy::Factory &CRF = State->get_context<ConstraintRange>();
// 1. If the merged classes have any constraints associated with them, we
// need to transfer them to the class we have left.
//
// Intersection here makes perfect sense because both of these constraints
// must hold for the whole new class.
if (std::optional<RangeSet> NewClassConstraint =
intersect(RangeFactory, getConstraint(State, *this),
getConstraint(State, Other))) {
// NOTE: Essentially, NewClassConstraint should NEVER be infeasible because
// range inferrer shouldn't generate ranges incompatible with
// equivalence classes. However, at the moment, due to imperfections
// in the solver, it is possible and the merge function can also
// return infeasible states aka null states.
if (NewClassConstraint->isEmpty())
// Infeasible state
return nullptr;
// No need in tracking constraints of a now-dissolved class.
Constraints = CRF.remove(Constraints, Other);
// Assign new constraints for this class.
Constraints = CRF.add(Constraints, *this, *NewClassConstraint);
assert(areFeasible(Constraints) && "Constraint manager shouldn't produce "
"a state with infeasible constraints");
State = State->set<ConstraintRange>(Constraints);
}
// 2. Get ALL equivalence-related maps
ClassMapTy Classes = State->get<ClassMap>();
ClassMapTy::Factory &CMF = State->get_context<ClassMap>();
ClassMembersTy Members = State->get<ClassMembers>();
ClassMembersTy::Factory &MF = State->get_context<ClassMembers>();
DisequalityMapTy DisequalityInfo = State->get<DisequalityMap>();
DisequalityMapTy::Factory &DF = State->get_context<DisequalityMap>();
ClassSet::Factory &CF = State->get_context<ClassSet>();
SymbolSet::Factory &F = getMembersFactory(State);
// 2. Merge members of the Other class into the current class.
SymbolSet NewClassMembers = MyMembers;
for (SymbolRef Sym : OtherMembers) {
NewClassMembers = F.add(NewClassMembers, Sym);
// *this is now the class for all these new symbols.
Classes = CMF.add(Classes, Sym, *this);
}
// 3. Adjust member mapping.
//
// No need in tracking members of a now-dissolved class.
Members = MF.remove(Members, Other);
// Now only the current class is mapped to all the symbols.
Members = MF.add(Members, *this, NewClassMembers);
// 4. Update disequality relations
ClassSet DisequalToOther = Other.getDisequalClasses(DisequalityInfo, CF);
// We are about to merge two classes but they are already known to be
// non-equal. This is a contradiction.
if (DisequalToOther.contains(*this))
return nullptr;
if (!DisequalToOther.isEmpty()) {
ClassSet DisequalToThis = getDisequalClasses(DisequalityInfo, CF);
DisequalityInfo = DF.remove(DisequalityInfo, Other);
for (EquivalenceClass DisequalClass : DisequalToOther) {
DisequalToThis = CF.add(DisequalToThis, DisequalClass);
// Disequality is a symmetric relation meaning that if
// DisequalToOther not null then the set for DisequalClass is not
// empty and has at least Other.
ClassSet OriginalSetLinkedToOther =
*DisequalityInfo.lookup(DisequalClass);
// Other will be eliminated and we should replace it with the bigger
// united class.
ClassSet NewSet = CF.remove(OriginalSetLinkedToOther, Other);
NewSet = CF.add(NewSet, *this);
DisequalityInfo = DF.add(DisequalityInfo, DisequalClass, NewSet);
}
DisequalityInfo = DF.add(DisequalityInfo, *this, DisequalToThis);
State = State->set<DisequalityMap>(DisequalityInfo);
}
// 5. Update the state
State = State->set<ClassMap>(Classes);
State = State->set<ClassMembers>(Members);
return State;
}
inline SymbolSet::Factory &
EquivalenceClass::getMembersFactory(ProgramStateRef State) {
return State->get_context<SymbolSet>();
}
SymbolSet EquivalenceClass::getClassMembers(ProgramStateRef State) const {
if (const SymbolSet *Members = State->get<ClassMembers>(*this))
return *Members;
// This class is trivial, so we need to construct a set
// with just that one symbol from the class.
SymbolSet::Factory &F = getMembersFactory(State);
return F.add(F.getEmptySet(), getRepresentativeSymbol());
}
bool EquivalenceClass::isTrivial(ProgramStateRef State) const {
return State->get<ClassMembers>(*this) == nullptr;
}
bool EquivalenceClass::isTriviallyDead(ProgramStateRef State,
SymbolReaper &Reaper) const {
return isTrivial(State) && Reaper.isDead(getRepresentativeSymbol());
}
inline ProgramStateRef EquivalenceClass::markDisequal(RangeSet::Factory &RF,
ProgramStateRef State,
SymbolRef First,
SymbolRef Second) {
return markDisequal(RF, State, find(State, First), find(State, Second));
}
inline ProgramStateRef EquivalenceClass::markDisequal(RangeSet::Factory &RF,
ProgramStateRef State,
EquivalenceClass First,
EquivalenceClass Second) {
return First.markDisequal(RF, State, Second);
}
inline ProgramStateRef
EquivalenceClass::markDisequal(RangeSet::Factory &RF, ProgramStateRef State,
EquivalenceClass Other) const {
// If we know that two classes are equal, we can only produce an infeasible
// state.
if (*this == Other) {
return nullptr;
}
DisequalityMapTy DisequalityInfo = State->get<DisequalityMap>();
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
// Disequality is a symmetric relation, so if we mark A as disequal to B,
// we should also mark B as disequalt to A.
if (!addToDisequalityInfo(DisequalityInfo, Constraints, RF, State, *this,
Other) ||
!addToDisequalityInfo(DisequalityInfo, Constraints, RF, State, Other,
*this))
return nullptr;
assert(areFeasible(Constraints) && "Constraint manager shouldn't produce "
"a state with infeasible constraints");
State = State->set<DisequalityMap>(DisequalityInfo);
State = State->set<ConstraintRange>(Constraints);
return State;
}
inline bool EquivalenceClass::addToDisequalityInfo(
DisequalityMapTy &Info, ConstraintRangeTy &Constraints,
RangeSet::Factory &RF, ProgramStateRef State, EquivalenceClass First,
EquivalenceClass Second) {
// 1. Get all of the required factories.
DisequalityMapTy::Factory &F = State->get_context<DisequalityMap>();
ClassSet::Factory &CF = State->get_context<ClassSet>();
ConstraintRangeTy::Factory &CRF = State->get_context<ConstraintRange>();
// 2. Add Second to the set of classes disequal to First.
const ClassSet *CurrentSet = Info.lookup(First);
ClassSet NewSet = CurrentSet ? *CurrentSet : CF.getEmptySet();
NewSet = CF.add(NewSet, Second);
Info = F.add(Info, First, NewSet);
// 3. If Second is known to be a constant, we can delete this point
// from the constraint asociated with First.
//
// So, if Second == 10, it means that First != 10.
// At the same time, the same logic does not apply to ranges.
if (const RangeSet *SecondConstraint = Constraints.lookup(Second))
if (const llvm::APSInt *Point = SecondConstraint->getConcreteValue()) {
RangeSet FirstConstraint = SymbolicRangeInferrer::inferRange(
RF, State, First.getRepresentativeSymbol());
FirstConstraint = RF.deletePoint(FirstConstraint, *Point);
// If the First class is about to be constrained with an empty
// range-set, the state is infeasible.
if (FirstConstraint.isEmpty())
return false;
Constraints = CRF.add(Constraints, First, FirstConstraint);
}
return true;
}
inline std::optional<bool> EquivalenceClass::areEqual(ProgramStateRef State,
SymbolRef FirstSym,
SymbolRef SecondSym) {
return EquivalenceClass::areEqual(State, find(State, FirstSym),
find(State, SecondSym));
}
inline std::optional<bool> EquivalenceClass::areEqual(ProgramStateRef State,
EquivalenceClass First,
EquivalenceClass Second) {
// The same equivalence class => symbols are equal.
if (First == Second)
return true;
// Let's check if we know anything about these two classes being not equal to
// each other.
ClassSet DisequalToFirst = First.getDisequalClasses(State);
if (DisequalToFirst.contains(Second))
return false;
// It is not clear.
return std::nullopt;
}
[[nodiscard]] ProgramStateRef
EquivalenceClass::removeMember(ProgramStateRef State, const SymbolRef Old) {
SymbolSet ClsMembers = getClassMembers(State);
assert(ClsMembers.contains(Old));
// Remove `Old`'s Class->Sym relation.
SymbolSet::Factory &F = getMembersFactory(State);
ClassMembersTy::Factory &EMFactory = State->get_context<ClassMembers>();
ClsMembers = F.remove(ClsMembers, Old);
// Ensure another precondition of the removeMember function (we can check
// this only with isEmpty, thus we have to do the remove first).
assert(!ClsMembers.isEmpty() &&
"Class should have had at least two members before member removal");
// Overwrite the existing members assigned to this class.
ClassMembersTy ClassMembersMap = State->get<ClassMembers>();
ClassMembersMap = EMFactory.add(ClassMembersMap, *this, ClsMembers);
State = State->set<ClassMembers>(ClassMembersMap);
// Remove `Old`'s Sym->Class relation.
ClassMapTy Classes = State->get<ClassMap>();
ClassMapTy::Factory &CMF = State->get_context<ClassMap>();
Classes = CMF.remove(Classes, Old);
State = State->set<ClassMap>(Classes);
return State;
}
// Re-evaluate an SVal with top-level `State->assume` logic.
[[nodiscard]] ProgramStateRef
reAssume(ProgramStateRef State, const RangeSet *Constraint, SVal TheValue) {
if (!Constraint)
return State;
const auto DefinedVal = TheValue.castAs<DefinedSVal>();
// If the SVal is 0, we can simply interpret that as `false`.
if (Constraint->encodesFalseRange())
return State->assume(DefinedVal, false);
// If the constraint does not encode 0 then we can interpret that as `true`
// AND as a Range(Set).
if (Constraint->encodesTrueRange()) {
State = State->assume(DefinedVal, true);
if (!State)
return nullptr;
// Fall through, re-assume based on the range values as well.
}
// Overestimate the individual Ranges with the RangeSet' lowest and
// highest values.
return State->assumeInclusiveRange(DefinedVal, Constraint->getMinValue(),
Constraint->getMaxValue(), true);
}
// Iterate over all symbols and try to simplify them. Once a symbol is
// simplified then we check if we can merge the simplified symbol's equivalence
// class to this class. This way, we simplify not just the symbols but the
// classes as well: we strive to keep the number of the classes to be the
// absolute minimum.
[[nodiscard]] ProgramStateRef
EquivalenceClass::simplify(SValBuilder &SVB, RangeSet::Factory &F,
ProgramStateRef State, EquivalenceClass Class) {
SymbolSet ClassMembers = Class.getClassMembers(State);
for (const SymbolRef &MemberSym : ClassMembers) {
const SVal SimplifiedMemberVal = simplifyToSVal(State, MemberSym);
const SymbolRef SimplifiedMemberSym = SimplifiedMemberVal.getAsSymbol();
// The symbol is collapsed to a constant, check if the current State is
// still feasible.
if (const auto CI = SimplifiedMemberVal.getAs<nonloc::ConcreteInt>()) {
const llvm::APSInt &SV = CI->getValue();
const RangeSet *ClassConstraint = getConstraint(State, Class);
// We have found a contradiction.
if (ClassConstraint && !ClassConstraint->contains(SV))
return nullptr;
}
if (SimplifiedMemberSym && MemberSym != SimplifiedMemberSym) {
// The simplified symbol should be the member of the original Class,
// however, it might be in another existing class at the moment. We
// have to merge these classes.
ProgramStateRef OldState = State;
State = merge(F, State, MemberSym, SimplifiedMemberSym);
if (!State)
return nullptr;
// No state change, no merge happened actually.
if (OldState == State)
continue;
// Be aware that `SimplifiedMemberSym` might refer to an already dead
// symbol. In that case, the eqclass of that might not be the same as the
// eqclass of `MemberSym`. This is because the dead symbols are not
// preserved in the `ClassMap`, hence
// `find(State, SimplifiedMemberSym)` will result in a trivial eqclass
// compared to the eqclass of `MemberSym`.
// These eqclasses should be the same if `SimplifiedMemberSym` is alive.
// --> assert(find(State, MemberSym) == find(State, SimplifiedMemberSym))
//
// Note that `MemberSym` must be alive here since that is from the
// `ClassMembers` where all the symbols are alive.
// Remove the old and more complex symbol.
State = find(State, MemberSym).removeMember(State, MemberSym);
// Query the class constraint again b/c that may have changed during the
// merge above.
const RangeSet *ClassConstraint = getConstraint(State, Class);
// Re-evaluate an SVal with top-level `State->assume`, this ignites
// a RECURSIVE algorithm that will reach a FIXPOINT.
//
// About performance and complexity: Let us assume that in a State we
// have N non-trivial equivalence classes and that all constraints and
// disequality info is related to non-trivial classes. In the worst case,
// we can simplify only one symbol of one class in each iteration. The
// number of symbols in one class cannot grow b/c we replace the old
// symbol with the simplified one. Also, the number of the equivalence
// classes can decrease only, b/c the algorithm does a merge operation
// optionally. We need N iterations in this case to reach the fixpoint.
// Thus, the steps needed to be done in the worst case is proportional to
// N*N.
//
// This worst case scenario can be extended to that case when we have
// trivial classes in the constraints and in the disequality map. This
// case can be reduced to the case with a State where there are only
// non-trivial classes. This is because a merge operation on two trivial
// classes results in one non-trivial class.
State = reAssume(State, ClassConstraint, SimplifiedMemberVal);
if (!State)
return nullptr;
}
}
return State;
}
inline ClassSet EquivalenceClass::getDisequalClasses(ProgramStateRef State,
SymbolRef Sym) {
return find(State, Sym).getDisequalClasses(State);
}
inline ClassSet
EquivalenceClass::getDisequalClasses(ProgramStateRef State) const {
return getDisequalClasses(State->get<DisequalityMap>(),
State->get_context<ClassSet>());
}
inline ClassSet
EquivalenceClass::getDisequalClasses(DisequalityMapTy Map,
ClassSet::Factory &Factory) const {
if (const ClassSet *DisequalClasses = Map.lookup(*this))
return *DisequalClasses;
return Factory.getEmptySet();
}
bool EquivalenceClass::isClassDataConsistent(ProgramStateRef State) {
ClassMembersTy Members = State->get<ClassMembers>();
for (std::pair<EquivalenceClass, SymbolSet> ClassMembersPair : Members) {
for (SymbolRef Member : ClassMembersPair.second) {
// Every member of the class should have a mapping back to the class.
if (find(State, Member) == ClassMembersPair.first) {
continue;
}
return false;
}
}
DisequalityMapTy Disequalities = State->get<DisequalityMap>();
for (std::pair<EquivalenceClass, ClassSet> DisequalityInfo : Disequalities) {
EquivalenceClass Class = DisequalityInfo.first;
ClassSet DisequalClasses = DisequalityInfo.second;
// There is no use in keeping empty sets in the map.
if (DisequalClasses.isEmpty())
return false;
// Disequality is symmetrical, i.e. for every Class A and B that A != B,
// B != A should also be true.
for (EquivalenceClass DisequalClass : DisequalClasses) {
const ClassSet *DisequalToDisequalClasses =
Disequalities.lookup(DisequalClass);
// It should be a set of at least one element: Class
if (!DisequalToDisequalClasses ||
!DisequalToDisequalClasses->contains(Class))
return false;
}
}
return true;
}
//===----------------------------------------------------------------------===//
// RangeConstraintManager implementation
//===----------------------------------------------------------------------===//
bool RangeConstraintManager::canReasonAbout(SVal X) const {
std::optional<nonloc::SymbolVal> SymVal = X.getAs<nonloc::SymbolVal>();
if (SymVal && SymVal->isExpression()) {
const SymExpr *SE = SymVal->getSymbol();
if (const SymIntExpr *SIE = dyn_cast<SymIntExpr>(SE)) {
switch (SIE->getOpcode()) {
// We don't reason yet about bitwise-constraints on symbolic values.
case BO_And:
case BO_Or:
case BO_Xor:
return false;
// We don't reason yet about these arithmetic constraints on
// symbolic values.
case BO_Mul:
case BO_Div:
case BO_Rem:
case BO_Shl:
case BO_Shr:
return false;
// All other cases.
default:
return true;
}
}
if (const SymSymExpr *SSE = dyn_cast<SymSymExpr>(SE)) {
// FIXME: Handle <=> here.
if (BinaryOperator::isEqualityOp(SSE->getOpcode()) ||
BinaryOperator::isRelationalOp(SSE->getOpcode())) {
// We handle Loc <> Loc comparisons, but not (yet) NonLoc <> NonLoc.
// We've recently started producing Loc <> NonLoc comparisons (that
// result from casts of one of the operands between eg. intptr_t and
// void *), but we can't reason about them yet.
if (Loc::isLocType(SSE->getLHS()->getType())) {
return Loc::isLocType(SSE->getRHS()->getType());
}
}
}
return false;
}
return true;
}
ConditionTruthVal RangeConstraintManager::checkNull(ProgramStateRef State,
SymbolRef Sym) {
const RangeSet *Ranges = getConstraint(State, Sym);
// If we don't have any information about this symbol, it's underconstrained.
if (!Ranges)
return ConditionTruthVal();
// If we have a concrete value, see if it's zero.
if (const llvm::APSInt *Value = Ranges->getConcreteValue())
return *Value == 0;
BasicValueFactory &BV = getBasicVals();
APSIntType IntType = BV.getAPSIntType(Sym->getType());
llvm::APSInt Zero = IntType.getZeroValue();
// Check if zero is in the set of possible values.
if (!Ranges->contains(Zero))
return false;
// Zero is a possible value, but it is not the /only/ possible value.
return ConditionTruthVal();
}
const llvm::APSInt *RangeConstraintManager::getSymVal(ProgramStateRef St,
SymbolRef Sym) const {
const RangeSet *T = getConstraint(St, Sym);
return T ? T->getConcreteValue() : nullptr;
}
const llvm::APSInt *RangeConstraintManager::getSymMinVal(ProgramStateRef St,
SymbolRef Sym) const {
const RangeSet *T = getConstraint(St, Sym);
if (!T || T->isEmpty())
return nullptr;
return &T->getMinValue();
}
const llvm::APSInt *RangeConstraintManager::getSymMaxVal(ProgramStateRef St,
SymbolRef Sym) const {
const RangeSet *T = getConstraint(St, Sym);
if (!T || T->isEmpty())
return nullptr;
return &T->getMaxValue();
}
//===----------------------------------------------------------------------===//
// Remove dead symbols from existing constraints
//===----------------------------------------------------------------------===//
/// Scan all symbols referenced by the constraints. If the symbol is not alive
/// as marked in LSymbols, mark it as dead in DSymbols.
ProgramStateRef
RangeConstraintManager::removeDeadBindings(ProgramStateRef State,
SymbolReaper &SymReaper) {
ClassMembersTy ClassMembersMap = State->get<ClassMembers>();
ClassMembersTy NewClassMembersMap = ClassMembersMap;
ClassMembersTy::Factory &EMFactory = State->get_context<ClassMembers>();
SymbolSet::Factory &SetFactory = State->get_context<SymbolSet>();
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
ConstraintRangeTy NewConstraints = Constraints;
ConstraintRangeTy::Factory &ConstraintFactory =
State->get_context<ConstraintRange>();
ClassMapTy Map = State->get<ClassMap>();
ClassMapTy NewMap = Map;
ClassMapTy::Factory &ClassFactory = State->get_context<ClassMap>();
DisequalityMapTy Disequalities = State->get<DisequalityMap>();
DisequalityMapTy::Factory &DisequalityFactory =
State->get_context<DisequalityMap>();
ClassSet::Factory &ClassSetFactory = State->get_context<ClassSet>();
bool ClassMapChanged = false;
bool MembersMapChanged = false;
bool ConstraintMapChanged = false;
bool DisequalitiesChanged = false;
auto removeDeadClass = [&](EquivalenceClass Class) {
// Remove associated constraint ranges.
Constraints = ConstraintFactory.remove(Constraints, Class);
ConstraintMapChanged = true;
// Update disequality information to not hold any information on the
// removed class.
ClassSet DisequalClasses =
Class.getDisequalClasses(Disequalities, ClassSetFactory);
if (!DisequalClasses.isEmpty()) {
for (EquivalenceClass DisequalClass : DisequalClasses) {
ClassSet DisequalToDisequalSet =
DisequalClass.getDisequalClasses(Disequalities, ClassSetFactory);
// DisequalToDisequalSet is guaranteed to be non-empty for consistent
// disequality info.
assert(!DisequalToDisequalSet.isEmpty());
ClassSet NewSet = ClassSetFactory.remove(DisequalToDisequalSet, Class);
// No need in keeping an empty set.
if (NewSet.isEmpty()) {
Disequalities =
DisequalityFactory.remove(Disequalities, DisequalClass);
} else {
Disequalities =
DisequalityFactory.add(Disequalities, DisequalClass, NewSet);
}
}
// Remove the data for the class
Disequalities = DisequalityFactory.remove(Disequalities, Class);
DisequalitiesChanged = true;
}
};
// 1. Let's see if dead symbols are trivial and have associated constraints.
for (std::pair<EquivalenceClass, RangeSet> ClassConstraintPair :
Constraints) {
EquivalenceClass Class = ClassConstraintPair.first;
if (Class.isTriviallyDead(State, SymReaper)) {
// If this class is trivial, we can remove its constraints right away.
removeDeadClass(Class);
}
}
// 2. We don't need to track classes for dead symbols.
for (std::pair<SymbolRef, EquivalenceClass> SymbolClassPair : Map) {
SymbolRef Sym = SymbolClassPair.first;
if (SymReaper.isDead(Sym)) {
ClassMapChanged = true;
NewMap = ClassFactory.remove(NewMap, Sym);
}
}
// 3. Remove dead members from classes and remove dead non-trivial classes
// and their constraints.
for (std::pair<EquivalenceClass, SymbolSet> ClassMembersPair :
ClassMembersMap) {
EquivalenceClass Class = ClassMembersPair.first;
SymbolSet LiveMembers = ClassMembersPair.second;
bool MembersChanged = false;
for (SymbolRef Member : ClassMembersPair.second) {
if (SymReaper.isDead(Member)) {
MembersChanged = true;
LiveMembers = SetFactory.remove(LiveMembers, Member);
}
}
// Check if the class changed.
if (!MembersChanged)
continue;
MembersMapChanged = true;
if (LiveMembers.isEmpty()) {
// The class is dead now, we need to wipe it out of the members map...
NewClassMembersMap = EMFactory.remove(NewClassMembersMap, Class);
// ...and remove all of its constraints.
removeDeadClass(Class);
} else {
// We need to change the members associated with the class.
NewClassMembersMap =
EMFactory.add(NewClassMembersMap, Class, LiveMembers);
}
}
// 4. Update the state with new maps.
//
// Here we try to be humble and update a map only if it really changed.
if (ClassMapChanged)
State = State->set<ClassMap>(NewMap);
if (MembersMapChanged)
State = State->set<ClassMembers>(NewClassMembersMap);
if (ConstraintMapChanged)
State = State->set<ConstraintRange>(Constraints);
if (DisequalitiesChanged)
State = State->set<DisequalityMap>(Disequalities);
assert(EquivalenceClass::isClassDataConsistent(State));
return State;
}
RangeSet RangeConstraintManager::getRange(ProgramStateRef State,
SymbolRef Sym) {
return SymbolicRangeInferrer::inferRange(F, State, Sym);
}
ProgramStateRef RangeConstraintManager::setRange(ProgramStateRef State,
SymbolRef Sym,
RangeSet Range) {
return ConstraintAssignor::assign(State, getSValBuilder(), F, Sym, Range);
}
//===------------------------------------------------------------------------===
// assumeSymX methods: protected interface for RangeConstraintManager.
//===------------------------------------------------------------------------===
// The syntax for ranges below is mathematical, using [x, y] for closed ranges
// and (x, y) for open ranges. These ranges are modular, corresponding with
// a common treatment of C integer overflow. This means that these methods
// do not have to worry about overflow; RangeSet::Intersect can handle such a
// "wraparound" range.
// As an example, the range [UINT_MAX-1, 3) contains five values: UINT_MAX-1,
// UINT_MAX, 0, 1, and 2.
ProgramStateRef
RangeConstraintManager::assumeSymNE(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
// Before we do any real work, see if the value can even show up.
APSIntType AdjustmentType(Adjustment);
if (AdjustmentType.testInRange(Int, true) != APSIntType::RTR_Within)
return St;
llvm::APSInt Point = AdjustmentType.convert(Int) - Adjustment;
RangeSet New = getRange(St, Sym);
New = F.deletePoint(New, Point);
return setRange(St, Sym, New);
}
ProgramStateRef
RangeConstraintManager::assumeSymEQ(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
// Before we do any real work, see if the value can even show up.
APSIntType AdjustmentType(Adjustment);
if (AdjustmentType.testInRange(Int, true) != APSIntType::RTR_Within)
return nullptr;
// [Int-Adjustment, Int-Adjustment]
llvm::APSInt AdjInt = AdjustmentType.convert(Int) - Adjustment;
RangeSet New = getRange(St, Sym);
New = F.intersect(New, AdjInt);
return setRange(St, Sym, New);
}
RangeSet RangeConstraintManager::getSymLTRange(ProgramStateRef St,
SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
// Before we do any real work, see if the value can even show up.
APSIntType AdjustmentType(Adjustment);
switch (AdjustmentType.testInRange(Int, true)) {
case APSIntType::RTR_Below:
return F.getEmptySet();
case APSIntType::RTR_Within:
break;
case APSIntType::RTR_Above:
return getRange(St, Sym);
}
// Special case for Int == Min. This is always false.
llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
llvm::APSInt Min = AdjustmentType.getMinValue();
if (ComparisonVal == Min)
return F.getEmptySet();
llvm::APSInt Lower = Min - Adjustment;
llvm::APSInt Upper = ComparisonVal - Adjustment;
--Upper;
RangeSet Result = getRange(St, Sym);
return F.intersect(Result, Lower, Upper);
}
ProgramStateRef
RangeConstraintManager::assumeSymLT(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
RangeSet New = getSymLTRange(St, Sym, Int, Adjustment);
return setRange(St, Sym, New);
}
RangeSet RangeConstraintManager::getSymGTRange(ProgramStateRef St,
SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
// Before we do any real work, see if the value can even show up.
APSIntType AdjustmentType(Adjustment);
switch (AdjustmentType.testInRange(Int, true)) {
case APSIntType::RTR_Below:
return getRange(St, Sym);
case APSIntType::RTR_Within:
break;
case APSIntType::RTR_Above:
return F.getEmptySet();
}
// Special case for Int == Max. This is always false.
llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
llvm::APSInt Max = AdjustmentType.getMaxValue();
if (ComparisonVal == Max)
return F.getEmptySet();
llvm::APSInt Lower = ComparisonVal - Adjustment;
llvm::APSInt Upper = Max - Adjustment;
++Lower;
RangeSet SymRange = getRange(St, Sym);
return F.intersect(SymRange, Lower, Upper);
}
ProgramStateRef
RangeConstraintManager::assumeSymGT(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
RangeSet New = getSymGTRange(St, Sym, Int, Adjustment);
return setRange(St, Sym, New);
}
RangeSet RangeConstraintManager::getSymGERange(ProgramStateRef St,
SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
// Before we do any real work, see if the value can even show up.
APSIntType AdjustmentType(Adjustment);
switch (AdjustmentType.testInRange(Int, true)) {
case APSIntType::RTR_Below:
return getRange(St, Sym);
case APSIntType::RTR_Within:
break;
case APSIntType::RTR_Above:
return F.getEmptySet();
}
// Special case for Int == Min. This is always feasible.
llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
llvm::APSInt Min = AdjustmentType.getMinValue();
if (ComparisonVal == Min)
return getRange(St, Sym);
llvm::APSInt Max = AdjustmentType.getMaxValue();
llvm::APSInt Lower = ComparisonVal - Adjustment;
llvm::APSInt Upper = Max - Adjustment;
RangeSet SymRange = getRange(St, Sym);
return F.intersect(SymRange, Lower, Upper);
}
ProgramStateRef
RangeConstraintManager::assumeSymGE(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
RangeSet New = getSymGERange(St, Sym, Int, Adjustment);
return setRange(St, Sym, New);
}
RangeSet
RangeConstraintManager::getSymLERange(llvm::function_ref<RangeSet()> RS,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
// Before we do any real work, see if the value can even show up.
APSIntType AdjustmentType(Adjustment);
switch (AdjustmentType.testInRange(Int, true)) {
case APSIntType::RTR_Below:
return F.getEmptySet();
case APSIntType::RTR_Within:
break;
case APSIntType::RTR_Above:
return RS();
}
// Special case for Int == Max. This is always feasible.
llvm::APSInt ComparisonVal = AdjustmentType.convert(Int);
llvm::APSInt Max = AdjustmentType.getMaxValue();
if (ComparisonVal == Max)
return RS();
llvm::APSInt Min = AdjustmentType.getMinValue();
llvm::APSInt Lower = Min - Adjustment;
llvm::APSInt Upper = ComparisonVal - Adjustment;
RangeSet Default = RS();
return F.intersect(Default, Lower, Upper);
}
RangeSet RangeConstraintManager::getSymLERange(ProgramStateRef St,
SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
return getSymLERange([&] { return getRange(St, Sym); }, Int, Adjustment);
}
ProgramStateRef
RangeConstraintManager::assumeSymLE(ProgramStateRef St, SymbolRef Sym,
const llvm::APSInt &Int,
const llvm::APSInt &Adjustment) {
RangeSet New = getSymLERange(St, Sym, Int, Adjustment);
return setRange(St, Sym, New);
}
ProgramStateRef RangeConstraintManager::assumeSymWithinInclusiveRange(
ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
const llvm::APSInt &To, const llvm::APSInt &Adjustment) {
RangeSet New = getSymGERange(State, Sym, From, Adjustment);
if (New.isEmpty())
return nullptr;
RangeSet Out = getSymLERange([&] { return New; }, To, Adjustment);
return setRange(State, Sym, Out);
}
ProgramStateRef RangeConstraintManager::assumeSymOutsideInclusiveRange(
ProgramStateRef State, SymbolRef Sym, const llvm::APSInt &From,
const llvm::APSInt &To, const llvm::APSInt &Adjustment) {
RangeSet RangeLT = getSymLTRange(State, Sym, From, Adjustment);
RangeSet RangeGT = getSymGTRange(State, Sym, To, Adjustment);
RangeSet New(F.add(RangeLT, RangeGT));
return setRange(State, Sym, New);
}
//===----------------------------------------------------------------------===//
// Pretty-printing.
//===----------------------------------------------------------------------===//
void RangeConstraintManager::printJson(raw_ostream &Out, ProgramStateRef State,
const char *NL, unsigned int Space,
bool IsDot) const {
printConstraints(Out, State, NL, Space, IsDot);
printEquivalenceClasses(Out, State, NL, Space, IsDot);
printDisequalities(Out, State, NL, Space, IsDot);
}
void RangeConstraintManager::printValue(raw_ostream &Out, ProgramStateRef State,
SymbolRef Sym) {
const RangeSet RS = getRange(State, Sym);
if (RS.isEmpty()) {
Out << "<empty rangeset>";
return;
}
Out << RS.getBitWidth() << (RS.isUnsigned() ? "u:" : "s:");
RS.dump(Out);
}
static std::string toString(const SymbolRef &Sym) {
std::string S;
llvm::raw_string_ostream O(S);
Sym->dumpToStream(O);
return O.str();
}
void RangeConstraintManager::printConstraints(raw_ostream &Out,
ProgramStateRef State,
const char *NL,
unsigned int Space,
bool IsDot) const {
ConstraintRangeTy Constraints = State->get<ConstraintRange>();
Indent(Out, Space, IsDot) << "\"constraints\": ";
if (Constraints.isEmpty()) {
Out << "null," << NL;
return;
}
std::map<std::string, RangeSet> OrderedConstraints;
for (std::pair<EquivalenceClass, RangeSet> P : Constraints) {
SymbolSet ClassMembers = P.first.getClassMembers(State);
for (const SymbolRef &ClassMember : ClassMembers) {
bool insertion_took_place;
std::tie(std::ignore, insertion_took_place) =
OrderedConstraints.insert({toString(ClassMember), P.second});
assert(insertion_took_place &&
"two symbols should not have the same dump");
}
}
++Space;
Out << '[' << NL;
bool First = true;
for (std::pair<std::string, RangeSet> P : OrderedConstraints) {
if (First) {
First = false;
} else {
Out << ',';
Out << NL;
}
Indent(Out, Space, IsDot)
<< "{ \"symbol\": \"" << P.first << "\", \"range\": \"";
P.second.dump(Out);
Out << "\" }";
}
Out << NL;
--Space;
Indent(Out, Space, IsDot) << "]," << NL;
}
static std::string toString(ProgramStateRef State, EquivalenceClass Class) {
SymbolSet ClassMembers = Class.getClassMembers(State);
llvm::SmallVector<SymbolRef, 8> ClassMembersSorted(ClassMembers.begin(),
ClassMembers.end());
llvm::sort(ClassMembersSorted,
[](const SymbolRef &LHS, const SymbolRef &RHS) {
return toString(LHS) < toString(RHS);
});
bool FirstMember = true;
std::string Str;
llvm::raw_string_ostream Out(Str);
Out << "[ ";
for (SymbolRef ClassMember : ClassMembersSorted) {
if (FirstMember)
FirstMember = false;
else
Out << ", ";
Out << "\"" << ClassMember << "\"";
}
Out << " ]";
return Out.str();
}
void RangeConstraintManager::printEquivalenceClasses(raw_ostream &Out,
ProgramStateRef State,
const char *NL,
unsigned int Space,
bool IsDot) const {
ClassMembersTy Members = State->get<ClassMembers>();
Indent(Out, Space, IsDot) << "\"equivalence_classes\": ";
if (Members.isEmpty()) {
Out << "null," << NL;
return;
}
std::set<std::string> MembersStr;
for (std::pair<EquivalenceClass, SymbolSet> ClassToSymbolSet : Members)
MembersStr.insert(toString(State, ClassToSymbolSet.first));
++Space;
Out << '[' << NL;
bool FirstClass = true;
for (const std::string &Str : MembersStr) {
if (FirstClass) {
FirstClass = false;
} else {
Out << ',';
Out << NL;
}
Indent(Out, Space, IsDot);
Out << Str;
}
Out << NL;
--Space;
Indent(Out, Space, IsDot) << "]," << NL;
}
void RangeConstraintManager::printDisequalities(raw_ostream &Out,
ProgramStateRef State,
const char *NL,
unsigned int Space,
bool IsDot) const {
DisequalityMapTy Disequalities = State->get<DisequalityMap>();
Indent(Out, Space, IsDot) << "\"disequality_info\": ";
if (Disequalities.isEmpty()) {
Out << "null," << NL;
return;
}
// Transform the disequality info to an ordered map of
// [string -> (ordered set of strings)]
using EqClassesStrTy = std::set<std::string>;
using DisequalityInfoStrTy = std::map<std::string, EqClassesStrTy>;
DisequalityInfoStrTy DisequalityInfoStr;
for (std::pair<EquivalenceClass, ClassSet> ClassToDisEqSet : Disequalities) {
EquivalenceClass Class = ClassToDisEqSet.first;
ClassSet DisequalClasses = ClassToDisEqSet.second;
EqClassesStrTy MembersStr;
for (EquivalenceClass DisEqClass : DisequalClasses)
MembersStr.insert(toString(State, DisEqClass));
DisequalityInfoStr.insert({toString(State, Class), MembersStr});
}
++Space;
Out << '[' << NL;
bool FirstClass = true;
for (std::pair<std::string, EqClassesStrTy> ClassToDisEqSet :
DisequalityInfoStr) {
const std::string &Class = ClassToDisEqSet.first;
if (FirstClass) {
FirstClass = false;
} else {
Out << ',';
Out << NL;
}
Indent(Out, Space, IsDot) << "{" << NL;
unsigned int DisEqSpace = Space + 1;
Indent(Out, DisEqSpace, IsDot) << "\"class\": ";
Out << Class;
const EqClassesStrTy &DisequalClasses = ClassToDisEqSet.second;
if (!DisequalClasses.empty()) {
Out << "," << NL;
Indent(Out, DisEqSpace, IsDot) << "\"disequal_to\": [" << NL;
unsigned int DisEqClassSpace = DisEqSpace + 1;
Indent(Out, DisEqClassSpace, IsDot);
bool FirstDisEqClass = true;
for (const std::string &DisEqClass : DisequalClasses) {
if (FirstDisEqClass) {
FirstDisEqClass = false;
} else {
Out << ',' << NL;
Indent(Out, DisEqClassSpace, IsDot);
}
Out << DisEqClass;
}
Out << "]" << NL;
}
Indent(Out, Space, IsDot) << "}";
}
Out << NL;
--Space;
Indent(Out, Space, IsDot) << "]," << NL;
}