cppcheck/lib/exprengine.cpp

1305 lines
52 KiB
C++

/*
* Cppcheck - A tool for static C/C++ code analysis
* Copyright (C) 2007-2019 Cppcheck team.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "exprengine.h"
#include "astutils.h"
#include "settings.h"
#include "symboldatabase.h"
#include "tokenize.h"
#include <limits>
#include <memory>
#include <iostream>
std::string ExprEngine::str(int128_t value)
{
std::ostringstream ostr;
#ifdef __GNUC__
if (value == (int)value) {
ostr << (int) value;
return ostr.str();
}
if (value < 0) {
ostr << "-";
value = -value;
}
uint64_t high = value >> 64;
uint64_t low = value;
if (high > 0)
ostr << "h" << std::hex << high << "l";
ostr << std::hex << low;
#else
ostr << value;
#endif
return ostr.str();
}
static ExprEngine::ValuePtr getValueRangeFromValueType(const std::string &name, const ValueType *vt, const cppcheck::Platform &platform);
namespace {
class TrackExecution {
public:
TrackExecution() : mDataIndex(0) {}
std::map<const Token *, std::vector<std::string>> map;
int getNewDataIndex() {
return mDataIndex++;
}
void symbolRange(const Token *tok, ExprEngine::ValuePtr value) {
if (!tok || !value)
return;
const std::string &symbolicExpression = value->getSymbolicExpression();
if (symbolicExpression[0] != '$')
return;
if (mSymbols.find(symbolicExpression) != mSymbols.end())
return;
mSymbols.insert(symbolicExpression);
map[tok].push_back(symbolicExpression + "=" + value->getRange());
}
void state(const Token *tok, const std::string &s) {
map[tok].push_back(s);
}
void print(std::ostream &out) {
std::set<std::pair<int,int>> locations;
for (auto it : map) {
locations.insert(std::pair<int,int>(it.first->linenr(), it.first->column()));
}
for (const std::pair<int,int> &loc : locations) {
int lineNumber = loc.first;
int column = loc.second;
for (auto &it : map) {
const Token *tok = it.first;
if (lineNumber != tok->linenr())
continue;
if (column != tok->column())
continue;
const std::vector<std::string> &dumps = it.second;
for (const std::string &dump : dumps)
out << lineNumber << ":" << column << ": " << dump << "\n";
}
}
}
private:
int mDataIndex;
std::set<std::string> mSymbols;
};
class Data : public ExprEngine::DataBase {
public:
Data(int *symbolValueIndex, const Tokenizer *tokenizer, const Settings *settings, const std::vector<ExprEngine::Callback> &callbacks, TrackExecution *trackExecution)
: DataBase(settings)
, symbolValueIndex(symbolValueIndex)
, tokenizer(tokenizer)
, callbacks(callbacks)
, mTrackExecution(trackExecution)
, mDataIndex(trackExecution->getNewDataIndex()) {}
typedef std::map<nonneg int, std::shared_ptr<ExprEngine::Value>> Memory;
Memory memory;
int * const symbolValueIndex;
const Tokenizer * const tokenizer;
const std::vector<ExprEngine::Callback> &callbacks;
void assignValue(const Token *tok, unsigned int varId, ExprEngine::ValuePtr value) {
mTrackExecution->symbolRange(tok, value);
if (value) {
if (auto arr = std::dynamic_pointer_cast<ExprEngine::ArrayValue>(value)) {
mTrackExecution->symbolRange(tok, arr->size);
for (const auto &indexAndValue: arr->data)
mTrackExecution->symbolRange(tok, indexAndValue.value);
} else if (auto s = std::dynamic_pointer_cast<ExprEngine::StructValue>(value)) {
for (const auto &m: s->member)
mTrackExecution->symbolRange(tok, m.second);
}
}
memory[varId] = value;
}
void assignStructMember(const Token *tok, ExprEngine::StructValue *structVal, const std::string &memberName, ExprEngine::ValuePtr value) {
mTrackExecution->symbolRange(tok, value);
structVal->member[memberName] = value;
}
std::vector<Data> getData(const Token *cond, bool trueData) {
std::vector<Data> ret;
ret.push_back(Data(symbolValueIndex, tokenizer, settings, callbacks, mTrackExecution));
for (Memory::const_iterator mem = memory.cbegin(); mem != memory.cend(); ++mem) {
for (Data &data : ret)
data.memory[mem->first] = mem->second;
if (cond->isComparisonOp() && cond->astOperand1()->varId() == mem->first && cond->astOperand2()->isNumber()) {
const int128_t rhsValue = MathLib::toLongNumber(cond->astOperand2()->str());
if (auto intRange = std::dynamic_pointer_cast<ExprEngine::IntRange>(mem->second)) {
if (cond->str() == ">") {
if (trueData) {
if (intRange->maxValue <= rhsValue)
return std::vector<Data>();
auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), rhsValue + 1, intRange->maxValue);
ret[0].assignValue(cond, mem->first, val);
} else { /* if (!trueData) */
if (intRange->maxValue <= rhsValue)
return std::vector<Data>();
auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), intRange->minValue, rhsValue);
ret[0].assignValue(cond, mem->first, val);
}
}
}
}
else if (cond->varId() == mem->first) {
if (auto intRange = std::dynamic_pointer_cast<ExprEngine::IntRange>(mem->second)) {
if (trueData) {
if (intRange->minValue == 0 && intRange->maxValue == 0)
return std::vector<Data>();
if (intRange->minValue < 0) {
auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), intRange->minValue, -1);
ret[0].assignValue(cond, mem->first, val);
}
if (intRange->maxValue > 0) {
auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), 1, intRange->maxValue);
if (intRange->minValue < 0) {
// create additional intrange..
ret.push_back(Data(symbolValueIndex, tokenizer, settings, callbacks, mTrackExecution));
ret.back().memory = ret[0].memory;
}
ret[0].assignValue(cond, mem->first, val);
}
} else { /* if (!trueData) */
if (intRange->maxValue < 0 || intRange->minValue > 0)
return std::vector<Data>();
auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), 0, 0);
ret[0].assignValue(cond, mem->first, val);
}
}
}
}
return ret;
}
std::string getNewSymbolName() override {
return "$" + std::to_string(++(*symbolValueIndex));
}
std::shared_ptr<ExprEngine::ArrayValue> getArrayValue(const Token *tok) {
const Memory::iterator it = memory.find(tok->varId());
if (it != memory.end())
return std::dynamic_pointer_cast<ExprEngine::ArrayValue>(it->second);
if (tok->varId() == 0)
return std::shared_ptr<ExprEngine::ArrayValue>();
auto val = std::make_shared<ExprEngine::ArrayValue>(this, tok->variable());
assignValue(tok, tok->varId(), val);
return val;
}
ExprEngine::ValuePtr getValue(unsigned int varId, const ValueType *valueType, const Token *tok) {
const Memory::const_iterator it = memory.find(varId);
if (it != memory.end())
return it->second;
if (!valueType)
return ExprEngine::ValuePtr();
ExprEngine::ValuePtr value = getValueRangeFromValueType(getNewSymbolName(), valueType, *settings);
if (value) {
assignValue(tok, varId, value);
}
return value;
}
void trackProgramState(const Token *tok) {
if (memory.empty())
return;
const SymbolDatabase * const symbolDatabase = tokenizer->getSymbolDatabase();
std::ostringstream s;
s << "{"; // << mDataIndex << ":";
for (auto mem : memory) {
ExprEngine::ValuePtr value = mem.second;
const Variable *var = symbolDatabase->getVariableFromVarId(mem.first);
if (!var)
continue;
s << " " << var->name() << "=";
if (!value)
s << "(null)";
else if (value->name[0] == '$' && value->getSymbolicExpression() != value->name)
s << "(" << value->name << "," << value->getSymbolicExpression() << ")";
else
s << value->name;
}
s << "}";
mTrackExecution->state(tok, s.str());
}
private:
TrackExecution * const mTrackExecution;
const int mDataIndex;
};
}
static ExprEngine::ValuePtr simplifyValue(ExprEngine::ValuePtr origValue)
{
auto b = std::dynamic_pointer_cast<ExprEngine::BinOpResult>(origValue);
if (!b)
return origValue;
if (!b->op1 || !b->op2)
return origValue;
auto intRange1 = std::dynamic_pointer_cast<ExprEngine::IntRange>(b->op1);
auto intRange2 = std::dynamic_pointer_cast<ExprEngine::IntRange>(b->op1);
if (intRange1 && intRange2 && intRange1->minValue == intRange1->maxValue && intRange2->minValue == intRange2->maxValue) {
const std::string &binop = b->binop;
int128_t v;
if (binop == "+")
v = intRange1->minValue + intRange2->minValue;
else if (binop == "-")
v = intRange1->minValue - intRange2->minValue;
else if (binop == "*")
v = intRange1->minValue * intRange2->minValue;
else if (binop == "/" && intRange2->minValue != 0)
v = intRange1->minValue / intRange2->minValue;
else if (binop == "%" && intRange2->minValue != 0)
v = intRange1->minValue % intRange2->minValue;
else
return origValue;
return std::make_shared<ExprEngine::IntRange>(ExprEngine::str(v), v, v);
}
return origValue;
}
static ExprEngine::ValuePtr translateUninitValueToRange(ExprEngine::ValuePtr value, const ::ValueType *valueType, Data &data)
{
if (!value)
return value;
if (value->type == ExprEngine::ValueType::UninitValue) {
auto rangeValue = getValueRangeFromValueType(data.getNewSymbolName(), valueType, *data.settings);
if (rangeValue)
return rangeValue;
}
if (auto conditionalValue = std::dynamic_pointer_cast<ExprEngine::ConditionalValue>(value)) {
if (conditionalValue->values.size() == 1 && conditionalValue->values[0].second && conditionalValue->values[0].second->type == ExprEngine::ValueType::UninitValue) {
auto rangeValue = getValueRangeFromValueType(data.getNewSymbolName(), valueType, *data.settings);
if (rangeValue)
return rangeValue;
}
}
return value;
}
static int128_t truncateInt(int128_t value, int bits, char sign)
{
value = value & (((int128_t)1 << bits) - 1);
// Sign extension
if (sign == 's' && value & (1ULL << (bits - 1)))
value |= ~(((int128_t)1 << bits) - 1);
return value;
}
ExprEngine::ArrayValue::ArrayValue(const std::string &name, ExprEngine::ValuePtr size, ExprEngine::ValuePtr value)
: Value(name, ExprEngine::ValueType::ArrayValue)
, size(size)
{
assign(ExprEngine::ValuePtr(), value);
}
ExprEngine::ArrayValue::ArrayValue(DataBase *data, const Variable *var)
: Value(data->getNewSymbolName(), ExprEngine::ValueType::ArrayValue)
{
if (var) {
int sz = 1;
for (const auto &dim : var->dimensions()) {
if (!dim.known) {
sz = -1;
break;
}
sz *= dim.num;
}
if (sz >= 1)
size = std::make_shared<ExprEngine::IntRange>(std::to_string(sz), sz, sz);
}
ValuePtr val;
if (!var->isGlobal() && !var->isStatic())
val = std::make_shared<ExprEngine::UninitValue>();
else {
if (var->valueType()) {
::ValueType vt(*var->valueType());
vt.pointer = 0;
val = getValueRangeFromValueType(data->getNewSymbolName(), &vt, *data->settings);
}
}
assign(ExprEngine::ValuePtr(), val);
}
void ExprEngine::ArrayValue::assign(ExprEngine::ValuePtr index, ExprEngine::ValuePtr value)
{
if (!index)
data.clear();
if (value) {
ExprEngine::ArrayValue::IndexAndValue indexAndValue = {index, value};
data.push_back(indexAndValue);
}
}
void ExprEngine::ArrayValue::clear()
{
data.clear();
ExprEngine::ArrayValue::IndexAndValue indexAndValue = {
ExprEngine::ValuePtr(), std::make_shared<ExprEngine::IntRange>("0", 0, 0)
};
data.push_back(indexAndValue);
}
static bool isEqual(ExprEngine::ValuePtr v1, ExprEngine::ValuePtr v2)
{
if (!v1 || !v2)
return !v1 && !v2;
return v1->name == v2->name;
}
static bool isNonOverlapping(ExprEngine::ValuePtr v1, ExprEngine::ValuePtr v2)
{
if (!v1 || !v2)
return false; // Don't know!
auto intRange1 = std::dynamic_pointer_cast<ExprEngine::IntRange>(v1);
auto intRange2 = std::dynamic_pointer_cast<ExprEngine::IntRange>(v2);
if (intRange1 && intRange2 && (intRange1->minValue > intRange2->maxValue || intRange1->maxValue < intRange2->maxValue))
return true;
return false;
}
ExprEngine::ConditionalValue::Vector ExprEngine::ArrayValue::read(ExprEngine::ValuePtr index) const
{
ExprEngine::ConditionalValue::Vector ret;
for (const auto indexAndValue : data) {
if (isEqual(index, indexAndValue.index))
ret.clear();
if (isNonOverlapping(index, indexAndValue.index))
continue;
// Array contains string literal data...
if (!indexAndValue.index && indexAndValue.value->type == ExprEngine::ValueType::StringLiteralValue) {
auto stringLiteral = std::dynamic_pointer_cast<ExprEngine::StringLiteralValue>(indexAndValue.value);
if (!stringLiteral) {
ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, std::make_shared<ExprEngine::IntRange>("", -128, 128)));
continue;
}
if (auto i = std::dynamic_pointer_cast<ExprEngine::IntRange>(index)) {
if (stringLiteral && i->minValue >= 0 && i->minValue == i->maxValue) {
int c = 0;
if (i->minValue < stringLiteral->size())
c = stringLiteral->string[i->minValue];
ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, std::make_shared<ExprEngine::IntRange>(std::to_string(c), c, c)));
continue;
}
}
int cmin = 0, cmax = 0;
for (char c : stringLiteral->string) {
if (c < cmin)
cmin = c;
else if (c > cmax)
cmax = c;
}
ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, std::make_shared<ExprEngine::IntRange>("", cmin, cmax)));
continue;
}
ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, indexAndValue.value));
}
if (ret.size() == 1)
ret[0].first = ExprEngine::ValuePtr();
else if (ret.size() == 2 && !ret[0].first) {
ret[0].first = std::make_shared<ExprEngine::BinOpResult>("!=", index, ret[1].first);
ret[1].first = std::make_shared<ExprEngine::BinOpResult>("==", index, ret[1].first);
} else {
// FIXME!!
ret.clear();
}
return ret;
}
std::string ExprEngine::ConditionalValue::getSymbolicExpression() const
{
std::ostringstream ostr;
ostr << "{";
bool first = true;
for (auto condvalue : values) {
ValuePtr cond = condvalue.first;
ValuePtr value = condvalue.second;
if (!first)
ostr << ",";
first = false;
ostr << "{"
<< (cond ? cond->getSymbolicExpression() : std::string("(null)"))
<< ","
<< value->getSymbolicExpression()
<< "}";
}
ostr << "}";
return ostr.str();
}
std::string ExprEngine::ArrayValue::getSymbolicExpression() const
{
std::ostringstream ostr;
ostr << "size=" << (size ? size->name : std::string("(null)"));
for (const auto indexAndValue : data) {
ostr << ",["
<< (!indexAndValue.index ? std::string(":") : indexAndValue.index->name)
<< "]="
<< indexAndValue.value->name;
}
return ostr.str();
}
std::string ExprEngine::StructValue::getSymbolicExpression() const
{
std::ostringstream ostr;
ostr << "{";
bool first = true;
for (const auto& m: member) {
const std::string &memberName = m.first;
auto memberValue = m.second;
if (!first)
ostr << ",";
first = false;
ostr << memberName << "=" << (memberValue ? memberValue->getSymbolicExpression() : std::string("(null)"));
}
ostr << "}";
return ostr.str();
}
std::string ExprEngine::PointerValue::getRange() const
{
std::string r;
if (data)
r = "->" + data->getSymbolicExpression();
if (null)
r += std::string(r.empty() ? "" : ",") + "null";
if (uninitData)
r += std::string(r.empty() ? "" : ",") + "->?";
return r;
}
std::string ExprEngine::BinOpResult::getRange() const
{
IntOrFloatValue minValue, maxValue;
getRange(&minValue, &maxValue);
const std::string s1 = minValue.isFloat()
? std::to_string(minValue.floatValue)
: str(minValue.intValue);
const std::string s2 = maxValue.isFloat()
? std::to_string(maxValue.floatValue)
: str(maxValue.intValue);
if (s1 == s2)
return s1;
return s1 + ":" + s2;
}
void ExprEngine::BinOpResult::getRange(ExprEngine::BinOpResult::IntOrFloatValue *minValue, ExprEngine::BinOpResult::IntOrFloatValue *maxValue) const
{
std::map<ValuePtr, int> valueBit;
// Assign a bit number for each leaf
int bit = 0;
for (ValuePtr v : mLeafs) {
if (auto intRange = std::dynamic_pointer_cast<IntRange>(v)) {
if (intRange->minValue == intRange->maxValue) {
valueBit[v] = 30;
continue;
}
}
valueBit[v] = bit++;
}
if (bit > 24)
throw std::runtime_error("Internal error: bits");
for (int test = 0; test < (1 << bit); ++test) {
auto result = evaluate(test, valueBit);
if (test == 0)
*minValue = *maxValue = result;
else if (result.isFloat()) {
if (result.floatValue < minValue->floatValue)
*minValue = result;
else if (result.floatValue > maxValue->floatValue)
*maxValue = result;
} else {
if (result.intValue < minValue->intValue)
*minValue = result;
else if (result.intValue > maxValue->intValue)
*maxValue = result;
}
}
}
std::string ExprEngine::IntegerTruncation::getSymbolicExpression() const
{
return sign + std::to_string(bits) + "(" + inputValue->getSymbolicExpression() + ")";
}
bool ExprEngine::BinOpResult::isIntValueInRange(int value) const
{
IntOrFloatValue minValue, maxValue;
getRange(&minValue, &maxValue);
return value >= minValue.intValue && value <= maxValue.intValue;
}
#define BINARY_OP(OP) \
if (binop == #OP) { \
struct ExprEngine::BinOpResult::IntOrFloatValue result(lhs); \
if (lhs.isFloat()) \
{ result.type = lhs.type; result.floatValue = lhs.floatValue OP (rhs.isFloat() ? rhs.floatValue : rhs.intValue); } \
else if (rhs.isFloat()) \
{ result.type = rhs.type; result.floatValue = lhs.intValue OP rhs.floatValue; } \
else { result.type = lhs.type; result.intValue = lhs.intValue OP rhs.intValue; } \
return result; \
}
#define BINARY_RELATIONAL_COMPARISON(OP) \
if (binop == #OP) { \
struct ExprEngine::BinOpResult::IntOrFloatValue result(lhs); \
if (lhs.isFloat()) \
{ result.setIntValue(lhs.floatValue OP (rhs.isFloat() ? rhs.floatValue : rhs.intValue)); } \
else if (rhs.isFloat()) \
{ result.setIntValue(lhs.intValue OP rhs.floatValue); } \
else { result.setIntValue(lhs.intValue OP rhs.intValue); } \
return result; \
}
#define BINARY_EQ_COMPARISON(OP) \
if (binop == #OP && !lhs.isFloat() && !rhs.isFloat()) { \
struct ExprEngine::BinOpResult::IntOrFloatValue result; \
result.setIntValue(lhs.intValue OP rhs.intValue); \
return result; \
}
#define BINARY_INT_OP(OP) \
if (binop == #OP) { \
struct ExprEngine::BinOpResult::IntOrFloatValue result; \
result.setIntValue(lhs.intValue OP rhs.intValue); \
return result; \
}
#define BINARY_OP_DIV(OP) \
if (binop == #OP) { \
struct ExprEngine::BinOpResult::IntOrFloatValue result(lhs); \
if (lhs.isFloat()) \
{ result.type = lhs.type; result.floatValue = lhs.floatValue OP (rhs.isFloat() ? rhs.floatValue : rhs.intValue); } \
else if (rhs.isFloat()) \
{ result.type = rhs.type; result.floatValue = lhs.intValue OP rhs.floatValue; } \
else if (rhs.intValue != 0) { result.type = lhs.type; result.intValue = lhs.intValue OP rhs.intValue; } \
return result; \
}
ExprEngine::BinOpResult::IntOrFloatValue ExprEngine::BinOpResult::evaluate(int test, const std::map<ExprEngine::ValuePtr, int> &valueBit) const
{
const ExprEngine::BinOpResult::IntOrFloatValue lhs = evaluateOperand(test, valueBit, op1);
const ExprEngine::BinOpResult::IntOrFloatValue rhs = evaluateOperand(test, valueBit, op2);
BINARY_OP(+)
BINARY_OP(-)
BINARY_OP(*)
BINARY_OP_DIV(/)
BINARY_INT_OP(&)
BINARY_INT_OP(|)
BINARY_INT_OP(^)
BINARY_INT_OP(<<)
BINARY_INT_OP(>>)
BINARY_EQ_COMPARISON(==)
BINARY_EQ_COMPARISON(!=)
BINARY_RELATIONAL_COMPARISON(>=)
BINARY_RELATIONAL_COMPARISON(>)
BINARY_RELATIONAL_COMPARISON(<=)
BINARY_RELATIONAL_COMPARISON(<)
if (binop == "%" && rhs.intValue != 0) {
struct ExprEngine::BinOpResult::IntOrFloatValue result;
result.setIntValue(lhs.intValue % rhs.intValue);
return result;
}
throw std::runtime_error("Internal error: Unhandled operator;" + binop);
}
ExprEngine::BinOpResult::IntOrFloatValue ExprEngine::BinOpResult::evaluateOperand(int test, const std::map<ExprEngine::ValuePtr, int> &valueBit, ExprEngine::ValuePtr value) const
{
if (!value)
throw std::runtime_error("Internal error: null value");
auto binOpResult = std::dynamic_pointer_cast<ExprEngine::BinOpResult>(value);
if (binOpResult)
return binOpResult->evaluate(test, valueBit);
auto it = valueBit.find(value);
if (it == valueBit.end())
throw std::runtime_error("Internal error: valueBit not set properly");
bool valueType = test & (1 << it->second);
if (auto intRange = std::dynamic_pointer_cast<IntRange>(value)) {
ExprEngine::BinOpResult::IntOrFloatValue result;
result.setIntValue(valueType ? intRange->minValue : intRange->maxValue);
return result;
}
if (auto floatRange = std::dynamic_pointer_cast<FloatRange>(value)) {
ExprEngine::BinOpResult::IntOrFloatValue result;
result.setFloatValue(valueType ? floatRange->minValue : floatRange->maxValue);
return result;
}
if (auto integerTruncation = std::dynamic_pointer_cast<IntegerTruncation>(value)) {
ExprEngine::BinOpResult::IntOrFloatValue result(evaluateOperand(test, valueBit, integerTruncation->inputValue));
if (result.isFloat())
result.setIntValue(truncateInt(result.floatValue, integerTruncation->bits, integerTruncation->sign));
else
result.setIntValue(truncateInt(result.intValue, integerTruncation->bits, integerTruncation->sign));
return result;
}
throw std::runtime_error("Internal error: Unhandled value:" + std::to_string((int)value->type));
}
// Todo: This is taken from ValueFlow and modified.. we should reuse it
static int getIntBitsFromValueType(const ValueType *vt, const cppcheck::Platform &platform)
{
if (!vt)
return 0;
switch (vt->type) {
case ValueType::Type::BOOL:
return 1;
case ValueType::Type::CHAR:
return platform.char_bit;
case ValueType::Type::SHORT:
return platform.short_bit;
case ValueType::Type::INT:
return platform.int_bit;
case ValueType::Type::LONG:
return platform.long_bit;
case ValueType::Type::LONGLONG:
return platform.long_long_bit;
default:
return 0;
};
}
static ExprEngine::ValuePtr getValueRangeFromValueType(const std::string &name, const ValueType *vt, const cppcheck::Platform &platform)
{
if (!vt || !(vt->isIntegral() || vt->isFloat()) || vt->pointer)
return ExprEngine::ValuePtr();
int bits = getIntBitsFromValueType(vt, platform);
if (bits == 1) {
return std::make_shared<ExprEngine::IntRange>(name, 0, 1);
} else if (bits > 1) {
if (vt->sign == ValueType::Sign::UNSIGNED) {
return std::make_shared<ExprEngine::IntRange>(name, 0, ((int128_t)1 << bits) - 1);
} else {
return std::make_shared<ExprEngine::IntRange>(name, -((int128_t)1 << (bits - 1)), ((int128_t)1 << (bits - 1)) - 1);
}
}
switch (vt->type) {
case ValueType::Type::FLOAT:
return std::make_shared<ExprEngine::FloatRange>(name, std::numeric_limits<float>::min(), std::numeric_limits<float>::max());
case ValueType::Type::DOUBLE:
return std::make_shared<ExprEngine::FloatRange>(name, std::numeric_limits<double>::min(), std::numeric_limits<double>::max());
case ValueType::Type::LONGDOUBLE:
return std::make_shared<ExprEngine::FloatRange>(name, std::numeric_limits<long double>::min(), std::numeric_limits<long double>::max());
default:
return ExprEngine::ValuePtr();
};
}
static void call(const std::vector<ExprEngine::Callback> &callbacks, const Token *tok, ExprEngine::ValuePtr value)
{
if (value) {
for (ExprEngine::Callback f : callbacks) {
f(tok, *value);
}
}
}
static ExprEngine::ValuePtr executeExpression(const Token *tok, Data &data);
static ExprEngine::ValuePtr executeReturn(const Token *tok, Data &data)
{
ExprEngine::ValuePtr retval = executeExpression(tok->astOperand1(), data);
call(data.callbacks, tok, retval);
return retval;
}
static ExprEngine::ValuePtr truncateValue(ExprEngine::ValuePtr val, const ValueType *valueType, Data &data)
{
if (!valueType)
return val;
if (valueType->pointer != 0)
return val;
if (!valueType->isIntegral())
return val; // TODO
int bits = getIntBitsFromValueType(valueType, *data.settings);
if (bits == 0)
// TODO
return val;
if (auto range = std::dynamic_pointer_cast<ExprEngine::IntRange>(val)) {
if (range->minValue == range->maxValue) {
int128_t newValue = truncateInt(range->minValue, bits, valueType->sign == ValueType::Sign::SIGNED ? 's' : 'u');
if (newValue == range->minValue)
return val;
return std::make_shared<ExprEngine::IntRange>(ExprEngine::str(newValue), newValue, newValue);
}
if (auto typeRange = getValueRangeFromValueType("", valueType, *data.settings)) {
auto typeIntRange = std::dynamic_pointer_cast<ExprEngine::IntRange>(typeRange);
if (typeIntRange) {
if (range->minValue >= typeIntRange->minValue && range->maxValue <= typeIntRange->maxValue)
return val;
}
}
return std::make_shared<ExprEngine::IntegerTruncation>(data.getNewSymbolName(), val, bits, valueType->sign == ValueType::Sign::SIGNED ? 's' : 'u');
}
// TODO
return val;
}
static ExprEngine::ValuePtr executeAssign(const Token *tok, Data &data)
{
ExprEngine::ValuePtr rhsValue = executeExpression(tok->astOperand2(), data);
ExprEngine::ValuePtr assignValue;
if (tok->str() == "=")
assignValue = rhsValue;
else {
// "+=" => "+"
std::string binop(tok->str());
binop = binop.substr(0, binop.size() - 1);
ExprEngine::ValuePtr lhsValue = executeExpression(tok->astOperand1(), data);
assignValue = simplifyValue(std::make_shared<ExprEngine::BinOpResult>(binop, lhsValue, rhsValue));
}
const Token *lhsToken = tok->astOperand1();
assignValue = truncateValue(assignValue, lhsToken->valueType(), data);
call(data.callbacks, tok, assignValue);
if (lhsToken->varId() > 0) {
data.assignValue(lhsToken, lhsToken->varId(), assignValue);
} else if (lhsToken->str() == "[") {
auto arrayValue = data.getArrayValue(lhsToken->astOperand1());
if (arrayValue) {
// Is it array initialization?
const Token *arrayInit = lhsToken->astOperand1();
if (arrayInit && arrayInit->variable() && arrayInit->variable()->nameToken() == arrayInit) {
if (assignValue->type == ExprEngine::ValueType::StringLiteralValue)
arrayValue->assign(ExprEngine::ValuePtr(), assignValue);
} else {
auto indexValue = executeExpression(lhsToken->astOperand2(), data);
arrayValue->assign(indexValue, assignValue);
}
}
} else if (lhsToken->isUnaryOp("*")) {
auto pval = executeExpression(lhsToken->astOperand1(), data);
if (pval && pval->type == ExprEngine::ValueType::AddressOfValue) {
auto val = std::dynamic_pointer_cast<ExprEngine::AddressOfValue>(pval);
if (val)
data.assignValue(lhsToken, val->varId, assignValue);
} else if (pval && pval->type == ExprEngine::ValueType::BinOpResult) {
auto b = std::dynamic_pointer_cast<ExprEngine::BinOpResult>(pval);
if (b && b->binop == "+") {
std::shared_ptr<ExprEngine::ArrayValue> arr;
ExprEngine::ValuePtr offset;
if (b->op1->type == ExprEngine::ValueType::ArrayValue) {
arr = std::dynamic_pointer_cast<ExprEngine::ArrayValue>(b->op1);
offset = b->op2;
} else {
arr = std::dynamic_pointer_cast<ExprEngine::ArrayValue>(b->op2);
offset = b->op1;
}
if (arr && offset) {
arr->assign(offset, assignValue);
}
}
}
} else if (Token::Match(lhsToken, ". %name%")) {
auto structVal = executeExpression(lhsToken->astOperand1(), data);
if (structVal && structVal->type == ExprEngine::ValueType::StructValue)
data.assignStructMember(tok, &*std::static_pointer_cast<ExprEngine::StructValue>(structVal), lhsToken->strAt(1), assignValue);
}
return assignValue;
}
static ExprEngine::ValuePtr executeFunctionCall(const Token *tok, Data &data)
{
std::vector<ExprEngine::ValuePtr> argValues;
for (const Token *argtok : getArguments(tok)) {
auto val = executeExpression(argtok, data);
argValues.push_back(val);
if (!argtok->valueType() || (argtok->valueType()->constness & 1) == 1)
continue;
if (auto arrayValue = std::dynamic_pointer_cast<ExprEngine::ArrayValue>(val)) {
ValueType vt(*argtok->valueType());
vt.pointer = 0;
auto anyVal = getValueRangeFromValueType(data.getNewSymbolName(), &vt, *data.settings);
arrayValue->assign(ExprEngine::ValuePtr(), anyVal);
} else if (auto addressOf = std::dynamic_pointer_cast<ExprEngine::AddressOfValue>(val)) {
ValueType vt(*argtok->valueType());
vt.pointer = 0;
if (vt.isIntegral() && argtok->valueType()->pointer == 1)
data.assignValue(argtok, addressOf->varId, getValueRangeFromValueType(data.getNewSymbolName(), &vt, *data.settings));
}
}
if (!tok->valueType() && tok->astParent())
throw std::runtime_error("Expression '" + tok->expressionString() + "' has unknown type!");
auto val = getValueRangeFromValueType(data.getNewSymbolName(), tok->valueType(), *data.settings);
call(data.callbacks, tok, val);
return val;
}
static ExprEngine::ValuePtr executeArrayIndex(const Token *tok, Data &data)
{
auto arrayValue = data.getArrayValue(tok->astOperand1());
if (arrayValue) {
auto indexValue = executeExpression(tok->astOperand2(), data);
auto conditionalValues = arrayValue->read(indexValue);
for (auto value: conditionalValues)
call(data.callbacks, tok, value.second);
return std::make_shared<ExprEngine::ConditionalValue>(data.getNewSymbolName(), conditionalValues);
}
// TODO: Pointer value..
executeExpression(tok->astOperand1(), data);
executeExpression(tok->astOperand2(), data);
return ExprEngine::ValuePtr();
}
static ExprEngine::ValuePtr executeCast(const Token *tok, Data &data)
{
const Token *expr = tok->astOperand2() ? tok->astOperand2() : tok->astOperand1();
auto val = executeExpression(expr, data);
if (expr->valueType() && expr->valueType()->type == ::ValueType::Type::VOID && expr->valueType()->pointer > 0) {
::ValueType vt(*tok->valueType());
vt.pointer = 0;
auto range = getValueRangeFromValueType(data.getNewSymbolName(), &vt, *data.settings);
if (tok->valueType()->pointer == 0)
return range;
bool uninit = false, null = false;
if (val && val->type == ExprEngine::ValueType::PointerValue) {
null = std::static_pointer_cast<ExprEngine::PointerValue>(val)->null;
uninit = std::static_pointer_cast<ExprEngine::PointerValue>(val)->uninitData;
}
return std::make_shared<ExprEngine::PointerValue>(data.getNewSymbolName(), range, null, uninit);
}
if (val)
// TODO: Cast this..
return val;
return getValueRangeFromValueType(data.getNewSymbolName(), tok->valueType(), *data.settings);
}
static ExprEngine::ValuePtr executeDot(const Token *tok, Data &data)
{
if (!tok->astOperand1() || !tok->astOperand1()->varId())
return ExprEngine::ValuePtr();
std::shared_ptr<ExprEngine::StructValue> structValue = std::dynamic_pointer_cast<ExprEngine::StructValue>(data.getValue(tok->astOperand1()->varId(), nullptr, nullptr));
if (!structValue) {
if (tok->originalName() == "->") {
std::shared_ptr<ExprEngine::PointerValue> pointerValue = std::dynamic_pointer_cast<ExprEngine::PointerValue>(data.getValue(tok->astOperand1()->varId(), nullptr, nullptr));
if (pointerValue) {
call(data.callbacks, tok->astOperand1(), pointerValue);
structValue = std::dynamic_pointer_cast<ExprEngine::StructValue>(pointerValue->data);
} else {
call(data.callbacks, tok->astOperand1(), data.getValue(tok->astOperand1()->varId(), nullptr, nullptr));
}
}
if (!structValue)
return ExprEngine::ValuePtr();
}
call(data.callbacks, tok->astOperand1(), structValue);
return structValue->getValueOfMember(tok->astOperand2()->str());
}
static ExprEngine::ValuePtr executeBinaryOp(const Token *tok, Data &data)
{
ExprEngine::ValuePtr v1 = executeExpression(tok->astOperand1(), data);
ExprEngine::ValuePtr v2 = executeExpression(tok->astOperand2(), data);
if (v1 && v2) {
auto result = simplifyValue(std::make_shared<ExprEngine::BinOpResult>(tok->str(), v1, v2));
call(data.callbacks, tok, result);
return result;
}
return ExprEngine::ValuePtr();
}
static ExprEngine::ValuePtr executeAddressOf(const Token *tok, Data &data)
{
auto addr = std::make_shared<ExprEngine::AddressOfValue>(data.getNewSymbolName(), tok->astOperand1()->varId());
call(data.callbacks, tok, addr);
return addr;
}
static ExprEngine::ValuePtr executeDeref(const Token *tok, Data &data)
{
ExprEngine::ValuePtr pval = executeExpression(tok->astOperand1(), data);
if (pval) {
auto addressOf = std::dynamic_pointer_cast<ExprEngine::AddressOfValue>(pval);
if (addressOf) {
auto val = data.getValue(addressOf->varId, tok->valueType(), tok);
call(data.callbacks, tok, val);
return val;
}
auto pointer = std::dynamic_pointer_cast<ExprEngine::PointerValue>(pval);
if (pointer) {
auto val = pointer->data;
call(data.callbacks, tok, val);
return val;
}
}
return ExprEngine::ValuePtr();
}
static ExprEngine::ValuePtr executeVariable(const Token *tok, Data &data)
{
auto val = data.getValue(tok->varId(), tok->valueType(), tok);
call(data.callbacks, tok, val);
return val;
}
static ExprEngine::ValuePtr executeKnownMacro(const Token *tok, Data &data)
{
auto val = std::make_shared<ExprEngine::IntRange>(data.getNewSymbolName(), tok->getKnownIntValue(), tok->getKnownIntValue());
call(data.callbacks, tok, val);
return val;
}
static ExprEngine::ValuePtr executeNumber(const Token *tok)
{
if (tok->valueType()->isFloat()) {
long double value = MathLib::toDoubleNumber(tok->str());
return std::make_shared<ExprEngine::FloatRange>(tok->str(), value, value);
}
int128_t value = MathLib::toLongNumber(tok->str());
return std::make_shared<ExprEngine::IntRange>(tok->str(), value, value);
}
static ExprEngine::ValuePtr executeStringLiteral(const Token *tok, Data &data)
{
std::string s = tok->str();
return std::make_shared<ExprEngine::StringLiteralValue>(data.getNewSymbolName(), s.substr(1, s.size()-2));
}
static ExprEngine::ValuePtr executeExpression1(const Token *tok, Data &data)
{
if (tok->str() == "return")
return executeReturn(tok, data);
if (tok->isAssignmentOp())
// TODO: Handle more operators
return executeAssign(tok, data);
if (tok->astOperand1() && tok->astOperand2() && tok->str() == "[")
return executeArrayIndex(tok, data);
if (tok->str() == "(") {
if (!tok->isCast())
return executeFunctionCall(tok, data);
return executeCast(tok, data);
}
if (tok->str() == ".")
return executeDot(tok, data);
if (tok->astOperand1() && tok->astOperand2())
return executeBinaryOp(tok, data);
if (tok->isUnaryOp("&") && Token::Match(tok->astOperand1(), "%var%"))
return executeAddressOf(tok, data);
if (tok->isUnaryOp("*"))
return executeDeref(tok, data);
if (tok->varId())
return executeVariable(tok, data);
if (tok->isName() && tok->hasKnownIntValue())
return executeKnownMacro(tok, data);
if (tok->isNumber() || tok->tokType() == Token::Type::eChar)
return executeNumber(tok);
if (tok->tokType() == Token::Type::eString)
return executeStringLiteral(tok, data);
return ExprEngine::ValuePtr();
}
static ExprEngine::ValuePtr executeExpression(const Token *tok, Data &data)
{
return translateUninitValueToRange(executeExpression1(tok, data), tok->valueType(), data);
}
static ExprEngine::ValuePtr createVariableValue(const Variable &var, Data &data);
static void execute(const Token *start, const Token *end, Data &data)
{
for (const Token *tok = start; tok != end; tok = tok->next()) {
if (Token::Match(tok, "[;{}]"))
data.trackProgramState(tok);
if (tok->variable() && tok->variable()->nameToken() == tok) {
if (Token::Match(tok, "%varid% ; %varid% =", tok->varId())) {
// if variable is not used in assignment rhs then we do not need to create a "confusing" variable value..
bool foundInRhs = false;
visitAstNodes(tok->tokAt(3)->astOperand2(), [&](const Token *rhs) {
if (rhs->varId()==tok->varId()) {
foundInRhs = true;
return ChildrenToVisit::done;
}
return ChildrenToVisit::op1_and_op2;
});
if (!foundInRhs) {
tok = tok->tokAt(2);
continue;
}
}
if (tok->variable()->isArray()) {
data.assignValue(tok, tok->varId(), std::make_shared<ExprEngine::ArrayValue>(&data, tok->variable()));
if (Token::Match(tok, "%name% ["))
tok = tok->linkAt(1);
} else if (Token::Match(tok, "%var% ;"))
data.assignValue(tok, tok->varId(), createVariableValue(*tok->variable(), data));
} else if (!tok->astParent() && (tok->astOperand1() || tok->astOperand2()))
executeExpression(tok, data);
else if (Token::simpleMatch(tok, "if (")) {
const Token *cond = tok->next()->astOperand2();
/*const ExprEngine::ValuePtr condValue =*/ executeExpression(cond,data);
std::vector<Data> trueData = data.getData(cond, true);
std::vector<Data> falseData = data.getData(cond, false);
const Token *thenStart = tok->linkAt(1)->next();
const Token *thenEnd = thenStart->link();
for (Data &d : trueData)
execute(thenStart->next(), end, d);
if (Token::simpleMatch(thenEnd, "} else {")) {
const Token *elseStart = thenEnd->tokAt(2);
for (Data &d : falseData)
execute(elseStart->next(), end, d);
} else {
for (Data &d : falseData)
execute(thenEnd->next(), end, d);
}
return;
}
if (Token::simpleMatch(tok, "} else {"))
tok = tok->linkAt(2);
}
}
void ExprEngine::executeAllFunctions(const Tokenizer *tokenizer, const Settings *settings, const std::vector<ExprEngine::Callback> &callbacks, std::ostream &trace)
{
const SymbolDatabase *symbolDatabase = tokenizer->getSymbolDatabase();
for (const Scope *functionScope : symbolDatabase->functionScopes) {
try {
executeFunction(functionScope, tokenizer, settings, callbacks, trace);
} catch (const std::exception &e) {
// FIXME.. there should not be exceptions
std::string functionName = functionScope->function->name();
std::cout << "Verify: Aborted analysis of function '" << functionName << "': " << e.what() << std::endl;
}
}
}
static ExprEngine::ValuePtr createStructVal(const Scope *structScope, bool uninitData, Data &data)
{
if (!structScope)
return ExprEngine::ValuePtr();
std::shared_ptr<ExprEngine::StructValue> structValue = std::make_shared<ExprEngine::StructValue>(data.getNewSymbolName());
auto uninitValue = std::make_shared<ExprEngine::UninitValue>();
for (const Variable &member : structScope->varlist) {
if (uninitData) {
if (member.isPointer()) {
structValue->member[member.name()] = uninitValue;
continue;
}
if (member.valueType() && member.valueType()->type >= ::ValueType::Type::CHAR) {
structValue->member[member.name()] = uninitValue;
continue;
}
}
ExprEngine::ValuePtr memberValue = createVariableValue(member, data);
if (memberValue)
structValue->member[member.name()] = memberValue;
}
return structValue;
}
static ExprEngine::ValuePtr createVariableValue(const Variable &var, Data &data)
{
if (!var.nameToken())
return ExprEngine::ValuePtr();
const ValueType *valueType = var.valueType();
if (!valueType || valueType->type == ValueType::Type::UNKNOWN_TYPE)
valueType = var.nameToken()->valueType();
if (!valueType || valueType->type == ValueType::Type::UNKNOWN_TYPE) {
// variable with unknown type
if (var.isLocal() && var.isPointer() && !var.isArray())
return std::make_shared<ExprEngine::UninitValue>();
return ExprEngine::ValuePtr();
}
if (valueType->pointer > 0) {
if (var.isLocal())
return std::make_shared<ExprEngine::UninitValue>();
ValueType vt(*valueType);
vt.pointer = 0;
auto range = getValueRangeFromValueType(data.getNewSymbolName(), &vt, *data.settings);
return std::make_shared<ExprEngine::PointerValue>(data.getNewSymbolName(), range, true, true);
}
if (var.isArray())
return std::make_shared<ExprEngine::ArrayValue>(&data, &var);
if (valueType->isIntegral())
return getValueRangeFromValueType(data.getNewSymbolName(), valueType, *data.settings);
if (valueType->type == ValueType::Type::RECORD)
return createStructVal(valueType->typeScope, var.isLocal() && !var.isStatic(), data);
if (valueType->smartPointerType) {
auto structValue = createStructVal(valueType->smartPointerType->classScope, var.isLocal() && !var.isStatic(), data);
return std::make_shared<ExprEngine::PointerValue>(data.getNewSymbolName(), structValue, true, false);
}
if (valueType->container && valueType->container->stdStringLike) {
auto size = std::make_shared<ExprEngine::IntRange>(data.getNewSymbolName(), 0, ~0ULL);
auto value = std::make_shared<ExprEngine::IntRange>(data.getNewSymbolName(), -128, 127);
return std::make_shared<ExprEngine::ArrayValue>(data.getNewSymbolName(), size, value);
}
return ExprEngine::ValuePtr();
}
void ExprEngine::executeFunction(const Scope *functionScope, const Tokenizer *tokenizer, const Settings *settings, const std::vector<ExprEngine::Callback> &callbacks, std::ostream &trace)
{
if (!functionScope->bodyStart)
return;
const Function *function = functionScope->function;
if (!function)
return;
if (functionScope->bodyStart->fileIndex() > 0)
// TODO.. what about functions in headers?
return;
int symbolValueIndex = 0;
TrackExecution trackExecution;
Data data(&symbolValueIndex, tokenizer, settings, callbacks, &trackExecution);
for (const Variable &arg : function->argumentList)
data.assignValue(functionScope->bodyStart, arg.declarationId(), createVariableValue(arg, data));
execute(functionScope->bodyStart, functionScope->bodyEnd, data);
if (settings->debugVerification) {
// TODO generate better output!!
trackExecution.print(trace);
}
}
void ExprEngine::runChecks(ErrorLogger *errorLogger, const Tokenizer *tokenizer, const Settings *settings)
{
std::function<void(const Token *, const ExprEngine::Value &)> divByZero = [=](const Token *tok, const ExprEngine::Value &value) {
if (!Token::Match(tok->astParent(), "[/%]"))
return;
if (tok->astParent()->astOperand2() == tok && value.isIntValueInRange(0)) {
std::list<const Token*> callstack{tok->astParent()};
ErrorLogger::ErrorMessage errmsg(callstack, &tokenizer->list, Severity::SeverityType::error, "verificationDivByZero", "There is division, cannot determine that there can't be a division by zero.", CWE(369), false);
errorLogger->reportErr(errmsg);
}
};
std::function<void(const Token *, const ExprEngine::Value &)> nullPointerDereference = [=](const Token *tok, const ExprEngine::Value &value) {
if (!tok->astParent())
return;
// Is pointer dereferenced?
bool deref = false;
deref |= tok->astParent()->isUnaryOp("*");
deref |= Token::simpleMatch(tok->astParent(), "[");
deref |= Token::simpleMatch(tok->astParent(), ".") && tok == tok->astParent()->astOperand1();
if (!deref)
return;
// Is this a null pointer value?
try {
if (auto pointerValue = dynamic_cast<const ExprEngine::PointerValue*>(&value)) {
if (!pointerValue->null)
return;
} else if (!value.isIntValueInRange(0))
return;
} catch (const std::exception &) {
return;
}
std::list<const Token*> callstack{tok->astParent()};
ErrorLogger::ErrorMessage errmsg(callstack, &tokenizer->list, Severity::SeverityType::error, "verificationNullPointerDereference", "There is pointer dereference, cannot determine that the pointer can't be NULL.", CWE(476), false);
errorLogger->reportErr(errmsg);
};
std::function<void(const Token *, const ExprEngine::Value &)> integerOverflow = [&](const Token *tok, const ExprEngine::Value &value) {
if (!tok->isArithmeticalOp() || !tok->valueType() || !tok->valueType()->isIntegral() || tok->valueType()->pointer > 0)
return;
const ExprEngine::BinOpResult *b = dynamic_cast<const ExprEngine::BinOpResult *>(&value);
if (!b)
return;
ExprEngine::BinOpResult::IntOrFloatValue minValue,maxValue;
b->getRange(&minValue, &maxValue);
if (minValue.isFloat() || maxValue.isFloat())
return;
int bits = getIntBitsFromValueType(tok->valueType(), *settings);
if (bits == 0)
return;
if (tok->valueType()->sign == ::ValueType::Sign::SIGNED) {
int128_t v = (int128_t)1 << (bits - 1);
if (minValue.intValue >= -v && maxValue.intValue < v)
return;
} else {
int128_t v = (int128_t)1 << bits;
if (minValue.intValue >= 0 && maxValue.intValue < v)
return;
}
std::string note;
if (tok->valueType()->sign == ::ValueType::Sign::UNSIGNED)
note = " Note that unsigned integer overflow is defined and will wrap around.";
std::list<const Token*> callstack{tok};
ErrorLogger::ErrorMessage errmsg(callstack, &tokenizer->list, Severity::SeverityType::error, "verificationIntegerOverflow", "Integer overflow, " + tok->valueType()->str() + " result." + note, false);
errorLogger->reportErr(errmsg);
};
std::vector<ExprEngine::Callback> callbacks;
callbacks.push_back(divByZero);
callbacks.push_back(nullPointerDereference);
#ifdef VERIFY_INTEGEROVERFLOW
callbacks.push_back(integerOverflow);
#endif
ExprEngine::executeAllFunctions(tokenizer, settings, callbacks, std::cout);
}