1141 lines
45 KiB
C++
1141 lines
45 KiB
C++
/*
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* Cppcheck - A tool for static C/C++ code analysis
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* Copyright (C) 2007-2019 Cppcheck team.
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "exprengine.h"
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#include "astutils.h"
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#include "settings.h"
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#include "symboldatabase.h"
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#include "tokenize.h"
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#include <limits>
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#include <memory>
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#include <iostream>
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std::string ExprEngine::str(int128_t value)
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{
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std::ostringstream ostr;
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#ifdef __GNUC__
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if (value == (int)value) {
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ostr << (int) value;
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return ostr.str();
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}
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if (value < 0) {
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ostr << "-";
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value = -value;
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}
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uint64_t high = value >> 64;
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uint64_t low = value;
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if (high > 0)
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ostr << "h" << std::hex << high << "l";
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ostr << std::hex << low;
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#else
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ostr << value;
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#endif
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return ostr.str();
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}
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static ExprEngine::ValuePtr getValueRangeFromValueType(const std::string &name, const ValueType *vt, const cppcheck::Platform &platform);
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namespace {
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class TrackExecution {
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public:
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TrackExecution() : mDataIndex(0) {}
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std::map<const Token *, std::vector<std::string>> map;
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int getNewDataIndex() {
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return mDataIndex++;
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}
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void symbolRange(const Token *tok, ExprEngine::ValuePtr value) {
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if (!tok || !value)
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return;
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const std::string &symbolicExpression = value->getSymbolicExpression();
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if (symbolicExpression[0] != '$')
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return;
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if (mSymbols.find(symbolicExpression) != mSymbols.end())
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return;
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mSymbols.insert(symbolicExpression);
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map[tok].push_back(symbolicExpression + "=" + value->getRange());
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}
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void state(const Token *tok, const std::string &s) {
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map[tok].push_back(s);
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}
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void print() {
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std::set<std::pair<int,int>> locations;
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for (auto it : map) {
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locations.insert(std::pair<int,int>(it.first->linenr(), it.first->column()));
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}
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for (const std::pair<int,int> &loc : locations) {
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int lineNumber = loc.first;
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int column = loc.second;
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for (auto &it : map) {
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const Token *tok = it.first;
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if (lineNumber != tok->linenr())
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continue;
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if (column != tok->column())
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continue;
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const std::vector<std::string> &dumps = it.second;
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for (const std::string &dump : dumps)
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std::cout << lineNumber << ":" << column << ": " << dump << "\n";
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}
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}
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}
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private:
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int mDataIndex;
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std::set<std::string> mSymbols;
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};
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class Data {
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public:
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Data(int *symbolValueIndex, const Tokenizer *tokenizer, const Settings *settings, const std::vector<ExprEngine::Callback> &callbacks, TrackExecution *trackExecution)
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: symbolValueIndex(symbolValueIndex)
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, tokenizer(tokenizer)
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, settings(settings)
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, callbacks(callbacks)
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, mTrackExecution(trackExecution)
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, mDataIndex(trackExecution->getNewDataIndex()) {}
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typedef std::map<nonneg int, std::shared_ptr<ExprEngine::Value>> Memory;
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Memory memory;
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int * const symbolValueIndex;
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const Tokenizer * const tokenizer;
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const Settings * const settings;
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const std::vector<ExprEngine::Callback> &callbacks;
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void assignValue(const Token *tok, unsigned int varId, ExprEngine::ValuePtr value) {
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mTrackExecution->symbolRange(tok, value);
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if (value) {
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if (auto arr = std::dynamic_pointer_cast<ExprEngine::ArrayValue>(value)) {
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mTrackExecution->symbolRange(tok, arr->size);
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for (const auto &indexAndValue: arr->data)
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mTrackExecution->symbolRange(tok, indexAndValue.value);
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} else if (auto s = std::dynamic_pointer_cast<ExprEngine::StructValue>(value)) {
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for (const auto &m: s->member)
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mTrackExecution->symbolRange(tok, m.second);
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}
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}
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memory[varId] = value;
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}
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void assignStructMember(const Token *tok, ExprEngine::StructValue *structVal, const std::string &memberName, ExprEngine::ValuePtr value) {
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mTrackExecution->symbolRange(tok, value);
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structVal->member[memberName] = value;
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}
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std::vector<Data> getData(const Token *cond, bool trueData) {
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std::vector<Data> ret;
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ret.push_back(Data(symbolValueIndex, tokenizer, settings, callbacks, mTrackExecution));
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for (Memory::const_iterator mem = memory.cbegin(); mem != memory.cend(); ++mem) {
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for (Data &data : ret)
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data.memory[mem->first] = mem->second;
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if (cond->isComparisonOp() && cond->astOperand1()->varId() == mem->first && cond->astOperand2()->isNumber()) {
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const int128_t rhsValue = MathLib::toLongNumber(cond->astOperand2()->str());
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if (auto intRange = std::dynamic_pointer_cast<ExprEngine::IntRange>(mem->second)) {
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if (cond->str() == ">") {
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if (trueData) {
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if (intRange->maxValue <= rhsValue)
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return std::vector<Data>();
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auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), rhsValue + 1, intRange->maxValue);
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ret[0].assignValue(cond, mem->first, val);
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} else { /* if (!trueData) */
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if (intRange->maxValue <= rhsValue)
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return std::vector<Data>();
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auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), intRange->minValue, rhsValue);
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ret[0].assignValue(cond, mem->first, val);
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}
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}
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}
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}
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else if (cond->varId() == mem->first) {
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if (auto intRange = std::dynamic_pointer_cast<ExprEngine::IntRange>(mem->second)) {
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if (trueData) {
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if (intRange->minValue == 0 && intRange->maxValue == 0)
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return std::vector<Data>();
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if (intRange->minValue < 0) {
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auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), intRange->minValue, -1);
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ret[0].assignValue(cond, mem->first, val);
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}
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if (intRange->maxValue > 0) {
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auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), 1, intRange->maxValue);
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if (intRange->minValue < 0) {
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// create additional intrange..
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ret.push_back(Data(symbolValueIndex, tokenizer, settings, callbacks, mTrackExecution));
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ret.back().memory = ret[0].memory;
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}
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ret[0].assignValue(cond, mem->first, val);
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}
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} else { /* if (!trueData) */
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if (intRange->maxValue < 0 || intRange->minValue > 0)
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return std::vector<Data>();
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auto val = std::make_shared<ExprEngine::IntRange>(getNewSymbolName(), 0, 0);
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ret[0].assignValue(cond, mem->first, val);
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}
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}
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}
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}
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return ret;
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}
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std::string getNewSymbolName() {
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return "$" + std::to_string(++(*symbolValueIndex));
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}
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std::shared_ptr<ExprEngine::ArrayValue> getArrayValue(const Token *tok) {
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const Memory::iterator it = memory.find(tok->varId());
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if (it != memory.end())
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return std::dynamic_pointer_cast<ExprEngine::ArrayValue>(it->second);
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if (tok->varId() == 0)
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return std::shared_ptr<ExprEngine::ArrayValue>();
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auto val = std::make_shared<ExprEngine::ArrayValue>(getNewSymbolName(), tok->variable());
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memory[tok->varId()] = val;
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return val;
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}
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ExprEngine::ValuePtr getValue(unsigned int varId, const ValueType *valueType, const Token *tok) {
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const Memory::const_iterator it = memory.find(varId);
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if (it != memory.end())
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return it->second;
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if (!valueType)
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return ExprEngine::ValuePtr();
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ExprEngine::ValuePtr value = getValueRangeFromValueType(getNewSymbolName(), valueType, *settings);
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if (value) {
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assignValue(tok, varId, value);
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}
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return value;
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}
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void trackProgramState(const Token *tok) {
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if (memory.empty())
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return;
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const SymbolDatabase * const symbolDatabase = tokenizer->getSymbolDatabase();
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std::ostringstream s;
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s << "{"; // << dataIndex << ":";
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for (auto mem : memory) {
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ExprEngine::ValuePtr value = mem.second;
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s << " " << symbolDatabase->getVariableFromVarId(mem.first)->name() << "=";
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if (!value)
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s << "(null)";
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else if (value->name[0] == '$' && value->getSymbolicExpression() != value->name)
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s << "(" << value->name << "," << value->getSymbolicExpression() << ")";
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else
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s << value->name;
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}
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s << "}";
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mTrackExecution->state(tok, s.str());
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}
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private:
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TrackExecution * const mTrackExecution;
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const int mDataIndex;
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};
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}
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static ExprEngine::ValuePtr simplifyValue(ExprEngine::ValuePtr origValue)
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{
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auto b = std::dynamic_pointer_cast<ExprEngine::BinOpResult>(origValue);
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if (!b)
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return origValue;
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if (!b->op1 || !b->op2)
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return origValue;
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auto intRange1 = std::dynamic_pointer_cast<ExprEngine::IntRange>(b->op1);
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auto intRange2 = std::dynamic_pointer_cast<ExprEngine::IntRange>(b->op1);
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if (intRange1 && intRange2 && intRange1->minValue == intRange1->maxValue && intRange2->minValue == intRange2->maxValue) {
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const std::string &binop = b->binop;
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int128_t v;
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if (binop == "+")
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v = intRange1->minValue + intRange2->minValue;
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else if (binop == "-")
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v = intRange1->minValue - intRange2->minValue;
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else if (binop == "*")
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v = intRange1->minValue * intRange2->minValue;
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else if (binop == "/" && intRange2->minValue != 0)
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v = intRange1->minValue / intRange2->minValue;
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else if (binop == "%" && intRange2->minValue != 0)
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v = intRange1->minValue % intRange2->minValue;
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else
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return origValue;
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return std::make_shared<ExprEngine::IntRange>(ExprEngine::str(v), v, v);
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}
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return origValue;
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}
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ExprEngine::ArrayValue::ArrayValue(const std::string &name, ExprEngine::ValuePtr size, ExprEngine::ValuePtr value)
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: Value(name, ExprEngine::ValueType::ArrayValue)
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, size(size)
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{
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assign(ExprEngine::ValuePtr(), value);
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}
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ExprEngine::ArrayValue::ArrayValue(const std::string &name, const Variable *var)
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: Value(name, ExprEngine::ValueType::ArrayValue)
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{
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if (var) {
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int sz = 1;
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for (const auto &dim : var->dimensions()) {
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if (!dim.known) {
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sz = -1;
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break;
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}
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sz *= dim.num;
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}
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if (sz >= 1)
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size = std::make_shared<ExprEngine::IntRange>(std::to_string(sz), sz, sz);
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}
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assign(ExprEngine::ValuePtr(), std::make_shared<ExprEngine::UninitValue>());
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}
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void ExprEngine::ArrayValue::assign(ExprEngine::ValuePtr index, ExprEngine::ValuePtr value)
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{
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if (!index)
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data.clear();
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if (value) {
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ExprEngine::ArrayValue::IndexAndValue indexAndValue = {index, value};
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data.push_back(indexAndValue);
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}
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}
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void ExprEngine::ArrayValue::clear()
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{
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data.clear();
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ExprEngine::ArrayValue::IndexAndValue indexAndValue = {
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ExprEngine::ValuePtr(), std::make_shared<ExprEngine::IntRange>("0", 0, 0)
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};
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data.push_back(indexAndValue);
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}
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static bool isEqual(ExprEngine::ValuePtr v1, ExprEngine::ValuePtr v2)
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{
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if (!v1 || !v2)
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return !v1 && !v2;
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return v1->name == v2->name;
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}
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static bool isNonOverlapping(ExprEngine::ValuePtr v1, ExprEngine::ValuePtr v2)
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{
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if (!v1 || !v2)
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return false; // Don't know!
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auto intRange1 = std::dynamic_pointer_cast<ExprEngine::IntRange>(v1);
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auto intRange2 = std::dynamic_pointer_cast<ExprEngine::IntRange>(v2);
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if (intRange1 && intRange2 && (intRange1->minValue > intRange2->maxValue || intRange1->maxValue < intRange2->maxValue))
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return true;
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return false;
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}
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ExprEngine::ConditionalValue::Vector ExprEngine::ArrayValue::read(ExprEngine::ValuePtr index) const
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{
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ExprEngine::ConditionalValue::Vector ret;
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for (const auto indexAndValue : data) {
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if (isEqual(index, indexAndValue.index))
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ret.clear();
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if (isNonOverlapping(index, indexAndValue.index))
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continue;
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// Array contains string literal data...
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if (!indexAndValue.index && indexAndValue.value->type == ExprEngine::ValueType::StringLiteralValue) {
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auto stringLiteral = std::dynamic_pointer_cast<ExprEngine::StringLiteralValue>(indexAndValue.value);
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if (!stringLiteral) {
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ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, std::make_shared<ExprEngine::IntRange>("", -128, 128)));
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continue;
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}
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if (auto i = std::dynamic_pointer_cast<ExprEngine::IntRange>(index)) {
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if (stringLiteral && i->minValue >= 0 && i->minValue == i->maxValue) {
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int c = 0;
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if (i->minValue < stringLiteral->size())
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c = stringLiteral->string[i->minValue];
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ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, std::make_shared<ExprEngine::IntRange>(std::to_string(c), c, c)));
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continue;
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}
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}
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int cmin = 0, cmax = 0;
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for (char c : stringLiteral->string) {
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if (c < cmin)
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cmin = c;
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else if (c > cmax)
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cmax = c;
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}
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ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, std::make_shared<ExprEngine::IntRange>("", cmin, cmax)));
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continue;
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}
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ret.push_back(std::pair<ValuePtr,ValuePtr>(indexAndValue.index, indexAndValue.value));
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}
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if (ret.size() == 1)
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ret[0].first = ExprEngine::ValuePtr();
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else if (ret.size() == 2 && !ret[0].first) {
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ret[0].first = std::make_shared<ExprEngine::BinOpResult>("!=", index, ret[1].first);
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ret[1].first = std::make_shared<ExprEngine::BinOpResult>("==", index, ret[1].first);
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} else {
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// FIXME!!
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ret.clear();
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}
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return ret;
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}
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std::string ExprEngine::ConditionalValue::getSymbolicExpression() const
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{
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std::ostringstream ostr;
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ostr << "{";
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bool first = true;
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for (auto condvalue : values) {
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ValuePtr cond = condvalue.first;
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ValuePtr value = condvalue.second;
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if (!first)
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ostr << ",";
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first = false;
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ostr << "{"
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<< (cond ? cond->getSymbolicExpression() : std::string("(null)"))
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<< ","
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<< value->getSymbolicExpression()
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<< "}";
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}
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ostr << "}";
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return ostr.str();
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}
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std::string ExprEngine::ArrayValue::getSymbolicExpression() const
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{
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std::ostringstream ostr;
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ostr << "size=" << (size ? size->name : std::string("(null)"));
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for (const auto indexAndValue : data) {
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ostr << ",["
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<< (!indexAndValue.index ? std::string(":") : indexAndValue.index->name)
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<< "]="
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<< indexAndValue.value->name;
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}
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return ostr.str();
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}
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std::string ExprEngine::StructValue::getSymbolicExpression() const
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{
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std::ostringstream ostr;
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ostr << "{";
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bool first = true;
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for (const auto& m: member) {
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const std::string &memberName = m.first;
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auto memberValue = m.second;
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if (!first)
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ostr << ",";
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first = false;
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ostr << memberName << "=" << (memberValue ? memberValue->getSymbolicExpression() : std::string("(null)"));
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}
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ostr << "}";
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return ostr.str();
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}
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std::string ExprEngine::PointerValue::getRange() const
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{
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std::string r;
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if (data)
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r = "->" + data->getSymbolicExpression();
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if (null)
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r += std::string(r.empty() ? "" : ",") + "null";
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if (uninitData)
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r += std::string(r.empty() ? "" : ",") + "->?";
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return r;
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}
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std::string ExprEngine::BinOpResult::getRange() const
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{
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IntOrFloatValue minValue, maxValue;
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getRange(&minValue, &maxValue);
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const std::string s1 = minValue.isFloat()
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? std::to_string(minValue.floatValue)
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: str(minValue.intValue);
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const std::string s2 = maxValue.isFloat()
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? std::to_string(maxValue.floatValue)
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: str(maxValue.intValue);
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if (s1 == s2)
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return s1;
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return s1 + ":" + s2;
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}
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void ExprEngine::BinOpResult::getRange(ExprEngine::BinOpResult::IntOrFloatValue *minValue, ExprEngine::BinOpResult::IntOrFloatValue *maxValue) const
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{
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std::map<ValuePtr, int> valueBit;
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// Assign a bit number for each leaf
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int bit = 0;
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for (ValuePtr v : mLeafs) {
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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;
|
|
}
|
|
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 = range->minValue;
|
|
newValue = newValue & (((int128_t)1 << bits) - 1);
|
|
// Sign extension
|
|
if (valueType->sign == ValueType::Sign::SIGNED && newValue & (1ULL << (bits - 1)))
|
|
newValue |= ~(((int128_t)1 << bits) - 1);
|
|
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));
|
|
}
|
|
}
|
|
|
|
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);
|
|
}
|
|
return ExprEngine::ValuePtr();
|
|
}
|
|
|
|
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)
|
|
return ExprEngine::ValuePtr();
|
|
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 executeExpression(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() == "(" && !tok->isCast())
|
|
return executeFunctionCall(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 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 (tok->variable()->isArray()) {
|
|
data.assignValue(tok, tok->varId(), std::make_shared<ExprEngine::ArrayValue>(data.getNewSymbolName(), 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)
|
|
{
|
|
const SymbolDatabase *symbolDatabase = tokenizer->getSymbolDatabase();
|
|
for (const Scope *functionScope : symbolDatabase->functionScopes) {
|
|
executeFunction(functionScope, tokenizer, settings, callbacks);
|
|
}
|
|
}
|
|
|
|
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)
|
|
return ExprEngine::ValuePtr();
|
|
|
|
if (valueType->pointer > 0) {
|
|
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 (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)
|
|
{
|
|
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->verification) {
|
|
// TODO generate better output!!
|
|
trackExecution.print();
|
|
}
|
|
}
|
|
|
|
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::simpleMatch(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", "Division by zero", 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 (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(integerOverflow);
|
|
ExprEngine::executeAllFunctions(tokenizer, settings, callbacks);
|
|
}
|