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https://github.com/ethereum/solidity
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Incremental LP solver.
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df50762498
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@ -24,7 +24,12 @@
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#include <libsolutil/LinearExpression.h>
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#include <libsolutil/LinearExpression.h>
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#include <libsolutil/CDCL.h>
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#include <libsolutil/CDCL.h>
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#if LPIncremental
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#include <libsolutil/LPIncremental.h>
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#else
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#include <libsolutil/LP.h>
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#include <libsolutil/LP.h>
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#endif
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#include <range/v3/view/enumerate.hpp>
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#include <range/v3/view/enumerate.hpp>
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#include <range/v3/view/transform.hpp>
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#include <range/v3/view/transform.hpp>
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@ -48,6 +53,7 @@ using rational = boost::rational<bigint>;
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//#define DEBUG
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//#define DEBUG
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namespace
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namespace
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{
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{
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template <class T>
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template <class T>
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@ -120,12 +126,16 @@ pair<CheckResult, vector<string>> BooleanLPSolver::check(vector<Expression> cons
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std::vector<std::string> booleanVariables;
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std::vector<std::string> booleanVariables;
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std::vector<Clause> clauses = state().clauses;
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std::vector<Clause> clauses = state().clauses;
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#if LPIncremental
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LPSolver lpSolver;
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#else
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// TODO we start building up a new set of solver
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// TODO we start building up a new set of solver
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// for each query, but we should also keep some
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// for each query, but we should also keep some
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// kind of cache across queries.
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// kind of cache across queries.
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std::vector<std::pair<size_t, LPSolver>> lpSolvers;
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std::vector<std::pair<size_t, LPSolver>> lpSolvers;
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lpSolvers.emplace_back(0, LPSolver{});
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lpSolvers.emplace_back(0, LPSolver{});
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LPSolver& lpSolver = lpSolvers.back().second;
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LPSolver& lpSolver = lpSolvers.back().second;
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#endif
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for (auto&& [index, bound]: state().bounds)
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for (auto&& [index, bound]: state().bounds)
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{
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{
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@ -136,6 +146,10 @@ pair<CheckResult, vector<string>> BooleanLPSolver::check(vector<Expression> cons
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}
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}
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for (Constraint const& c: state().fixedConstraints)
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for (Constraint const& c: state().fixedConstraints)
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lpSolver.addConstraint(c);
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lpSolver.addConstraint(c);
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#if LPIncremental
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for (auto&& [index, constraint]: state().conditionalConstraints)
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lpSolver.addConditionalConstraint(constraint, index);
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#endif
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// TODO this way, it will result in a lot of gaps in both sets of variables.
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// TODO this way, it will result in a lot of gaps in both sets of variables.
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// should we compress them and store a mapping?
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// should we compress them and store a mapping?
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@ -146,6 +160,9 @@ pair<CheckResult, vector<string>> BooleanLPSolver::check(vector<Expression> cons
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else
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else
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lpSolver.setVariableName(index, name);
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lpSolver.setVariableName(index, name);
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#ifdef DEBUG
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cerr << "Performing preliminary check." << endl;
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#endif
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if (lpSolver.check().first == LPResult::Infeasible)
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if (lpSolver.check().first == LPResult::Infeasible)
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{
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{
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#ifdef DEBUG
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#ifdef DEBUG
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@ -156,17 +173,32 @@ pair<CheckResult, vector<string>> BooleanLPSolver::check(vector<Expression> cons
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auto theorySolver = [&](size_t _trailSize, map<size_t, bool> const& _newBooleanAssignment) -> optional<Clause>
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auto theorySolver = [&](size_t _trailSize, map<size_t, bool> const& _newBooleanAssignment) -> optional<Clause>
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{
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{
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#if LPIncremental
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lpSolver.setTrailSize(_trailSize);
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#else
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lpSolvers.emplace_back(_trailSize, LPSolver(lpSolvers.back().second));
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lpSolvers.emplace_back(_trailSize, LPSolver(lpSolvers.back().second));
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#endif
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for (auto&& [constraintIndex, value]: _newBooleanAssignment)
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for (auto&& [constraintIndex, value]: _newBooleanAssignment)
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{
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{
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if (!value || !state().conditionalConstraints.count(constraintIndex))
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if (!value || !state().conditionalConstraints.count(constraintIndex))
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continue;
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continue;
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#if LPIncremental
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lpSolver.activateConstraint(constraintIndex);
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#else
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// "reason" is already stored for those constraints.
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// "reason" is already stored for those constraints.
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Constraint const& constraint = state().conditionalConstraints.at(constraintIndex);
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Constraint const& constraint = state().conditionalConstraints.at(constraintIndex);
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lpSolvers.back().second.addConstraint(constraint, constraintIndex);
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lpSolvers.back().second.addConstraint(constraint, constraintIndex);
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#endif
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}
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}
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#ifdef DEBUG
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cerr << "Performing incremental check." << endl;
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#endif
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#if LPIncremental
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auto&& [result, reasonSet] = lpSolver.check();
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#else
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auto&& [result, reasonSet] = lpSolvers.back().second.check();
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auto&& [result, reasonSet] = lpSolvers.back().second.check();
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#endif
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// We can only really use the result "infeasible". Everything else should be "sat".
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// We can only really use the result "infeasible". Everything else should be "sat".
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if (result == LPResult::Infeasible)
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if (result == LPResult::Infeasible)
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{
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{
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@ -184,8 +216,12 @@ pair<CheckResult, vector<string>> BooleanLPSolver::check(vector<Expression> cons
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};
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};
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auto backtrackNotify = [&](size_t _trailSize)
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auto backtrackNotify = [&](size_t _trailSize)
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{
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{
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#if LPIncremental
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lpSolver.setTrailSize(_trailSize);
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#else
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while (lpSolvers.back().first > _trailSize)
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while (lpSolvers.back().first > _trailSize)
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lpSolvers.pop_back();
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lpSolvers.pop_back();
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#endif
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};
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};
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auto optionalModel = CDCL{move(booleanVariables), clauses, theorySolver, backtrackNotify}.solve();
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auto optionalModel = CDCL{move(booleanVariables), clauses, theorySolver, backtrackNotify}.solve();
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@ -19,7 +19,13 @@
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#include <libsmtutil/SolverInterface.h>
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#include <libsmtutil/SolverInterface.h>
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#define LPIncremental 1
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#if LPIncremental
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#include <libsolutil/LPIncremental.h>
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#else
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#include <libsolutil/LP.h>
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#include <libsolutil/LP.h>
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#endif
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#include <libsolutil/CDCL.h>
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#include <libsolutil/CDCL.h>
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#include <boost/rational.hpp>
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#include <boost/rational.hpp>
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@ -29,6 +29,8 @@ set(sources
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LEB128.h
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LEB128.h
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LP.cpp
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LP.cpp
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LP.h
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LP.h
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LPIncremental.cpp
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LPIncremental.h
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Numeric.cpp
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Numeric.cpp
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Numeric.h
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Numeric.h
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picosha2.h
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picosha2.h
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@ -18,6 +18,8 @@
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#include <libsolutil/LP.h>
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#include <libsolutil/LP.h>
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#ifndef LPIncremental
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#include <libsolutil/CommonData.h>
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#include <libsolutil/CommonData.h>
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#include <libsolutil/CommonIO.h>
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#include <libsolutil/CommonIO.h>
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#include <libsolutil/StringUtils.h>
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#include <libsolutil/StringUtils.h>
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@ -51,7 +53,7 @@ using namespace solidity::util;
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using rational = boost::rational<bigint>;
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using rational = boost::rational<bigint>;
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#define DEBUG
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//#define DEBUG
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namespace
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namespace
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{
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{
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@ -833,3 +835,5 @@ void LPSolver::SubProblem::pivotAndUpdate(
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pivot(_oldBasicVar, _newBasicVar);
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pivot(_oldBasicVar, _newBasicVar);
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}
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}
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#endif
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@ -19,7 +19,10 @@
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// use sparse matrices
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// use sparse matrices
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#define SPARSE 1
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#define SPARSE 1
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#define DEBUG
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//#define DEBUG
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#define LPIncremental 1
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#ifndef LPIncremental
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#include <libsolutil/Numeric.h>
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#include <libsolutil/Numeric.h>
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#include <libsolutil/LinearExpression.h>
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#include <libsolutil/LinearExpression.h>
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@ -257,3 +260,4 @@ private:
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};
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};
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}
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}
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#endif
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741
libsolutil/LPIncremental.cpp
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741
libsolutil/LPIncremental.cpp
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@ -0,0 +1,741 @@
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/*
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This file is part of solidity.
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solidity 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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solidity 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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You should have received a copy of the GNU General Public License
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along with solidity. If not, see <http://www.gnu.org/licenses/>.
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*/
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// SPDX-License-Identifier: GPL-3.0
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#include <libsolutil/LPIncremental.h>
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#include <libsolutil/CommonData.h>
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#include <libsolutil/CommonIO.h>
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#include <libsolutil/StringUtils.h>
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#include <libsolutil/LinearExpression.h>
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#include <libsolutil/cxx20.h>
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#include <liblangutil/Exceptions.h>
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#include <range/v3/view/enumerate.hpp>
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#include <range/v3/view/reverse.hpp>
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#include <range/v3/view/transform.hpp>
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#include <range/v3/view/filter.hpp>
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#include <range/v3/view/tail.hpp>
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#include <range/v3/view/iota.hpp>
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#include <range/v3/algorithm/all_of.hpp>
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#include <range/v3/algorithm/any_of.hpp>
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#include <range/v3/algorithm/max.hpp>
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#include <range/v3/algorithm/count_if.hpp>
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#include <range/v3/iterator/operations.hpp>
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#include <boost/range/algorithm_ext/erase.hpp>
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#include <optional>
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#include <stack>
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using namespace std;
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using namespace solidity;
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using namespace solidity::util;
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using rational = boost::rational<bigint>;
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//#define DEBUG
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namespace
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{
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/// Disjunctively combined two vectors of bools.
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inline std::vector<bool>& operator|=(std::vector<bool>& _x, std::vector<bool> const& _y)
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{
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solAssert(_x.size() == _y.size(), "");
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for (size_t i = 0; i < _x.size(); ++i)
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if (_y[i])
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_x[i] = true;
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return _x;
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}
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string toString(rational const& _x)
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{
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if (_x == bigint(1) << 256)
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return "2**256";
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else if (_x == (bigint(1) << 256) - 1)
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return "2**256-1";
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else if (_x.denominator() == 1)
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return ::toString(_x.numerator());
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else
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return ::toString(_x.numerator()) + "/" + ::toString(_x.denominator());
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}
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/*
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string reasonToString(ReasonSet const& _reasons, size_t _minSize)
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{
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auto reasonsAsStrings = _reasons | ranges::views::transform([](size_t _r) { return to_string(_r); });
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string result = "[" + joinHumanReadable(reasonsAsStrings) + "]";
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if (result.size() < _minSize)
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result.resize(_minSize, ' ');
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return result;
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}
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*/
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}
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bool Constraint::operator<(Constraint const& _other) const
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{
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if (kind != _other.kind)
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return kind < _other.kind;
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for (size_t i = 0; i < max(data.size(), _other.data.size()); ++i)
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if (rational diff = data.get(i) - _other.data.get(i))
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{
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//cerr << "Exit after " << i << endl;
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return diff < 0;
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}
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//cerr << "full traversal of " << max(data.size(), _other.data.size()) << endl;
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return false;
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}
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bool Constraint::operator==(Constraint const& _other) const
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{
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if (kind != _other.kind)
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return false;
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for (size_t i = 0; i < max(data.size(), _other.data.size()); ++i)
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if (data.get(i) != _other.data.get(i))
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{
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//cerr << "Exit after " << i << endl;
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return false;
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}
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//cerr << "full traversal of " << max(data.size(), _other.data.size()) << endl;
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return true;
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}
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string RationalWithDelta::toString() const
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{
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string result = ::toString(m_main);
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if (m_delta)
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result +=
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(m_delta > 0 ? "+" : "-") +
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(abs(m_delta) == 1 ? "" : ::toString(abs(m_delta))) +
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"d";
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return result;
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}
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void LPSolver::addConstraint(Constraint const& _constraint)
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{
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#ifdef DEBUG
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cerr << "Adding constraint." << endl;
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#endif
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result = nullopt;
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auto&& [varIndex, bounds] = constraintIntoVariableBounds(_constraint);
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addBounds(varIndex, bounds);
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}
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void LPSolver::addLowerBound(size_t _variable, RationalWithDelta _bound)
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{
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#ifdef DEBUG
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cerr << "Adding lower bound." << endl;
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#endif
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result = nullopt;
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size_t innerIndex = maybeAddOuterVariable(_variable);
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addBounds(innerIndex, Bounds{move(_bound), {}});
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}
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void LPSolver::addUpperBound(size_t _variable, RationalWithDelta _bound)
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{
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#ifdef DEBUG
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cerr << "Adding upper bound." << endl;
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#endif
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// TODO we could only reset the result if the bound changed anything.
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// then we could check if we already have a result insiche "check()"
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// and return early. Although this might be better done inside
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// activateConstraint.
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result = nullopt;
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size_t innerIndex = maybeAddOuterVariable(_variable);
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addBounds(innerIndex, Bounds{{}, move(_bound)});
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}
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void LPSolver::addConditionalConstraint(Constraint const& _constraint, size_t _reason)
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{
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#ifdef DEBUG
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cerr << "Adding conditional constraint." << endl;
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#endif
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auto&& [varIndex, bounds] = constraintIntoVariableBounds(_constraint);
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solAssert(!reasonToBounds.count(_reason));
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reasonToBounds[_reason] = make_pair(varIndex, move(bounds));
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}
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void LPSolver::activateConstraint(size_t _reason)
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{
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#ifdef DEBUG
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cerr << "Activating constraint." << endl;
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#endif
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result = nullopt;
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auto&& [varIndex, bounds] = reasonToBounds.at(_reason);
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Variable& var = variables[varIndex];
|
||||||
|
bool savedBounds = false;
|
||||||
|
if (bounds.lower && (!var.bounds.lower || *var.bounds.lower < *bounds.lower))
|
||||||
|
{
|
||||||
|
storedBounds.emplace_back(make_tuple(trailSize, varIndex, var.bounds, var.lowerReason, var.upperReason));
|
||||||
|
savedBounds = true;
|
||||||
|
var.bounds.lower = bounds.lower;
|
||||||
|
var.lowerReason = _reason;
|
||||||
|
if (var.value < *var.bounds.lower)
|
||||||
|
variablesPotentiallyOutOfBounds.insert(varIndex);
|
||||||
|
}
|
||||||
|
if (bounds.upper && (!var.bounds.upper || *var.bounds.upper > *bounds.upper))
|
||||||
|
{
|
||||||
|
if (!savedBounds)
|
||||||
|
storedBounds.emplace_back(make_tuple(trailSize, varIndex, var.bounds, var.lowerReason, var.upperReason));
|
||||||
|
savedBounds = true;
|
||||||
|
var.bounds.upper = bounds.upper;
|
||||||
|
var.upperReason = _reason;
|
||||||
|
if (var.value > *var.bounds.upper)
|
||||||
|
variablesPotentiallyOutOfBounds.insert(varIndex);
|
||||||
|
}
|
||||||
|
#ifdef DEBUG
|
||||||
|
if (!savedBounds)
|
||||||
|
cerr << "Did not change anything." << endl;
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
void LPSolver::setTrailSize(size_t _trailSize)
|
||||||
|
{
|
||||||
|
// solAssert(_trailSize == 0 || _trailSize != trailSize);
|
||||||
|
if (_trailSize > trailSize)
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << "=== Advancing from " << trailSize << " to " << _trailSize << endl;
|
||||||
|
#endif
|
||||||
|
solAssert(result == LPResult::Feasible);
|
||||||
|
previousGoodValues.resize(variables.size());
|
||||||
|
for (size_t i = 0; i < variables.size(); i++)
|
||||||
|
previousGoodValues[i] = variables[i].value;
|
||||||
|
variablesPotentiallyOutOfBounds.clear();
|
||||||
|
}
|
||||||
|
else if (_trailSize < trailSize)
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << "=== Backtracking from " << trailSize << " to " << _trailSize << endl;
|
||||||
|
#endif
|
||||||
|
while (!storedBounds.empty())
|
||||||
|
{
|
||||||
|
auto&& [ts, varIndex, bounds, lowerReason, upperReason] = storedBounds.back();
|
||||||
|
//TODO should this be "<"?
|
||||||
|
if (ts <= _trailSize)
|
||||||
|
break;
|
||||||
|
variables[varIndex].bounds = bounds;
|
||||||
|
variables[varIndex].lowerReason = lowerReason;
|
||||||
|
variables[varIndex].upperReason = upperReason;
|
||||||
|
// TODO I think this is not needed because of "previousGoodValues
|
||||||
|
// we can maybe assert it.
|
||||||
|
//variablesPotentiallyOutOfBounds.insert(varIndex);
|
||||||
|
storedBounds.pop_back();
|
||||||
|
}
|
||||||
|
for (size_t i = 0; i < previousGoodValues.size(); i++)
|
||||||
|
variables.at(i).value = previousGoodValues[i];
|
||||||
|
variablesPotentiallyOutOfBounds.clear();
|
||||||
|
result = LPResult::Feasible;
|
||||||
|
}
|
||||||
|
trailSize = _trailSize;
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
void LPSolver::setVariableName(size_t _variable, string _name)
|
||||||
|
{
|
||||||
|
size_t index = maybeAddOuterVariable(_variable);
|
||||||
|
variables[index].name = move(_name);
|
||||||
|
}
|
||||||
|
#else
|
||||||
|
void LPSolver::setVariableName(size_t, string)
|
||||||
|
{
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
pair<LPResult, ReasonSet> LPSolver::check()
|
||||||
|
{
|
||||||
|
// TODO below is an old comment - but maybe we can optimize something to that effect
|
||||||
|
// by moving functionality to 'activateConstraint'.
|
||||||
|
|
||||||
|
// TODO one third of the computing time (inclusive) in this function
|
||||||
|
// is spent on "operator<" - maybe we can cache "is in bounds" for variables
|
||||||
|
// and invalidate that in the update procedures.
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << "checking..." << endl;
|
||||||
|
cerr << toString() << endl;
|
||||||
|
cerr << "----------------------------" << endl;
|
||||||
|
// cerr << "fixing non-basic..." << endl;
|
||||||
|
#endif
|
||||||
|
if (result == LPResult::Feasible)
|
||||||
|
return make_pair(LPResult::Feasible, std::set<size_t>());
|
||||||
|
result = nullopt;
|
||||||
|
// Adjust the assignments so we satisfy the bounds of the non-basic variables.
|
||||||
|
if (!correctNonbasic())
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << "---> infeasible" << endl;
|
||||||
|
#endif
|
||||||
|
result = LPResult::Infeasible;
|
||||||
|
return make_pair(LPResult::Infeasible, reasons);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Now try to make the basic variables happy, pivoting if necessary.
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
// cerr << "fixed non-basic." << endl;
|
||||||
|
// cerr << toString() << endl;
|
||||||
|
// cerr << "----------------------------" << endl;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
// TODO bound number of iterations
|
||||||
|
while (auto bvi = firstConflictingBasicVariable())
|
||||||
|
{
|
||||||
|
Variable const& basicVar = variables[*bvi];
|
||||||
|
#ifdef DEBUG
|
||||||
|
// cerr << "----------------------------" << endl;
|
||||||
|
// cerr << "Fixing basic " << basicVar.name << endl;
|
||||||
|
#endif
|
||||||
|
if (basicVar.bounds.lower && basicVar.bounds.upper)
|
||||||
|
solAssert(*basicVar.bounds.lower <= *basicVar.bounds.upper);
|
||||||
|
if (basicVar.bounds.lower && basicVar.value < *basicVar.bounds.lower)
|
||||||
|
{
|
||||||
|
if (auto replacementVar = firstReplacementVar(*bvi, true))
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
// cerr << "Replacing by " << variables[*replacementVar].name << endl;
|
||||||
|
// cerr << "Setting basic var to to " << basicVar.bounds.lower->m_main << endl;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
pivotAndUpdate(*bvi, *basicVar.bounds.lower, *replacementVar);
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << "---> infeasible" << endl;
|
||||||
|
#endif
|
||||||
|
result = LPResult::Infeasible;
|
||||||
|
reasons = reasonsForUnsat(*bvi, true);
|
||||||
|
return make_pair(LPResult::Infeasible, reasons);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else if (basicVar.bounds.upper && basicVar.value > *basicVar.bounds.upper)
|
||||||
|
{
|
||||||
|
if (auto replacementVar = firstReplacementVar(*bvi, false))
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
// cerr << "Replacing by " << variables[*replacementVar].name << endl;
|
||||||
|
#endif
|
||||||
|
pivotAndUpdate(*bvi, *basicVar.bounds.upper, *replacementVar);
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << "---> infeasible" << endl;
|
||||||
|
#endif
|
||||||
|
result = LPResult::Infeasible;
|
||||||
|
reasons = reasonsForUnsat(*bvi, false);
|
||||||
|
return make_pair(LPResult::Infeasible, reasons);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
#ifdef DEBUG
|
||||||
|
// cerr << "Fixed basic " << basicVar.name << endl;
|
||||||
|
// cerr << toString() << endl;
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
result = LPResult::Feasible;
|
||||||
|
#ifdef DEBUG
|
||||||
|
cerr << toString() << endl;
|
||||||
|
cerr << "---> FEAsible" << endl;
|
||||||
|
#endif
|
||||||
|
return make_pair(LPResult::Feasible, std::set<size_t>());
|
||||||
|
}
|
||||||
|
|
||||||
|
string LPSolver::toString() const
|
||||||
|
{
|
||||||
|
string resultString = "LP Solver state (trail size " + to_string(trailSize) + "):\n";
|
||||||
|
auto varName = [&](size_t _i) {
|
||||||
|
#ifdef DEBUG
|
||||||
|
return variables[_i].name;
|
||||||
|
#else
|
||||||
|
return "x" + to_string(_i);
|
||||||
|
#endif
|
||||||
|
};
|
||||||
|
for (auto&& [i, v]: variables | ranges::views::enumerate)
|
||||||
|
{
|
||||||
|
if (v.bounds.lower)
|
||||||
|
resultString += v.bounds.lower->toString() + " <= ";
|
||||||
|
else
|
||||||
|
resultString += " ";
|
||||||
|
resultString += varName(i);
|
||||||
|
if (v.bounds.upper)
|
||||||
|
resultString += " <= " + v.bounds.upper->toString();
|
||||||
|
else
|
||||||
|
resultString += " ";
|
||||||
|
resultString += " := " + v.value.toString() + "\n";
|
||||||
|
}
|
||||||
|
for (size_t rowIndex = 0; rowIndex < factors.rows(); rowIndex++)
|
||||||
|
{
|
||||||
|
string basicVarPrefix;
|
||||||
|
string rowString;
|
||||||
|
for (auto&& entry: const_cast<SparseMatrix&>(factors).iterateRow(rowIndex))
|
||||||
|
{
|
||||||
|
rational const& f = entry.value;
|
||||||
|
solAssert(!!f);
|
||||||
|
size_t i = entry.col;
|
||||||
|
if (basicVariables.count(i) && basicVariables.at(i) == rowIndex)
|
||||||
|
{
|
||||||
|
solAssert(f == -1);
|
||||||
|
solAssert(basicVarPrefix.empty());
|
||||||
|
basicVarPrefix = varName(i) + " = ";
|
||||||
|
}
|
||||||
|
else if (f != 0)
|
||||||
|
{
|
||||||
|
string joiner = f < 0 ? " - " : f > 0 && !rowString.empty() ? " + " : " ";
|
||||||
|
string factor = f == 1 || f == -1 ? "" : ::toString(abs(f)) + " ";
|
||||||
|
string var = varName(i);
|
||||||
|
rowString += joiner + factor + var;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
resultString += basicVarPrefix + rowString + "\n";
|
||||||
|
}
|
||||||
|
if (result)
|
||||||
|
{
|
||||||
|
if (*result == LPResult::Feasible)
|
||||||
|
resultString += "result: feasible\n";
|
||||||
|
else
|
||||||
|
resultString += "result: infeasible\n";
|
||||||
|
}
|
||||||
|
else
|
||||||
|
resultString += "result: unknown\n";
|
||||||
|
|
||||||
|
|
||||||
|
return resultString + "----\n";
|
||||||
|
}
|
||||||
|
|
||||||
|
map<string, rational> LPSolver::model() const
|
||||||
|
{
|
||||||
|
map<string, rational> result;
|
||||||
|
#ifdef DEBUG
|
||||||
|
for (auto&& [outerIndex, innerIndex]: varMapping)
|
||||||
|
// TODO assign proper value to "delta"
|
||||||
|
result[variables[innerIndex].name] =
|
||||||
|
variables[innerIndex].value.m_main +
|
||||||
|
variables[innerIndex].value.m_delta / rational(100000);
|
||||||
|
#endif
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
pair<size_t, LPSolver::Bounds> LPSolver::constraintIntoVariableBounds(Constraint const& _constraint)
|
||||||
|
{
|
||||||
|
size_t numVariables = 0;
|
||||||
|
size_t latestVariableIndex = size_t(-1);
|
||||||
|
// Make all variables available and check if it is a simple bound on a variable.
|
||||||
|
for (auto const& [index, entry]: _constraint.data.enumerateTail())
|
||||||
|
if (entry)
|
||||||
|
{
|
||||||
|
latestVariableIndex = index;
|
||||||
|
numVariables++;
|
||||||
|
if (!varMapping.count(index))
|
||||||
|
addOuterVariable(index);
|
||||||
|
}
|
||||||
|
if (numVariables == 1)
|
||||||
|
{
|
||||||
|
// Add this as direct bound.
|
||||||
|
rational factor = _constraint.data[latestVariableIndex];
|
||||||
|
RationalWithDelta bound = _constraint.data.front();
|
||||||
|
if (_constraint.kind == Constraint::LESS_THAN)
|
||||||
|
bound -= RationalWithDelta::delta();
|
||||||
|
bound /= factor;
|
||||||
|
Bounds bounds;
|
||||||
|
if (factor > 0 || _constraint.kind == Constraint::EQUAL)
|
||||||
|
bounds.upper = bound;
|
||||||
|
if (factor < 0 || _constraint.kind == Constraint::EQUAL)
|
||||||
|
bounds.lower = bound;
|
||||||
|
return make_pair(varMapping.at(latestVariableIndex), move(bounds));
|
||||||
|
}
|
||||||
|
|
||||||
|
// TODO do we need to introduce a slack variable if we have a (potentially new)
|
||||||
|
// non-basic variable, or if we have an equality constraint?
|
||||||
|
|
||||||
|
// Introduce the slack variable.
|
||||||
|
size_t slackIndex = addNewVariable();
|
||||||
|
// Name is only needed for printing
|
||||||
|
#ifdef DEBUG
|
||||||
|
variables[slackIndex].name = "_s" + to_string(m_slackVariableCounter++);
|
||||||
|
#endif
|
||||||
|
basicVariables[slackIndex] = factors.rows();
|
||||||
|
|
||||||
|
// Compress the constraint, i.e. turn outer variable indices into
|
||||||
|
// inner variable indices.
|
||||||
|
RationalWithDelta valueForSlack;
|
||||||
|
size_t row = factors.rows();
|
||||||
|
// First, handle the basic variables.
|
||||||
|
for (auto const& [outerIndex, entry]: _constraint.data.enumerateTail())
|
||||||
|
if (entry)
|
||||||
|
{
|
||||||
|
size_t innerIndex = varMapping.at(outerIndex);
|
||||||
|
if (basicVariables.count(innerIndex))
|
||||||
|
{
|
||||||
|
factors.addMultipleOfRow(
|
||||||
|
basicVariables[innerIndex],
|
||||||
|
row,
|
||||||
|
entry
|
||||||
|
);
|
||||||
|
factors.remove(factors.entry(row, innerIndex));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// Now the non-basic.
|
||||||
|
for (auto const& [outerIndex, entry]: _constraint.data.enumerateTail())
|
||||||
|
if (entry)
|
||||||
|
{
|
||||||
|
size_t innerIndex = varMapping.at(outerIndex);
|
||||||
|
if (!basicVariables.count(innerIndex))
|
||||||
|
{
|
||||||
|
SparseMatrix::Entry& e = factors.entry(row, innerIndex);
|
||||||
|
e.value += entry;
|
||||||
|
if (!e.value)
|
||||||
|
factors.remove(e);
|
||||||
|
}
|
||||||
|
valueForSlack += variables[innerIndex].value * entry;
|
||||||
|
}
|
||||||
|
|
||||||
|
factors.entry(row, slackIndex).value = -1;
|
||||||
|
|
||||||
|
// TODO do we really not need to add this to "potentially out of bounds"?
|
||||||
|
|
||||||
|
basicVariables[slackIndex] = row;
|
||||||
|
variables[slackIndex].value = valueForSlack;
|
||||||
|
|
||||||
|
Bounds bounds;
|
||||||
|
if (_constraint.kind == Constraint::EQUAL)
|
||||||
|
bounds.lower = _constraint.data[0];
|
||||||
|
bounds.upper = _constraint.data[0];
|
||||||
|
if (_constraint.kind == Constraint::LESS_THAN)
|
||||||
|
*bounds.upper -= RationalWithDelta::delta();
|
||||||
|
return make_pair(slackIndex, move(bounds));
|
||||||
|
}
|
||||||
|
|
||||||
|
void LPSolver::addBounds(size_t _variable, Bounds _bounds)
|
||||||
|
{
|
||||||
|
Variable& var = variables[_variable];
|
||||||
|
if (_bounds.lower && (!var.bounds.lower || *var.bounds.lower < *_bounds.lower))
|
||||||
|
{
|
||||||
|
var.bounds.lower = move(_bounds.lower);
|
||||||
|
if (var.value < var.bounds.lower)
|
||||||
|
variablesPotentiallyOutOfBounds.insert(_variable);
|
||||||
|
}
|
||||||
|
if (_bounds.upper && (!var.bounds.upper || *var.bounds.upper > *_bounds.upper))
|
||||||
|
{
|
||||||
|
var.bounds.upper = move(_bounds.upper);
|
||||||
|
if (var.value > var.bounds.upper)
|
||||||
|
variablesPotentiallyOutOfBounds.insert(_variable);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
set<size_t> LPSolver::collectReasonsForVariable(size_t _variable)
|
||||||
|
{
|
||||||
|
set<size_t> reasons;
|
||||||
|
if (variables[_variable].lowerReason)
|
||||||
|
reasons.insert(*variables[_variable].lowerReason);
|
||||||
|
if (variables[_variable].upperReason)
|
||||||
|
reasons.insert(*variables[_variable].upperReason);
|
||||||
|
return reasons;
|
||||||
|
}
|
||||||
|
|
||||||
|
void LPSolver::addOuterVariable(size_t _outerIndex)
|
||||||
|
{
|
||||||
|
size_t index = addNewVariable();
|
||||||
|
varMapping.emplace(_outerIndex, index);
|
||||||
|
}
|
||||||
|
|
||||||
|
size_t LPSolver::maybeAddOuterVariable(size_t _outerIndex)
|
||||||
|
{
|
||||||
|
if (varMapping.count(_outerIndex))
|
||||||
|
return varMapping.at(_outerIndex);
|
||||||
|
size_t index = addNewVariable();
|
||||||
|
varMapping.emplace(_outerIndex, index);
|
||||||
|
return index;
|
||||||
|
}
|
||||||
|
|
||||||
|
size_t LPSolver::addNewVariable()
|
||||||
|
{
|
||||||
|
size_t index = variables.size();
|
||||||
|
variables.emplace_back();
|
||||||
|
return index;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
bool LPSolver::correctNonbasic()
|
||||||
|
{
|
||||||
|
set<size_t> toCorrect;
|
||||||
|
swap(toCorrect, variablesPotentiallyOutOfBounds);
|
||||||
|
for (size_t i: toCorrect)
|
||||||
|
{
|
||||||
|
Variable& var = variables.at(i);
|
||||||
|
if (var.bounds.lower && var.bounds.upper && *var.bounds.lower > *var.bounds.upper)
|
||||||
|
{
|
||||||
|
reasons = collectReasonsForVariable(i);
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
if (basicVariables.count(i))
|
||||||
|
{
|
||||||
|
variablesPotentiallyOutOfBounds.insert(i);
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
if (!var.bounds.lower && !var.bounds.upper)
|
||||||
|
continue;
|
||||||
|
if (var.bounds.lower && var.value < *var.bounds.lower)
|
||||||
|
update(i, *var.bounds.lower);
|
||||||
|
else if (var.bounds.upper && var.value > *var.bounds.upper)
|
||||||
|
update(i, *var.bounds.upper);
|
||||||
|
}
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
void LPSolver::update(size_t _varIndex, RationalWithDelta const& _value)
|
||||||
|
{
|
||||||
|
RationalWithDelta delta = _value - variables[_varIndex].value;
|
||||||
|
variables[_varIndex].value = _value;
|
||||||
|
|
||||||
|
// TODO can we store that?
|
||||||
|
map<size_t, size_t> basicVarForRow = invertMap(basicVariables);
|
||||||
|
for (auto&& entry: factors.iterateColumn(_varIndex))
|
||||||
|
if (entry.value && basicVarForRow.count(entry.row))
|
||||||
|
{
|
||||||
|
size_t j = basicVarForRow[entry.row];
|
||||||
|
variables[j].value += delta * entry.value;
|
||||||
|
//variablesPotentiallyOutOfBounds.insert(j);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
optional<size_t> LPSolver::firstConflictingBasicVariable() const
|
||||||
|
{
|
||||||
|
// TODO we could use "variablesPotentiallyOutOfBounds" here.
|
||||||
|
for (auto&& [i, row]: basicVariables)
|
||||||
|
{
|
||||||
|
Variable const& variable = variables[i];
|
||||||
|
if (
|
||||||
|
(variable.bounds.lower && variable.value < *variable.bounds.lower) ||
|
||||||
|
(variable.bounds.upper && variable.value > *variable.bounds.upper)
|
||||||
|
)
|
||||||
|
return i;
|
||||||
|
}
|
||||||
|
return nullopt;
|
||||||
|
}
|
||||||
|
|
||||||
|
optional<size_t> LPSolver::firstReplacementVar(
|
||||||
|
size_t _basicVarToReplace,
|
||||||
|
bool _increasing
|
||||||
|
) const
|
||||||
|
{
|
||||||
|
for (auto&& entry: const_cast<SparseMatrix&>(factors).iterateRow(basicVariables.at(_basicVarToReplace)))
|
||||||
|
{
|
||||||
|
size_t i = entry.col;
|
||||||
|
rational const& factor = entry.value;
|
||||||
|
if (i == _basicVarToReplace || !factor)
|
||||||
|
continue;
|
||||||
|
bool positive = factor > 0;
|
||||||
|
if (!_increasing)
|
||||||
|
positive = !positive;
|
||||||
|
Variable const& candidate = variables.at(i);
|
||||||
|
if (positive && (!candidate.bounds.upper || candidate.value < *candidate.bounds.upper))
|
||||||
|
return i;
|
||||||
|
if (!positive && (!candidate.bounds.lower || candidate.value > *candidate.bounds.lower))
|
||||||
|
return i;
|
||||||
|
}
|
||||||
|
return nullopt;
|
||||||
|
}
|
||||||
|
|
||||||
|
set<size_t> LPSolver::reasonsForUnsat(
|
||||||
|
size_t _basicVarToReplace,
|
||||||
|
bool _increasing
|
||||||
|
) const
|
||||||
|
{
|
||||||
|
set<size_t> r;
|
||||||
|
if (_increasing && variables[_basicVarToReplace].lowerReason)
|
||||||
|
r.insert(*variables[_basicVarToReplace].lowerReason);
|
||||||
|
else if (!_increasing && variables[_basicVarToReplace].upperReason)
|
||||||
|
r.insert(*variables[_basicVarToReplace].upperReason);
|
||||||
|
|
||||||
|
for (auto&& entry: const_cast<SparseMatrix&>(factors).iterateRow(basicVariables.at(_basicVarToReplace)))
|
||||||
|
{
|
||||||
|
size_t i = entry.col;
|
||||||
|
rational const& factor = entry.value;
|
||||||
|
if (i == _basicVarToReplace || !factor)
|
||||||
|
continue;
|
||||||
|
bool positive = factor > 0;
|
||||||
|
if (!_increasing)
|
||||||
|
positive = !positive;
|
||||||
|
Variable const& candidate = variables.at(i);
|
||||||
|
if (positive && candidate.upperReason)
|
||||||
|
r.insert(*candidate.upperReason);
|
||||||
|
if (!positive && candidate.lowerReason)
|
||||||
|
r.insert(*candidate.lowerReason);
|
||||||
|
}
|
||||||
|
return r;
|
||||||
|
}
|
||||||
|
|
||||||
|
void LPSolver::pivot(size_t _old, size_t _new)
|
||||||
|
{
|
||||||
|
// Transform pivotRow such that the coefficient for _new is -1
|
||||||
|
// Then use that to set all other coefficients for _new to zero.
|
||||||
|
size_t pivotRow = basicVariables[_old];
|
||||||
|
|
||||||
|
rational pivot = factors.entry(pivotRow, _new).value;
|
||||||
|
solAssert(pivot != 0, "");
|
||||||
|
if (pivot != -1)
|
||||||
|
factors.multiplyRowByFactor(pivotRow, rational{-1} / pivot);
|
||||||
|
|
||||||
|
for (auto it = factors.iterateColumn(_new).begin(); it != factors.iterateColumn(_new).end(); )
|
||||||
|
{
|
||||||
|
SparseMatrix::Entry& entry = *it;
|
||||||
|
// Increment becasue "addMultipleOfRow" might invalidate the iterator
|
||||||
|
++it;
|
||||||
|
if (entry.row != pivotRow)
|
||||||
|
factors.addMultipleOfRow(pivotRow, entry.row, entry.value);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
basicVariables.erase(_old);
|
||||||
|
basicVariables[_new] = pivotRow;
|
||||||
|
}
|
||||||
|
|
||||||
|
void LPSolver::pivotAndUpdate(
|
||||||
|
size_t _oldBasicVar,
|
||||||
|
RationalWithDelta const& _newValue,
|
||||||
|
size_t _newBasicVar
|
||||||
|
)
|
||||||
|
{
|
||||||
|
RationalWithDelta theta = (_newValue - variables[_oldBasicVar].value) / factors.entry(basicVariables[_oldBasicVar], _newBasicVar).value;
|
||||||
|
|
||||||
|
variables[_oldBasicVar].value = _newValue;
|
||||||
|
variables[_newBasicVar].value += theta;
|
||||||
|
|
||||||
|
// TODO can we store that?
|
||||||
|
map<size_t, size_t> basicVarForRow = invertMap(basicVariables);
|
||||||
|
for (auto&& entry: factors.iterateColumn(_newBasicVar))
|
||||||
|
if (basicVarForRow.count(entry.row))
|
||||||
|
{
|
||||||
|
size_t i = basicVarForRow[entry.row];
|
||||||
|
if (i != _oldBasicVar)
|
||||||
|
variables[i].value += theta * entry.value;
|
||||||
|
}
|
||||||
|
|
||||||
|
pivot(_oldBasicVar, _newBasicVar);
|
||||||
|
}
|
241
libsolutil/LPIncremental.h
Normal file
241
libsolutil/LPIncremental.h
Normal file
@ -0,0 +1,241 @@
|
|||||||
|
/*
|
||||||
|
This file is part of solidity.
|
||||||
|
|
||||||
|
solidity 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.
|
||||||
|
|
||||||
|
solidity 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 solidity. If not, see <http://www.gnu.org/licenses/>.
|
||||||
|
*/
|
||||||
|
// SPDX-License-Identifier: GPL-3.0
|
||||||
|
#pragma once
|
||||||
|
|
||||||
|
//#define DEBUG 1
|
||||||
|
|
||||||
|
#include <libsolutil/Numeric.h>
|
||||||
|
#include <libsolutil/LinearExpression.h>
|
||||||
|
|
||||||
|
#include <boost/rational.hpp>
|
||||||
|
|
||||||
|
#include <vector>
|
||||||
|
#include <variant>
|
||||||
|
#include <functional>
|
||||||
|
|
||||||
|
namespace solidity::util
|
||||||
|
{
|
||||||
|
|
||||||
|
using rational = boost::rational<bigint>;
|
||||||
|
using Model = std::map<std::string, rational>;
|
||||||
|
using ReasonSet = std::set<size_t>;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Constraint of the form
|
||||||
|
* - data[1] * x_1 + data[2] * x_2 + ... <= data[0] (LESS_OR_EQUAL)
|
||||||
|
* - data[1] * x_1 + data[2] * x_2 + ... < data[0] (LESS_THAN)
|
||||||
|
* - data[1] * x_1 + data[2] * x_2 + ... = data[0] (EQUAL)
|
||||||
|
* The set and order of variables is implied.
|
||||||
|
*/
|
||||||
|
struct Constraint
|
||||||
|
{
|
||||||
|
LinearExpression data;
|
||||||
|
enum Kind { EQUAL, LESS_THAN, LESS_OR_EQUAL };
|
||||||
|
Kind kind = LESS_OR_EQUAL;
|
||||||
|
|
||||||
|
bool operator<(Constraint const& _other) const;
|
||||||
|
bool operator==(Constraint const& _other) const;
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* A two-dimensional rational number "a + b*delta" that can be used to perform strict comparisons:
|
||||||
|
* x > 0 is transformed into x >= 1*delta, where delta is assumed to be "small". Its value
|
||||||
|
* is never explicitly computed / set, it is just a symbolic parameter.
|
||||||
|
*/
|
||||||
|
struct RationalWithDelta
|
||||||
|
{
|
||||||
|
RationalWithDelta(rational _x = {}): m_main(move(_x)) {}
|
||||||
|
static RationalWithDelta delta()
|
||||||
|
{
|
||||||
|
RationalWithDelta x(0);
|
||||||
|
x.m_delta = 1;
|
||||||
|
return x;
|
||||||
|
}
|
||||||
|
|
||||||
|
RationalWithDelta& operator+=(RationalWithDelta const& _other)
|
||||||
|
{
|
||||||
|
m_main += _other.m_main;
|
||||||
|
m_delta += _other.m_delta;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
RationalWithDelta& operator-=(RationalWithDelta const& _other)
|
||||||
|
{
|
||||||
|
m_main -= _other.m_main;
|
||||||
|
m_delta -= _other.m_delta;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
RationalWithDelta operator-(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
RationalWithDelta ret = *this;
|
||||||
|
ret -= _other;
|
||||||
|
return ret;
|
||||||
|
}
|
||||||
|
RationalWithDelta& operator*=(rational const& _factor)
|
||||||
|
{
|
||||||
|
m_main *= _factor;
|
||||||
|
m_delta *= _factor;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
RationalWithDelta operator*(rational const& _factor) const
|
||||||
|
{
|
||||||
|
RationalWithDelta ret = *this;
|
||||||
|
ret *= _factor;
|
||||||
|
return ret;
|
||||||
|
}
|
||||||
|
RationalWithDelta& operator/=(rational const& _factor)
|
||||||
|
{
|
||||||
|
m_main /= _factor;
|
||||||
|
m_delta /= _factor;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
RationalWithDelta operator/(rational const& _factor) const
|
||||||
|
{
|
||||||
|
RationalWithDelta ret = *this;
|
||||||
|
ret /= _factor;
|
||||||
|
return ret;
|
||||||
|
}
|
||||||
|
bool operator<=(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
return std::tie(m_main, m_delta) <= std::tie(_other.m_main, _other.m_delta);
|
||||||
|
}
|
||||||
|
bool operator>=(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
return std::tie(m_main, m_delta) >= std::tie(_other.m_main, _other.m_delta);
|
||||||
|
}
|
||||||
|
bool operator<(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
return std::tie(m_main, m_delta) < std::tie(_other.m_main, _other.m_delta);
|
||||||
|
}
|
||||||
|
bool operator>(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
return std::tie(m_main, m_delta) > std::tie(_other.m_main, _other.m_delta);
|
||||||
|
}
|
||||||
|
bool operator==(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
return std::tie(m_main, m_delta) == std::tie(_other.m_main, _other.m_delta);
|
||||||
|
}
|
||||||
|
bool operator!=(RationalWithDelta const& _other) const
|
||||||
|
{
|
||||||
|
return std::tie(m_main, m_delta) != std::tie(_other.m_main, _other.m_delta);
|
||||||
|
}
|
||||||
|
|
||||||
|
std::string toString() const;
|
||||||
|
|
||||||
|
rational m_main;
|
||||||
|
rational m_delta;
|
||||||
|
};
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
namespace solidity::util
|
||||||
|
{
|
||||||
|
|
||||||
|
enum class LPResult
|
||||||
|
{
|
||||||
|
Unknown,
|
||||||
|
Unbounded, ///< System has a solution, but it can have an arbitrary objective value.
|
||||||
|
Feasible, ///< System has a solution (it might be unbounded, though).
|
||||||
|
Infeasible ///< System does not have any solution.
|
||||||
|
};
|
||||||
|
|
||||||
|
class LPSolver
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
void addConstraint(Constraint const& _constraint);
|
||||||
|
void addLowerBound(size_t _variable, RationalWithDelta _bound);
|
||||||
|
void addUpperBound(size_t _variable, RationalWithDelta _bound);
|
||||||
|
/// Add the conditional constraint but do not activate it yet.
|
||||||
|
void addConditionalConstraint(Constraint const& _constraint, size_t _reason);
|
||||||
|
void activateConstraint(size_t _reason);
|
||||||
|
void setTrailSize(size_t _trailSize);
|
||||||
|
|
||||||
|
void setVariableName(size_t _variable, std::string _name);
|
||||||
|
|
||||||
|
std::pair<LPResult, ReasonSet> check();
|
||||||
|
|
||||||
|
std::string toString() const;
|
||||||
|
std::map<std::string, rational> model() const;
|
||||||
|
|
||||||
|
private:
|
||||||
|
struct Bounds
|
||||||
|
{
|
||||||
|
std::optional<RationalWithDelta> lower;
|
||||||
|
std::optional<RationalWithDelta> upper;
|
||||||
|
};
|
||||||
|
struct Variable
|
||||||
|
{
|
||||||
|
#ifdef DEBUG
|
||||||
|
std::string name = {};
|
||||||
|
#endif
|
||||||
|
RationalWithDelta value = {};
|
||||||
|
Bounds bounds = {};
|
||||||
|
std::optional<size_t> lowerReason;
|
||||||
|
std::optional<size_t> upperReason;
|
||||||
|
};
|
||||||
|
|
||||||
|
/// Consumes a constraint and returns a controlling variable (can be a new slack
|
||||||
|
/// but does not need to) and corresponding bounds.
|
||||||
|
/// If it adds a slack variable, updates the factors and properly sets the value
|
||||||
|
/// for the slack variable (which will be a new basic variable).
|
||||||
|
std::pair<size_t, Bounds> constraintIntoVariableBounds(Constraint const& _constraint);
|
||||||
|
void addBounds(size_t _variable, Bounds _bounds);
|
||||||
|
std::set<size_t> collectReasonsForVariable(size_t _variable);
|
||||||
|
|
||||||
|
bool correctNonbasic();
|
||||||
|
/// Set value of non-basic variable.
|
||||||
|
void update(size_t _varIndex, RationalWithDelta const& _value);
|
||||||
|
/// @returns the index of the first basic variable violating its bounds.
|
||||||
|
std::optional<size_t> firstConflictingBasicVariable() const;
|
||||||
|
std::optional<size_t> firstReplacementVar(size_t _basicVarToReplace, bool _increasing) const;
|
||||||
|
/// @returns the set of reasons in case "firstReplacementVar" failed.
|
||||||
|
std::set<size_t> reasonsForUnsat(size_t _basicVarToReplace, bool _increasing) const;
|
||||||
|
|
||||||
|
void pivot(size_t _old, size_t _new);
|
||||||
|
void pivotAndUpdate(size_t _oldBasicVar, RationalWithDelta const& _newValue, size_t _newBasicVar);
|
||||||
|
|
||||||
|
void addOuterVariable(size_t _outerIndex);
|
||||||
|
/// Adds a new outer variable if it is not known yet and returns the inner index in any case.
|
||||||
|
size_t maybeAddOuterVariable(size_t _outerIndex);
|
||||||
|
size_t addNewVariable();
|
||||||
|
|
||||||
|
/// Counter to enable unique names for the slack variables.
|
||||||
|
size_t m_slackVariableCounter = 0;
|
||||||
|
std::optional<LPResult> result = std::nullopt;
|
||||||
|
size_t trailSize = 0;
|
||||||
|
SparseMatrix factors;
|
||||||
|
std::vector<Variable> variables;
|
||||||
|
/// Stack of (trail size, variable index, bounds, lower reason, upper reason).
|
||||||
|
std::vector<std::tuple<size_t, size_t, Bounds, std::optional<size_t>, std::optional<size_t>>> storedBounds;
|
||||||
|
/// Last known satisfying values for variables.
|
||||||
|
std::vector<RationalWithDelta> previousGoodValues;
|
||||||
|
std::set<size_t> variablesPotentiallyOutOfBounds;
|
||||||
|
/// Variable index to constraint it controls.
|
||||||
|
std::map<size_t, size_t> basicVariables;
|
||||||
|
/// Maps outer indices to inner indices.
|
||||||
|
std::map<size_t, size_t> varMapping = {};
|
||||||
|
/// Mapping from reason (constraint ID) to variable it controls and bounds for it.
|
||||||
|
/// A variable can be controlled by multiple constraints.
|
||||||
|
/// TODO do we want to store the reverse mapping?
|
||||||
|
std::map<size_t, std::pair<size_t, Bounds>> reasonToBounds;
|
||||||
|
std::set<size_t> reasons;
|
||||||
|
|
||||||
|
|
||||||
|
};
|
||||||
|
|
||||||
|
}
|
@ -267,7 +267,8 @@ BOOST_AUTO_TEST_CASE(magic_square_3)
|
|||||||
solver.addAssertion(1 <= var && var <= 9);
|
solver.addAssertion(1 <= var && var <= 9);
|
||||||
for (size_t i = 0; i < 9; i++)
|
for (size_t i = 0; i < 9; i++)
|
||||||
for (size_t j = i + 1; j < 9; j++)
|
for (size_t j = i + 1; j < 9; j++)
|
||||||
solver.addAssertion(vars[i] != vars[j]);
|
//solver.addAssertion(vars[i] != vars[j]);
|
||||||
|
solver.addAssertion(vars[i] <= vars[j] - 1 || vars[i] >= vars[j] + 1);
|
||||||
for (size_t i = 0; i < 3; i++)
|
for (size_t i = 0; i < 3; i++)
|
||||||
solver.addAssertion(vars[i] + vars[i + 3] + vars[i + 6] == sum);
|
solver.addAssertion(vars[i] + vars[i + 3] + vars[i + 6] == sum);
|
||||||
for (size_t i = 0; i < 9; i += 3)
|
for (size_t i = 0; i < 9; i += 3)
|
||||||
@ -292,7 +293,7 @@ BOOST_AUTO_TEST_CASE(magic_square_4)
|
|||||||
solver.addAssertion(1 <= var && var <= 16);
|
solver.addAssertion(1 <= var && var <= 16);
|
||||||
for (size_t i = 0; i < 16; i++)
|
for (size_t i = 0; i < 16; i++)
|
||||||
for (size_t j = i + 1; j < 16; j++)
|
for (size_t j = i + 1; j < 16; j++)
|
||||||
solver.addAssertion(vars[i] != vars[j]);
|
solver.addAssertion(vars[i] <= vars[j] - 1 || vars[i] >= vars[j] + 1);
|
||||||
for (size_t i = 0; i < 4; i++)
|
for (size_t i = 0; i < 4; i++)
|
||||||
solver.addAssertion(vars[i] + vars[i + 4] + vars[i + 8] + vars[i + 12] == sum);
|
solver.addAssertion(vars[i] + vars[i + 4] + vars[i + 8] + vars[i + 12] == sum);
|
||||||
for (size_t i = 0; i < 16; i += 4)
|
for (size_t i = 0; i < 16; i += 4)
|
||||||
|
@ -16,7 +16,13 @@
|
|||||||
*/
|
*/
|
||||||
// SPDX-License-Identifier: GPL-3.0
|
// SPDX-License-Identifier: GPL-3.0
|
||||||
|
|
||||||
|
#define LPIncremental 1
|
||||||
|
|
||||||
|
#if LPIncremental
|
||||||
|
#include <libsolutil/LPIncremental.h>
|
||||||
|
#else
|
||||||
#include <libsolutil/LP.h>
|
#include <libsolutil/LP.h>
|
||||||
|
#endif
|
||||||
#include <libsolutil/LinearExpression.h>
|
#include <libsolutil/LinearExpression.h>
|
||||||
#include <libsolutil/CommonIO.h>
|
#include <libsolutil/CommonIO.h>
|
||||||
#include <libsmtutil/Sorts.h>
|
#include <libsmtutil/Sorts.h>
|
||||||
@ -25,6 +31,8 @@
|
|||||||
|
|
||||||
#include <boost/test/unit_test.hpp>
|
#include <boost/test/unit_test.hpp>
|
||||||
|
|
||||||
|
#if 0
|
||||||
|
|
||||||
using namespace std;
|
using namespace std;
|
||||||
using namespace solidity::smtutil;
|
using namespace solidity::smtutil;
|
||||||
using namespace solidity::util;
|
using namespace solidity::util;
|
||||||
@ -496,3 +504,4 @@ BOOST_AUTO_TEST_CASE(fuzzer2)
|
|||||||
BOOST_AUTO_TEST_SUITE_END()
|
BOOST_AUTO_TEST_SUITE_END()
|
||||||
|
|
||||||
}
|
}
|
||||||
|
#endif
|
||||||
|
Loading…
Reference in New Issue
Block a user