protected override void AddControllerOverflow(Microsoft.Z3.Context ctx, Microsoft.Z3.Solver solver, string varName)
{
FixedPointNumber var = discreteVariablesByName[varName];
FixedPointNumber expr = assigns[varName];
solver.Assert(expr.overflow);
}
static public BoolExprWithOverflow MkFPSBetween(this Context ctx, FixedPointNumber E, FixedPointNumber L, FixedPointNumber U)
{
var calc = ctx.MkAnd(ctx.MkFPSGE(E, L).bv, ctx.MkFPSLE(E, U).bv);
var overflow = ctx.MkOr(E.overflow, L.overflow, U.overflow);
return(new BoolExprWithOverflow(calc, overflow, String.Format("{0}<={1}<={2}", L.Expr, E.Expr, U.Expr)));
}
/// <summary>
/// Add controller code for output/memory variable 'var'
/// </summary>
/// <param name="ctx"></param>
/// <param name="solver"></param>
/// <param name="variable"></param>
protected override void AddController(Microsoft.Z3.Context ctx, Microsoft.Z3.Solver solver, string varName)
{
FixedPointNumber var = discreteVariablesByName[varName];
FixedPointNumber expr = assigns[varName];
BoolExprWithOverflow assert = ctx.MkFPEq(var, expr);
solver.Assert(assert.bv);
}
static public FixedPointNumber MkFPMax(this Context ctx, FixedPointNumber A, FixedPointNumber B)
{
Contract.Requires(A != null);
Contract.Requires(B != null);
Contract.Requires(A.bits == B.bits);
Contract.Requires(A.decimals == B.decimals);
var overflow = ctx.MkOr(A.overflow, B.overflow);
return(new FixedPointNumber(A.bits, A.decimals, (BitVecExpr)ctx.MkITE(ctx.MkBVSGE(A.bv, B.bv), A.bv, B.bv), overflow, String.Format("max({0},{1})", A.Expr, B.Expr)));
}
static public BoolExprWithOverflow MkFPSGT(this Context ctx, FixedPointNumber A, FixedPointNumber B)
{
Contract.Requires(A != null);
Contract.Requires(B != null);
Contract.Requires(A.bits == B.bits);
Contract.Requires(A.decimals == B.decimals);
var calc = ctx.MkBVSGT(A.bv, B.bv);
var overflow = ctx.MkOr(A.overflow, B.overflow);
return(new BoolExprWithOverflow(calc, overflow, String.Format("{0}>{1}", A.Expr, B.Expr)));
}
protected override Dictionary <string, DoubleInterval> Hold(State q)
{
Dictionary <string, DoubleInterval> result = new Dictionary <string, DoubleInterval>();
foreach (var kvp in hold)
{
VAR c = kvp.Value;
FixedPointNumber fp = kvp.Key;
int i = Array.FindIndex(q.discreteNames, x => x.Equals(fp.Expr));
result.Add(c.name, q.discreteState.axes[i].ToDoubleInterval());
}
return(result);
}
static public FixedPointNumber MkFPNeg(this Context ctx, FixedPointNumber A)
{
var zero = ctx.MkBV(0, A.bits);
var calc = ctx.MkBVSub(zero, A.bv);
var o1 = ctx.MkNot(ctx.MkBVSubNoOverflow(zero, A.bv));
var o2 = ctx.MkNot(ctx.MkBVSubNoUnderflow(zero, A.bv, true));
var overflow =
ctx.MkOr(
A.overflow,
o1, o2);
return(new FixedPointNumber(A.bits, A.decimals, calc, overflow, String.Format("(-{0})", A.Expr)));
}
protected override Dictionary <string, FPIntegerInterval> Sample(State q)
{
Dictionary <string, FPIntegerInterval> result = new Dictionary <string, FPIntegerInterval>();
Dictionary <string, DoubleInterval> values = q.ToDictionary();
foreach (var kvp in sample)
{
AST c = kvp.Key;
FixedPointNumber fp = kvp.Value;
var valueOfAST = c.Eval(values);
result.Add(fp.Expr, Measure(valueOfAST, fp.bits, fp.decimals));
}
return(result);
}
static public FixedPointNumber MkFPSub(this Context ctx, FixedPointNumber A, FixedPointNumber B)
{
Contract.Requires(A != null);
Contract.Requires(B != null);
Contract.Requires(A.bits == B.bits);
Contract.Requires(A.decimals == B.decimals);
var calc = ctx.MkBVSub(A.bv, B.bv);
var o1 = ctx.MkNot(ctx.MkBVSubNoOverflow(A.bv, B.bv));
var o2 = ctx.MkNot(ctx.MkBVSubNoUnderflow(A.bv, B.bv, true));
var overflow =
ctx.MkOr(
A.overflow, B.overflow,
o1, o2);
return(new FixedPointNumber(A.bits, A.decimals, calc, overflow, String.Format("({0}-{1})", A.Expr, B.Expr)));
}
static public FixedPointNumber MkFPSDiv(this Context ctx, FixedPointNumber A, FixedPointNumber B)
{
Contract.Requires(A != null);
Contract.Requires(B != null);
Contract.Requires(A.bits == B.bits);
Contract.Requires(A.decimals == B.decimals);
var extA = ctx.MkSignExt(A.bits, A.bv);
var extB = ctx.MkSignExt(A.bits, B.bv);
var AB = ctx.MkBVSDiv(ctx.MkBVMul(extA, ctx.MkBV(1 << (int)A.decimals, 2 * A.bits)), extB);
var calc = ctx.MkExtract(A.bits - 1, 0, AB);
int maxV = (1 << (int)(A.bits - 1)) - 1;
int minV = -(1 << (int)(A.bits - 1));
var overflow =
ctx.MkOr(
A.overflow, B.overflow,
ctx.MkBVSGT(AB, ctx.MkBV(maxV, A.bits * 2)),
ctx.MkBVSLT(AB, ctx.MkBV(minV, A.bits * 2)));
return(new FixedPointNumber(A.bits, A.decimals, calc, overflow, String.Format("{0}/{1}*{2}", A.Expr, B.Expr, (1 << (int)A.decimals))));
}
public void Load(string filename, string modelname)
{
Env env = new Microsoft.Formula.API.Env();
InstallResult result;
env.Install(filename, out result);
if (result.Succeeded)
{
ProgramName pname = new ProgramName(filename);
Task <ObjectGraphResult> resTask;
Domain.SHSystem_Root.CreateObjectGraph(env, pname, modelname, out resTask);
resTask.Wait();
ObjectGraphResult model = resTask.Result;
var body = Microsoft.Formula.API.Factory.Instance.MkBody();
var find = Microsoft.Formula.API.Factory.Instance.MkFind(null, Microsoft.Formula.API.Factory.Instance.MkId("conforms"));
body = Microsoft.Formula.API.Factory.Instance.AddConjunct(body, find);
List <Microsoft.Formula.API.AST <Microsoft.Formula.API.Nodes.Body> > bodies = new List <AST <Microsoft.Formula.API.Nodes.Body> >();
bodies.Add(body);
List <Flag> flags;
Task <QueryResult> task;
Microsoft.Formula.Common.Rules.ExecuterStatistics exeStats;
if (!env.Query(pname, modelname, bodies, true, true, out flags, out task, out exeStats))
{
throw new Exception(String.Format("Could not start query at {0}/{1}", filename, modelname));
}
if (task == null)
{
throw new Exception(String.Format("Could not query {0}/{1}", filename, modelname));
}
task.Start();
task.Wait();
if (task.Result.Conclusion != LiftedBool.True)
{
throw new Exception(String.Format("Model does not conform at {0}/{1}", filename, modelname));
}
//body.Print(Console.Out);
foreach (var m in model.Objects)
{
if (m is SHSystem_Root.O.DiffEq)
{
var t = (SHSystem_Root.O.DiffEq)m;
VAR v = (VAR)ExtractContinuousModel(t.x);
AST rhs = ExtractContinuousModel(t.rhs);
odes.Add(v.name, rhs);
}
else if (m is SHSystem_Root.C.Assign)
{
var t = (SHSystem_Root.C.Assign)m;
FixedPointNumber var = ExtractDiscreteModel(t.var);
FixedPointNumber rhs = ExtractDiscreteModel(t.rhs);
assigns.Add(var.Expr, rhs);
}
else if (m is SHSystem_Root.Safe)
{
var t = (SHSystem_Root.Safe)m;
safetyFormula.Add(ExtractSafetyFormula(t.formula));
}
else if (m is SHSystem_Root.Sample)
{
var t = (SHSystem_Root.Sample)m;
AST c = ExtractContinuousModel(t.lhs);
FixedPointNumber d = ExtractDiscreteModel(t.rhs);
sample.Add(new KeyValuePair <AST, FixedPointNumber>(c, d));
}
else if (m is SHSystem_Root.Hold)
{
var t = (SHSystem_Root.Hold)m;
FixedPointNumber d = ExtractDiscreteModel(t.lhs);
VAR c = (VAR)ExtractContinuousModel(t.rhs);
hold.Add(new KeyValuePair <FixedPointNumber, VAR>(d, c));
}
else if (m is SHSystem_Root.Reset)
{
var t = (SHSystem_Root.Reset)m;
AST d = ExtractContinuousModel(t.lhs);
VAR c = (VAR)ExtractContinuousModel(t.rhs);
reset.Add(new KeyValuePair <AST, VAR>(d, c));
}
else if (m is SHSystem_Root.InitialRangeC)
{
var t = (SHSystem_Root.InitialRangeC)m;
VAR v = (VAR)ExtractContinuousModel(t.var);
double lower = ExtractDouble(t.lower);
double upper = ExtractDouble(t.upper);
cVariables.Add(v, new DoubleInterval(lower, upper));
}
else if (m is SHSystem_Root.InitialRangeD)
{
var t = (SHSystem_Root.InitialRangeD)m;
FixedPointNumber v = ExtractDiscreteModel(t.var);
int lower = ExtractInteger(t.lower);
int upper = ExtractInteger(t.upper);
dVariables.Add(v, new FPIntegerInterval(lower, upper, v.bits, v.decimals));
}
else if (m is SHSystem_Root.DiscretePeriod)
{
var t = (SHSystem_Root.DiscretePeriod)m;
period = ExtractDouble(t._0);
}
else if (m is SHSystem_Root.Order)
{
var t = (SHSystem_Root.Order)m;
order = ExtractInteger(t._0);
}
else if (m is SHSystem_Root.StepBound)
{
var t = (SHSystem_Root.StepBound)m;
stepBound = ExtractInteger(t._0);
}
else if (m is SHSystem_Root.CutoffThreshold)
{
var t = (SHSystem_Root.CutoffThreshold)m;
cutoffThreshold = ExtractDouble(t.threshold);
}
else if (m is SHSystem_Root.ErrorEstimate)
{
var t = (SHSystem_Root.ErrorEstimate)m;
errorEstimate = ExtractDouble(t.estimate);
}
else if (m is SHSystem_Root.SolverStep)
{
var t = (SHSystem_Root.SolverStep)m;
solverStep = ExtractDouble(t.step);
solverMiniStep = ExtractDouble(t.ministep);
}
else if (m is SHSystem_Root.SearchProcedure)
{
var t = (SHSystem_Root.SearchProcedure)m;
string name = (string)t.proc.Symbol;
if (name.Equals("BFS"))
{
searchProcedure = SearchProcedures.BFS;
}
else if (name.Equals("BFS_exhaustive"))
{
searchProcedure = SearchProcedures.BFS_exhaustive;
}
else if (name.Equals("BFS_refinement"))
{
searchProcedure = SearchProcedures.BFS_refinement;
}
else if (name.Equals("DFS"))
{
searchProcedure = SearchProcedures.DFS;
}
else if (name.Equals("DFS_exhaustive"))
{
searchProcedure = SearchProcedures.DFS_exhaustive;
}
else if (name.Equals("DFS_refinement"))
{
searchProcedure = SearchProcedures.DFS_refinement;
}
}
else if (m is SHSystem_Root.AxisX)
{
var t = (SHSystem_Root.AxisX)m;
axisTitle[0] = (string)t.title.Symbol;
if (t.var is SHSystem_Root.UserCnst)
{
timeAxis = true;
}
else
{
axisValue[0] = ExtractContinuousModel(t.var);
}
axisMin[0] = ExtractDouble(t.minValue);
axisMax[0] = ExtractDouble(t.maxValue);
}
else if (m is SHSystem_Root.AxisY)
{
var t = (SHSystem_Root.AxisY)m;
axisTitle[1] = (string)t.title.Symbol;
axisValue[1] = ExtractContinuousModel(t.var);
axisMin[1] = ExtractDouble(t.minValue);
axisMax[1] = ExtractDouble(t.maxValue);
}
else if (m is SHSystem_Root.AxisZ)
{
var t = (SHSystem_Root.AxisZ)m;
axisTitle[2] = (string)t.title.Symbol;
if (t.var is SHSystem_Root.UserCnst)
{
searchIndexAxis = true;
}
else
{
axisValue[2] = ExtractContinuousModel(t.var);
}
axisMin[2] = ExtractDouble(t.minValue);
axisMax[2] = ExtractDouble(t.maxValue);
}
}
}
else
{
StringBuilder msg = new StringBuilder();
msg.Append("Could not load ").AppendLine(filename);
foreach (var flag in result.Flags)
{
msg.AppendFormat("{0} in line {1}, column {2}", flag.Item2.Message, flag.Item2.Span.StartLine, flag.Item2.Span.StartCol).AppendLine();
}
throw new Exception(msg.ToString());
}
}
public FixedPointNumber ExtractDiscreteModel(Microsoft.Formula.API.Generators.ICSharpTerm model)
{
if (model is SHSystem_Root.C.Const)
{
var t = (SHSystem_Root.C.Const)model;
return(ctx.MkFPscaled(ExtractInteger(t.value), (uint)ExtractInteger(t.bits), (uint)ExtractInteger(t.decimals)));
}
if (model is SHSystem_Root.C.RConst)
{
var t = (SHSystem_Root.C.RConst)model;
return(ctx.MkFPfromReal(ExtractDouble(t.value), (uint)ExtractInteger(t.bits), (uint)ExtractInteger(t.decimals)));
}
else if (model is SHSystem_Root.C.Var)
{
var t = (SHSystem_Root.C.Var)model;
var name = (string)t.name.Symbol;
var var = ctx.MkFPConst(name, (uint)ExtractInteger(t.bits), (uint)ExtractInteger(t.decimals));
if (!discreteVariablesByName.ContainsKey(name))
{
discreteVariablesByName.Add(name, var);
}
return(var);
}
else if (model is SHSystem_Root.C.Neg)
{
var t = (Domain.SHSystem_Root.C.Neg)model;
return(ctx.MkFPNeg(ExtractDiscreteModel(t.arg1)));
}
else if (model is SHSystem_Root.C.Pre)
{
var t = (Domain.SHSystem_Root.C.Pre)model;
string name = ExtractPre(t);
FixedPointNumber arg1 = ExtractDiscreteModel(t.arg1);
var var = ctx.MkFPConst(name, arg1.bits, arg1.decimals);
if (!discreteVariablesByName.ContainsKey(name))
{
assigns.Add(name, arg1);
discreteVariablesByName.Add(name, var);
}
return(var);
}
else if (model is SHSystem_Root.C.Add)
{
var t = (Domain.SHSystem_Root.C.Add)model;
return(ctx.MkFPAdd(ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
else if (model is SHSystem_Root.C.Sub)
{
var t = (Domain.SHSystem_Root.C.Sub)model;
return(ctx.MkFPSub(ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
else if (model is SHSystem_Root.C.Mul)
{
var t = (Domain.SHSystem_Root.C.Mul)model;
return(ctx.MkFPMul(ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
else if (model is SHSystem_Root.C.Div)
{
var t = (Domain.SHSystem_Root.C.Div)model;
return(ctx.MkFPSDiv(ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
else if (model is SHSystem_Root.C.Min)
{
var t = (Domain.SHSystem_Root.C.Min)model;
return(ctx.MkFPMin(ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
else if (model is SHSystem_Root.C.Max)
{
var t = (Domain.SHSystem_Root.C.Max)model;
return(ctx.MkFPMax(ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
else if (model is SHSystem_Root.C.ITE)
{
var t = (Domain.SHSystem_Root.C.ITE)model;
return(ctx.MkFPITE(ExtractDiscreteBoolModel(t.test), ExtractDiscreteModel(t.arg1), ExtractDiscreteModel(t.arg2)));
}
throw new Exception(String.Format("Unsupported language element: {0}", model.Symbol));
}
public FormulaSystem(string filename, Plot3d plotter)
: base()
{
axisValue[0] = new REAL(0.0);
axisValue[1] = new REAL(0.0);
axisValue[2] = new REAL(0.0);
Load(filename, "M");
string[] cNames = new string[cVariables.Count];
string[] dNames = new string[dVariables.Count];
DoubleInterval[] cInitial = new DoubleInterval[cVariables.Count];
FPIntegerInterval[] dInitial = new FPIntegerInterval[dVariables.Count];
int i = 0;
foreach (var kvp in cVariables)
{
cNames[i] = kvp.Key.name;
cInitial[i] = kvp.Value.Clone();
i++;
}
i = 0;
foreach (var kvp in dVariables)
{
dNames[i] = kvp.Key.Expr;
dInitial[i] = kvp.Value.Clone();
i++;
}
// build the ODEs
ode = new List <AST>();
foreach (var kvp in cVariables)
{
AST f;
if (odes.TryGetValue(kvp.Key.name, out f))
{
ode.Add(f);
}
}
Print(Log.Output);
Print(Log.Debug);
Initialize(cNames, cInitial, dNames, dInitial, order, period);
if (IsPolynomial)
{
Log.WriteLine("Using polynomial solver");
}
else if (ContainsSqrt)
{
Log.WriteLine("Using approximate Taylor expansion solver");
}
else
{
Log.WriteLine("Using non-polynomial Taylor model solver");
}
// look for lower and upper bounds
foreach (var kvp in dVariables)
{
FixedPointNumber fp = kvp.Key;
int lo = -(1 << ((int)fp.bits - 1));
int up = (1 << ((int)fp.bits - 1)) - 1;
var solver = ctx.MkSimpleSolver();
AddController(ctx, solver, kvp.Key.Expr);
lo = LowerBound(ctx, solver, fp.Expr, fp.bits, lo, up);
up = UpperBound(ctx, solver, fp.Expr, fp.bits, lo, up);
var ival = new FPIntegerInterval(lo, up, fp.bits, fp.decimals);
controlBounds.Add(fp.Expr, ival);
Log.Debug.WriteLine("Control variable '{0}' always in {1}", kvp.Key, ival);
}
Dictionary <string, DoubleInterval> initialValues = GetSystemState(initialState); // initialState.ToDictionary();
if (!timeAxis)
{
axisInitialValue[0] = axisValue[0].Eval(initialValues);
}
axisInitialValue[1] = axisValue[1].Eval(initialValues);
if (!searchIndexAxis)
{
axisInitialValue[2] = axisValue[2].Eval(initialValues);
}
this.plotter = plotter;
if (plotter != null)
{
plotter.SetMinMax(axisMin[0], axisMax[0], axisMin[1], axisMax[1], axisMin[2], axisMax[2]);
plotter.DefaultSettings();
plotter.DrawEvent += Draw;
}
}
static public FixedPointNumber MkFPITE(this Context ctx, BoolExprWithOverflow test, FixedPointNumber A, FixedPointNumber B)
{
Contract.Requires(A != null);
Contract.Requires(B != null);
Contract.Requires(A.bits == B.bits);
Contract.Requires(A.decimals == B.decimals);
var overflow = ctx.MkOr(test.overflow, A.overflow, B.overflow);
return(new FixedPointNumber(A.bits, A.decimals, (BitVecExpr)ctx.MkITE(test.bv, A.bv, B.bv), overflow, String.Format("ITE({0},{1},{2})", test.Expr, A.Expr, B.Expr)));
}