private IGate SimplifyProductOfInputs(Product dict)
{
IGate result = null;
var factors = new List <Factor>();
foreach (var f in dict.Factors)
{
if (f.IsConstant)
{
if (f.Constant is FalseGate)
{
result = f.Constant;
break;
}
}
else
{
factors.Add(f);
}
}
if (null == result)
{
var gatelist = factors.SelectMany(e => e.ToGateList()).GetEnumerator();
if (!gatelist.MoveNext())
{
result = new TrueGate();
}
else
{
result = Gate.Simplify(gatelist.Current);
if (gatelist.MoveNext())
{
var and = new ANDGate();
and.AddInput(result);
do
{
var e = Gate.Simplify(gatelist.Current);
and.AddInput(e);
}while (gatelist.MoveNext());
result = and;
}
}
}
return(result);
}
private static void SimplifyConstants(ref IGate gate)
{
var inputs = gate.GetInputs();
var list = new List <IGate>();
foreach (var i in inputs)
{
if (i is TrueGate)
{
// sum is constant => TRUE
gate = new TrueGate();
return;
}
else if (i is FalseGate)
{
// remove any FALSE gates ...
}
else if (i.GetNestingLevel() > 1)
{
var r = i.Simplify();
if (r.Type == GateType.OR)
{
list.AddRange(r.GetInputs());
}
else
{
list.Add(r);
}
}
else
{
var r = i.Simplify();
list.Add(r);
}
}
gate = ConsolidateList(list);
}
/// <summary>
/// Returns a gate that represents the inverted output of another gate.
/// </summary>
/// <param name="a">The gate to be inverted.</param>
/// <returns>The inverted gate.</returns>
public static IGate Invert(IGate g)
{
IGate result;
IGate a = Decompose(g);
if (a.Type == GateType.OR)
{
var it = a.GetInputs().GetEnumerator();
it.MoveNext();
var r = Invert(it.Current);
while (it.MoveNext())
{
r = ComposeAND(r, Invert(it.Current));
}
result = r;
}
else if (a.Type == GateType.AND)
{
var it = a.GetInputs().GetEnumerator();
it.MoveNext();
var r = Invert(it.Current);
while (it.MoveNext())
{
r = ComposeOR(r, Invert(it.Current));
}
result = r;
}
else if (a.Type == GateType.Input)
{
result = ((IInput)a).Invert();
}
else if(a.Type == GateType.Fixed)
{
if(a is TrueGate)
{
result = new FalseGate();
}
else
{
result = new TrueGate();
}
}
else
{
throw new ArgumentException();
}
result = Simplify(result);
TraceCompose(g, result, "invert");
return result;
}
public static IGate ComposeAND(IEnumerable<IGate> gates)
{
IGate r = new TrueGate();
var it = gates.GetEnumerator();
while (it.MoveNext())
{
r = ComposeAND(r, it.Current);
}
return r;
}
/// <summary>
/// Composes two gates with the logical AND operator.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns>The resulting gate.</returns>
public static IGate ComposeAND(IGate a, IGate b)
{
IGate result;
DecomposeExchange(ref a, ref b);
if(a.Type == GateType.Fixed && b.Type == GateType.Fixed)
{
if(a is TrueGate && b is TrueGate)
{
result = new TrueGate();
}
else
{
result = new FalseGate();
}
}
else if(b.Type == GateType.Fixed)
{
if(b is TrueGate)
{
result = a;
}
else
{
result = new FalseGate();
}
}
else if (a.Type == GateType.OR && b.Type == GateType.OR)
{
result = Multiply(a.GetInputs(), b.GetInputs());
}
else if (a.Type == GateType.OR)
{
result = Multiply(a.GetInputs(), b);
}
else if (a.Type == GateType.AND && b.Type == GateType.AND)
{
// compose
var r = new ANDGate();
r.AddInputRange(a.GetInputs());
r.AddInputRange(b.GetInputs());
result = r;
}
else if (a.Type == GateType.AND)
{
// compose
var r = new ANDGate();
r.AddInputRange(a.GetInputs());
r.AddInput(b);
result = r;
}
else
{
var r = new ANDGate();
r.AddInput(a);
r.AddInput(b);
result = r;
}
// simplify and cache
result = Simplify(result);
TraceCompose(a, b, result, "AND");
return result;
}
private IGate SimplifyProductOfInputs(Product dict)
{
IGate result = null;
var factors = new List<Factor>();
foreach (var f in dict.Factors)
{
if (f.IsConstant)
{
if (f.Constant is FalseGate)
{
result = f.Constant;
break;
}
}
else
{
factors.Add(f);
}
}
if (null == result)
{
var gatelist = factors.SelectMany(e => e.ToGateList()).GetEnumerator();
if (!gatelist.MoveNext())
{
result = new TrueGate();
}
else
{
result = Gate.Simplify(gatelist.Current);
if (gatelist.MoveNext())
{
var and = new ANDGate();
and.AddInput(result);
do
{
var e = Gate.Simplify(gatelist.Current);
and.AddInput(e);
}
while (gatelist.MoveNext());
result = and;
}
}
}
return result;
}
private static void SimplifyConstants(ref IGate gate)
{
var inputs = gate.GetInputs();
var list = new List<IGate>();
foreach (var i in inputs)
{
if (i is TrueGate)
{
// sum is constant => TRUE
gate = new TrueGate();
return;
}
else if (i is FalseGate)
{
// remove any FALSE gates ...
}
else if (i.GetNestingLevel() > 1)
{
var r = i.Simplify();
if (r.Type == GateType.OR)
{
list.AddRange(r.GetInputs());
}
else
{
list.Add(r);
}
}
else
{
var r = i.Simplify();
list.Add(r);
}
}
gate = ConsolidateList(list);
}
/// <summary>
/// Looks for common subfactors.
/// </summary>
/// <param name="gate"></param>
private bool SimplifyRule2(ref IGate gate)
{
var originalgate = gate;
var gset = gate.GetSOP();
// try all elementary factors ...
foreach (var elementaryfactor in gset.GetPrimitiveFactors().ToArray())
{
// Trace("trying factor {0}", elementaryfactor);
// collect all products that contain the factor as candidates
var candidates = new List<Product>();
foreach (var p in gset)
{
if (1 == p.ContainsFactor(elementaryfactor))
{
candidates.Add(p);
}
}
// need at least two
if (candidates.Count < 2)
{
continue;
}
TraceSimplify("common factor {0} found in {1} ...", elementaryfactor, candidates.ToSeparatorList());
// construct a new gate consisting of the sum of remaining products
var reducedsum = new ORGate();
Gate newgate = reducedsum;
foreach (var involvedproduct in candidates)
{
var reducedproduct = involvedproduct.Clone();
reducedproduct.Remove(elementaryfactor);
if (reducedproduct.Factors.Any())
{
reducedsum.AddInput(reducedproduct.ToGate());
}
else
{
// candidate equals elementary factor => TRUE
newgate = new TrueGate();
break;
}
}
// remove original elements from the set
foreach (var x in candidates)
{
gset.Remove(x);
}
// simplify the resulting gate recursively
var partialsum = newgate.Simplify();
var factor = elementaryfactor.ToGate();
TraceSimplify(" is ({0}) AND {1}", partialsum, factor);
if (partialsum.Type == GateType.Fixed)
{
if (partialsum is TrueGate)
{
// factor only
gate = factor;
}
else
{
// simplification yields FALSE
gate = partialsum;
}
}
else if (partialsum.Type == GateType.AND)
{
// multiply with factor
gate = Gate.Multiply(factor.GetInputs(), partialsum);
}
else if (partialsum.Type == GateType.OR)
{
// multiply with all factors
gate = Gate.Multiply(factor.GetInputs(), partialsum.GetInputs());
}
else
{
// multiply with factor
gate = Gate.Multiply(factor.GetInputs(), partialsum);
}
// compose with the remaining terms
foreach (var term in gset.Select(e => e.ToGate()))
{
gate = Gate.ComposeOR(gate, term, ComposeOptions.NoSimplify);
}
break;
}
if (gate != originalgate)
{
Gate.TraceSimplify(originalgate, gate, "simplify OR (2)");
}
return gate != originalgate;
}
/// <summary>
/// Looks for common subfactors.
/// </summary>
/// <param name="gate"></param>
private bool SimplifyRule2(ref IGate gate)
{
var originalgate = gate;
var gset = gate.GetSOP();
// try all elementary factors ...
foreach (var elementaryfactor in gset.GetPrimitiveFactors().ToArray())
{
// Trace("trying factor {0}", elementaryfactor);
// collect all products that contain the factor as candidates
var candidates = new List <Product>();
foreach (var p in gset)
{
if (1 == p.ContainsFactor(elementaryfactor))
{
candidates.Add(p);
}
}
// need at least two
if (candidates.Count < 2)
{
continue;
}
TraceSimplify("common factor {0} found in {1} ...", elementaryfactor, candidates.ToSeparatorList());
// construct a new gate consisting of the sum of remaining products
var reducedsum = new ORGate();
Gate newgate = reducedsum;
foreach (var involvedproduct in candidates)
{
var reducedproduct = involvedproduct.Clone();
reducedproduct.Remove(elementaryfactor);
if (reducedproduct.Factors.Any())
{
reducedsum.AddInput(reducedproduct.ToGate());
}
else
{
// candidate equals elementary factor => TRUE
newgate = new TrueGate();
break;
}
}
// remove original elements from the set
foreach (var x in candidates)
{
gset.Remove(x);
}
// simplify the resulting gate recursively
var partialsum = newgate.Simplify();
var factor = elementaryfactor.ToGate();
TraceSimplify(" is ({0}) AND {1}", partialsum, factor);
if (partialsum.Type == GateType.Fixed)
{
if (partialsum is TrueGate)
{
// factor only
gate = factor;
}
else
{
// simplification yields FALSE
gate = partialsum;
}
}
else if (partialsum.Type == GateType.AND)
{
// multiply with factor
gate = Gate.Multiply(factor.GetInputs(), partialsum);
}
else if (partialsum.Type == GateType.OR)
{
// multiply with all factors
gate = Gate.Multiply(factor.GetInputs(), partialsum.GetInputs());
}
else
{
// multiply with factor
gate = Gate.Multiply(factor.GetInputs(), partialsum);
}
// compose with the remaining terms
foreach (var term in gset.Select(e => e.ToGate()))
{
gate = Gate.ComposeOR(gate, term, ComposeOptions.NoSimplify);
}
break;
}
if (gate != originalgate)
{
Gate.TraceSimplify(originalgate, gate, "simplify OR (2)");
}
return(gate != originalgate);
}