public static IGate SimplifyMultiplicate(IGate g)
{
Debug.Assert(g.Type == GateType.AND);
var or = new ORGate();
or.AddInput(new TrueGate());
IGate r = or;
foreach (var e in g.GetInputs())
{
if (e.Type == GateType.OR)
{
r = Gate.Multiply(r.GetInputs(), e.GetInputs());
}
else
{
r = Gate.Multiply(r.GetInputs(), e);
}
}
r = Gate.Simplify(r);
TraceSimplify(g, r, "simplify AND");
return r;
}
public static IGate SimplifyMultiplicate(IGate g)
{
Debug.Assert(g.Type == GateType.AND);
var or = new ORGate();
or.AddInput(new TrueGate());
IGate r = or;
foreach (var e in g.GetInputs())
{
if (e.Type == GateType.OR)
{
r = Gate.Multiply(r.GetInputs(), e.GetInputs());
}
else
{
r = Gate.Multiply(r.GetInputs(), e);
}
}
r = Gate.Simplify(r);
TraceSimplify(g, r, "simplify AND");
return(r);
}
/// <summary>
/// Multiplies two sums of products
/// </summary>
/// <param name="list1"></param>
/// <param name="list2"></param>
/// <returns></returns>
public static IGate Multiply(IEnumerable<IGate> list1, IEnumerable<IGate> list2)
{
var r = new ORGate();
foreach (var a in list1)
{
foreach (var b in list2)
{
r.AddInput(ComposeAND(a, b));
}
}
return r;
}
public static IGate ExtractCommonFactors(IGate gate)
{
var original = gate;
if (gate.Type == GateType.OR)
{
// TraceOptimize("extract common factors from {0} ...", gate);
var sop = gate.GetSOP();
// count how many times each factor appears
var inmap = new Dictionary<int, IInput>();
var dict = new SortedList<int, int>();
foreach (var p in sop.GetPrimitiveFactors())
{
// a gate representing the factors (may be multiple per state variable)
var pg = p.ToGate();
foreach (var i in pg.GetInputs().OfType<IInput>())
{
var address = i.Address;
// TraceOptimize("check factor {0} @ {1:X6}", i, address);
if (!inmap.ContainsKey(i.Address))
{
inmap.Add(i.Address, i);
}
if (!dict.ContainsKey(address))
{
dict[address] = 1;
}
else
{
dict[address]++;
}
}
}
var m = dict.Values.Max();
// TraceOptimize("maximum factor count {0}", m);
if (m > 1)
{
// go for it, take the first input with maximum multiplicity, inputs are ordered.
var pivotindex = dict.Where(e => e.Value == m).Select(e => e.Key).First();
var pivot = inmap[pivotindex];
var pivotlist = new List<Product>();
var otherlist = new List<Product>();
TraceOptimize("use pivot {0:X6} ...", pivot);
// split sop into two groups: factor or not
foreach (var p in sop)
{
if (p.ContainsFactor(pivot))
{
p.RemoveInput(pivot);
pivotlist.Add(p);
}
else
{
otherlist.Add(p);
}
}
IGate and = new ANDGate();
and.AddInput(pivot);
IGate inneror = new ORGate();
foreach (var p in pivotlist)
{
var z = p.ToGate().Simplify();
// Debug.Assert(z.GetInputs().Count() > 1);
Trace("adding pivot {0} [{1}]", z, z.GetType().Name);
inneror.AddInput(z);
}
inneror = ExtractCommonFactors(inneror);
and.AddInput(inneror);
if (otherlist.Any())
{
//var rh = ExtractCommonFactors(otherlist);
var or = new ORGate();
or.AddInput(and);
foreach (var p in otherlist)
{
var z = p.ToGate();
or.AddInput(z.Simplify());
}
gate = or;
}
else
{
gate = and;
}
}
}
if (gate != original && TraceFlags.ShowOptimize)
{
Log.TraceGateOp2(original, gate, "optimize AND");
}
return gate;
}
/// <summary>
/// Composes two gates with the logical OR operator.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns>The resulting gate.</returns>
public static IGate ComposeOR(IGate a, IGate b, ComposeOptions options = ComposeOptions.None)
{
IGate result;
DecomposeExchange(ref a, ref b);
if (a.Type == GateType.OR && b.Type == GateType.OR)
{
var r = new ORGate();
r.AddInputRange(a.GetInputs());
r.AddInputRange(b.GetInputs());
result = r;
}
else if (a.Type == GateType.OR)
{
var r = new ORGate();
r.AddInputRange(a.GetInputs());
r.AddInput(b);
result = r;
}
else
{
var r = new ORGate();
r.AddInput(a);
r.AddInput(b);
result = r;
}
if (0 == (options & ComposeOptions.NoSimplify))
{
result = Simplify(result);
}
TraceCompose(a, b, result, "OR");
return result;
}
/// <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;
}
private bool SimplifyRule1(ref IGate gate)
{
var original = gate;
var garg = gate as ORGate;
if(null == garg) return false;
// handle the rules:
// A + !A B = A + B
// A + A B = A
var gset = garg.GetSOP();
int changes = 0;
var gplan = gset.OrderBy(e => e.Inputs.Count()).ToList();
for (int j = 0; j < gplan.Count; ++j)
{
var glist = gplan[j];
if (glist.IsEmpty) continue;
TraceSimplify(" product [{0}] : {1}", glist.Signature, glist.ToGate());
for (int k = j + 1; k < gplan.Count; ++k)
{
var olist = gplan[k];
switch (olist.ContainsFactor(glist))
{
case 1:
// contains the sequence => eliminate entry?
TraceSimplify(" is contained in {0} ...", olist.ToGate());
olist.Clear();
changes++;
break;
case 2:
// contains negation => remove negations
TraceSimplify(" negation is contained in {0} ...", olist.ToGate());
olist.Remove(glist);
if(olist.IsEmpty)
{
// full negation ==> ALL
glist.Clear();
gset.Fixed = new TrueGate();
}
changes++;
break;
}
}
}
gset.Purge();
if (gset.Fixed != null)
{
gate = gset.Fixed;
}
else
{
// construct an OR expression containing the ordered factors
var or = new ORGate();
foreach (var glist in gset.OrderBy(e => e.Signature, StringComparer.Ordinal))
{
or.AddInput(glist.ToGate().Simplify());
}
if (or.Inputs.Count() == 0)
{
gate = new FalseGate();
}
else if (or.Inputs.Count() == 1)
{
gate = or.Inputs.First();
}
else
{
gate = or;
}
}
if (changes > 0)
{
TraceSimplify(original, gate, "simplify OR (1)");
}
return changes > 0;
}
private bool SimplifyRule1(ref IGate gate)
{
var original = gate;
var garg = gate as ORGate;
if (null == garg)
{
return(false);
}
// handle the rules:
// A + !A B = A + B
// A + A B = A
var gset = garg.GetSOP();
int changes = 0;
var gplan = gset.OrderBy(e => e.Inputs.Count()).ToList();
for (int j = 0; j < gplan.Count; ++j)
{
var glist = gplan[j];
if (glist.IsEmpty)
{
continue;
}
TraceSimplify(" product [{0}] : {1}", glist.Signature, glist.ToGate());
for (int k = j + 1; k < gplan.Count; ++k)
{
var olist = gplan[k];
switch (olist.ContainsFactor(glist))
{
case 1:
// contains the sequence => eliminate entry?
TraceSimplify(" is contained in {0} ...", olist.ToGate());
olist.Clear();
changes++;
break;
case 2:
// contains negation => remove negations
TraceSimplify(" negation is contained in {0} ...", olist.ToGate());
olist.Remove(glist);
if (olist.IsEmpty)
{
// full negation ==> ALL
glist.Clear();
gset.Fixed = new TrueGate();
}
changes++;
break;
}
}
}
gset.Purge();
if (gset.Fixed != null)
{
gate = gset.Fixed;
}
else
{
// construct an OR expression containing the ordered factors
var or = new ORGate();
foreach (var glist in gset.OrderBy(e => e.Signature, StringComparer.Ordinal))
{
or.AddInput(glist.ToGate().Simplify());
}
if (or.Inputs.Count() == 0)
{
gate = new FalseGate();
}
else if (or.Inputs.Count() == 1)
{
gate = or.Inputs.First();
}
else
{
gate = or;
}
}
if (changes > 0)
{
TraceSimplify(original, gate, "simplify OR (1)");
}
return(changes > 0);
}
/// <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);
}