/**
* Quantify local primary input and auxiliary variables.
*/
BDD BddTrAttachment::quantifyLocalInputs(
vector<BDD>& conjuncts,
const BDD& qcube,
unsigned int limit,
Options::Verbosity verbosity) const
{
// A -1 means "not yet seen."
// A -2 means "seen in more than one conjunct."
vector<int> whereSeen(bddManager().ReadSize(),-1);
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
vector<unsigned int> support = conjuncts[i].SupportIndices();
for (vector<unsigned int>::const_iterator j = support.begin();
j != support.end(); ++j) {
if (whereSeen[*j] == -1)
whereSeen[*j] = i;
else
whereSeen[*j] = -2;
}
}
// Attempt quantification of variables seen exactly once, but
// back off if this blows up the conjunct.
vector<unsigned int> qvars = qcube.SupportIndices();
BDD ret = bddManager().bddOne();
for (vector<unsigned int>::size_type i = 0; i != qvars.size(); ++i) {
unsigned int index = qvars[i];
BDD bvar = bddManager().bddVar(qvars[i]);
int ws = whereSeen[index];
if (ws >= 0) {
int currentLimit = conjuncts[ws].nodeCount();
BDD tmp = conjuncts[ws].ExistAbstract(bvar, currentLimit);
if (tmp && tmp.nodeCount() <= currentLimit) {
conjuncts[ws] = tmp;
#if 0
cout << "Eliminated local variable " << index
<< " from conjunct " << ws << endl;
#endif
} else {
#if 0
cout << "Failed to eliminate local variable " << index
<< " from conjunct " << ws << endl;
#endif
ret &= bvar;
}
} else {
ret &= bvar;
}
}
assert(qcube <= ret);
if (verbosity > Options::Terse)
cout << "Number of clusters/nodes = " << conjuncts.size()
<< "/" << bddManager().SharingSize(conjuncts) << endl;
return ret;
} // BddTrAttachment::quantifyLocalInputs
/**
* Compose auxiliary functions recursively into a BDD.
*/
void BddTrAttachment::composeAuxiliaryFunctions(
BddAttachment const * bat,
BDD & f,
unordered_map<int, ID> const & index2id)
{
vector<unsigned int> support = f.SupportIndices();
queue< vector<unsigned int> > q;
q.push(support);
while (!q.empty()) {
vector<unsigned int> supp = q.front();
q.pop();
for (vector<unsigned int>::const_iterator j = supp.begin();
j != supp.end(); ++j) {
unordered_map<int,ID>::const_iterator cit = index2id.find(*j);
if (cit != index2id.end()) {
BDD g = bat->bdd(cit->second);
BDD a = bddManager().bddVar(*j);
f = f.AndAbstract(a.Xnor(g),a);
vector<unsigned int> addSupp = g.SupportIndices();
q.push(addSupp);
}
}
}
}
/**
* Eliminate auxiliary variables from output function.
*/
BDD BddTrAttachment::flattenOutput(
const vector<BDD>& conjuncts,
const BDD& wCube)
{
vector<BDD> schedule;
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
schedule.push_back(bddManager().bddOne());
}
// For each variable appearing in the conjuncts find the last
// conjunct in which it appears.
vector<int> lastSeen(bddManager().ReadSize(),-1);
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
vector<unsigned int> support = conjuncts[i].SupportIndices();
for (vector<unsigned int>::const_iterator j = support.begin();
j != support.end(); ++j) {
lastSeen[*j] = i;
}
}
vector<unsigned int> wVars = wCube.SupportIndices();
#if 0
printVector("wVars", wVars); // Diagnostic printout.
#endif
for (vector<unsigned int>::size_type i = 0; i != wVars.size(); ++i) {
unsigned int index = wVars[i];
int ls = lastSeen[index];
if (ls >= 0) {
BDD var = bddManager().bddVar(index);
schedule[ls] &= var;
}
}
BDD ret = bddManager().bddOne();
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
ret = ret.AndAbstract(conjuncts[i], schedule[i]);
}
return ret;
} // BddTrAttachment::flattenOutput
/**
* Compute the quantification schedule for the primary inputs and the
* auxiliary variables.
*/
void BddTrAttachment::computeSchedule(
const vector<BDD>& conjuncts,
const BDD& wCube)
{
vector<BDD> fwSchedule, bwSchedule;
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
fwSchedule.push_back(bddManager().bddOne());
bwSchedule.push_back(bddManager().bddOne());
}
_prequantx = bddManager().bddOne();
_prequanty = bddManager().bddOne();
// For each variable appearing in the conjuncts find the last
// conjunct in which it appears.
vector<int> lastSeen(bddManager().ReadSize(),-1);
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
vector<unsigned int> support = conjuncts[i].SupportIndices();
for (vector<unsigned int>::const_iterator j = support.begin();
j != support.end(); ++j) {
lastSeen[*j] = i;
}
}
vector<unsigned int> wVars = wCube.SupportIndices();
#if 0
printVector("wVars", wVars); // Diagnostic printout.
#endif
for (vector<unsigned int>::size_type i = 0; i != wVars.size(); ++i) {
unsigned int index = wVars[i];
int ls = lastSeen[index];
if (ls >= 0) {
BDD var = bddManager().bddVar(index);
fwSchedule[ls] &= var;
bwSchedule[ls] &= var;
}
}
for (vector<BDD>::size_type i = 0; i != _xvars.size(); ++i) {
unsigned int index = _xvars[i].NodeReadIndex();
int ls = lastSeen[index];
if (ls >= 0) {
fwSchedule[ls] &= _xvars[i];
} else {
_prequantx &= _xvars[i];
}
}
for (vector<BDD>::size_type i = 0; i != _yvars.size(); ++i) {
unsigned int index = _yvars[i].NodeReadIndex();
int ls = lastSeen[index];
if (ls >= 0) {
bwSchedule[ls] &= _yvars[i];
} else {
_prequanty &= _yvars[i];
}
}
for (vector<BDD>::size_type i = 0; i != conjuncts.size(); ++i) {
_tr.push_back(RelPart(conjuncts[i], fwSchedule[i], bwSchedule[i]));
}
} // BddTrAttachment::computeSchedule
vector<BDD> BddTrAttachment::clusterConjuncts(
vector<BDD>& conjuncts,
const BDD& qcube,
unsigned int limit,
Options::Verbosity verbosity) const
{
vector<BDD> clusters;
if (conjuncts.size() == 0) {
clusters.push_back(bddManager().bddOne());
return clusters;
}
// Create records of occurrence of all variables in the conjuncts.
// The variables that occur in no conjuncts end up with
// earliest > latest. For the others, we know the first and last
// conjunct in which they occur.
unsigned int numvars = bddManager().ReadSize();
unsigned int nconjuncts = conjuncts.size();
vector<VarRec> occurrence;
occurrence.reserve(numvars);
for (unsigned int i = 0; i != numvars; ++i) {
occurrence.push_back(VarRec(i,nconjuncts,-1));
}
for (vector<BDD>::size_type i = 0; i != nconjuncts; ++i) {
vector<unsigned int> support = conjuncts[i].SupportIndices();
for (vector<unsigned int>::const_iterator j = support.begin();
j != support.end(); ++j) {
if (occurrence[*j].earliest() > (int) i)
occurrence[*j].setEarliest((int) i);
if (occurrence[*j].latest() < (int) i)
occurrence[*j].setLatest((int) i);
}
}
// Filter variables that are not candidates for quantification
// and are not present in the conjuncts.
vector<unsigned int> qvars = qcube.SupportIndices();
unordered_set<unsigned int> qset(qvars.begin(), qvars.end());
vector<VarRec> candidate;
candidate.reserve(qvars.size());
for (vector<VarRec>::const_iterator i = occurrence.begin();
i != occurrence.end(); ++i) {
if (qset.find(i->index()) != qset.end() &&
i->earliest() <= i->latest())
candidate.push_back(*i);
}
// Sort occurrence records according to latest occurrence
// using earliest occurrence as tie breaker.
stable_sort(candidate.begin(), candidate.end());
#if 0
// Diagnostic printout.
for (vector<VarRec>::const_iterator i = candidate.begin();
i != candidate.end(); ++i) {
cout << "Variable: " << i->index() << " ("
<< i->earliest() << "," << i->latest() << ")\n";
}
#endif
// We are now ready for clustering having collected the
// information of which variables may be quantified when.
// In the following, i points to the first conjunct in the cluster.
// (Conjunct of highest index since we go backwards.)
int i = conjuncts.size() - 1;
BDD cluster = conjuncts[i];
conjuncts.pop_back();
// j points to the conjuncts that is being added to the cluster.
int j = i - 1;
// k points to the candidates for quantification
vector<VarRec>::size_type k = 0;
while (j >= 0) {
reportBDD("conjunct", conjuncts[j], numvars, verbosity, Options::Informative);
// Find variables that are local to cluster. A variable is local to
// the current cluster if its lifespan is entirely contained between
// i and j.
BDD qcube = bddManager().bddOne();
while (k < candidate.size() && candidate[k].latest() > (int) i)
k++;
while (k < candidate.size() && candidate[k].earliest() >= (int) j) {
qcube &= bddManager().bddVar(candidate[k].index());
k++;
}
BDD tmp = cluster.AndAbstract(conjuncts[j], qcube, limit);
if (tmp && (unsigned int) tmp.nodeCount() <= 2*limit) {
cluster = tmp;
} else {
reportBDD("Cluster", cluster, numvars, verbosity, Options::Informative);
clusters.push_back(cluster);
i = j;
cluster = conjuncts[i];
}
j--;
conjuncts.pop_back();
}
reportBDD("Cluster", cluster, numvars, verbosity, Options::Informative);
clusters.push_back(cluster);
return clusters;
} // BddTrAttachment::clusterConjuncts