/**Function*************************************************************
Synopsis [Returns 1 if the miter is unsat; 0 if sat; -1 if undecided.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Fraig_ManCheckMiter( Fraig_Man_t * p )
{
Fraig_Node_t * pNode;
int i;
FREE( p->pModel );
for ( i = 0; i < p->vOutputs->nSize; i++ )
{
// get the output node (it can be complemented!)
pNode = p->vOutputs->pArray[i];
// if the miter is constant 0, the problem is UNSAT
if ( pNode == Fraig_Not(p->pConst1) )
continue;
// consider the special case when the miter is constant 1
if ( pNode == p->pConst1 )
{
// in this case, any counter example will do to distinquish it from constant 0
// here we pick the counter example composed of all zeros
p->pModel = Fraig_ManAllocCounterExample( p );
return 0;
}
// save the counter example
p->pModel = Fraig_ManSaveCounterExample( p, pNode );
// if the model is not found, return undecided
if ( p->pModel == NULL )
return -1;
else
return 0;
}
return 1;
}
/**Function*************************************************************
Synopsis [Tries to prove the final miter.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Fraig_ManProveMiter( Fraig_Man_t * p )
{
Fraig_Node_t * pNode;
int i, clk;
if ( !p->fTryProve )
return;
clk = clock();
// consider all outputs of the multi-output miter
for ( i = 0; i < p->vOutputs->nSize; i++ )
{
pNode = Fraig_Regular(p->vOutputs->pArray[i]);
// skip already constant nodes
if ( pNode == p->pConst1 )
continue;
// skip nodes that are different according to simulation
if ( !Fraig_CompareSimInfo( pNode, p->pConst1, p->nWordsRand, 1 ) )
continue;
if ( Fraig_NodeIsEquivalent( p, p->pConst1, pNode, -1, p->nSeconds ) )
{
if ( Fraig_IsComplement(p->vOutputs->pArray[i]) ^ Fraig_NodeComparePhase(p->pConst1, pNode) )
p->vOutputs->pArray[i] = Fraig_Not(p->pConst1);
else
p->vOutputs->pArray[i] = p->pConst1;
}
}
if ( p->fVerboseP )
{
// PRT( "Final miter proof time", clock() - clk );
}
}
/**Function*************************************************************
Synopsis [Checks equivalence of two nodes.]
Description [Returns 1 iff the nodes are equivalent.]
SideEffects []
SeeAlso []
***********************************************************************/
int Fraig_NodesAreEqual( Fraig_Man_t * p, Fraig_Node_t * pNode1, Fraig_Node_t * pNode2, int nBTLimit, int nTimeLimit )
{
if ( pNode1 == pNode2 )
return 1;
if ( pNode1 == Fraig_Not(pNode2) )
return 0;
return Fraig_NodeIsEquivalent( p, Fraig_Regular(pNode1), Fraig_Regular(pNode2), nBTLimit, nTimeLimit );
}
/**Function*************************************************************
Synopsis [Perfoms the MUX operation with functional hashing.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Fraig_Node_t * Fraig_NodeMux( Fraig_Man_t * p, Fraig_Node_t * pC, Fraig_Node_t * pT, Fraig_Node_t * pE )
{
Fraig_Node_t * pAnd1, * pAnd2, * pRes;
pAnd1 = Fraig_NodeAndCanon( p, pC, pT ); Fraig_Ref( pAnd1 );
pAnd2 = Fraig_NodeAndCanon( p, Fraig_Not(pC), pE ); Fraig_Ref( pAnd2 );
pRes = Fraig_NodeOr( p, pAnd1, pAnd2 );
Fraig_RecursiveDeref( p, pAnd1 );
Fraig_RecursiveDeref( p, pAnd2 );
Fraig_Deref( pRes );
return pRes;
}
/**Function*************************************************************
Synopsis [Returns 1 if the node is the root of EXOR/NEXOR gate.]
Description [The node can be complemented.]
SideEffects []
SeeAlso []
***********************************************************************/
int Fraig_NodeIsExorType( Fraig_Node_t * pNode )
{
Fraig_Node_t * pNode1, * pNode2;
// make the node regular (it does not matter for EXOR/NEXOR)
pNode = Fraig_Regular(pNode);
// if the node or its children are not ANDs or not compl, this cannot be EXOR type
if ( !Fraig_NodeIsAnd(pNode) )
return 0;
if ( !Fraig_NodeIsAnd(pNode->p1) || !Fraig_IsComplement(pNode->p1) )
return 0;
if ( !Fraig_NodeIsAnd(pNode->p2) || !Fraig_IsComplement(pNode->p2) )
return 0;
// get children
pNode1 = Fraig_Regular(pNode->p1);
pNode2 = Fraig_Regular(pNode->p2);
assert( pNode1->Num < pNode2->Num );
// compare grandchildren
return pNode1->p1 == Fraig_Not(pNode2->p1) && pNode1->p2 == Fraig_Not(pNode2->p2);
}
/**Function*************************************************************
Synopsis [Returns 1 if the node is the root of MUX or EXOR/NEXOR.]
Description [The node can be complemented.]
SideEffects []
SeeAlso []
***********************************************************************/
int Fraig_NodeIsMuxType( Fraig_Node_t * pNode )
{
Fraig_Node_t * pNode1, * pNode2;
// make the node regular (it does not matter for EXOR/NEXOR)
pNode = Fraig_Regular(pNode);
// if the node or its children are not ANDs or not compl, this cannot be EXOR type
if ( !Fraig_NodeIsAnd(pNode) )
return 0;
if ( !Fraig_NodeIsAnd(pNode->p1) || !Fraig_IsComplement(pNode->p1) )
return 0;
if ( !Fraig_NodeIsAnd(pNode->p2) || !Fraig_IsComplement(pNode->p2) )
return 0;
// get children
pNode1 = Fraig_Regular(pNode->p1);
pNode2 = Fraig_Regular(pNode->p2);
assert( pNode1->Num < pNode2->Num );
// compare grandchildren
// node is an EXOR/NEXOR
if ( pNode1->p1 == Fraig_Not(pNode2->p1) && pNode1->p2 == Fraig_Not(pNode2->p2) )
return 1;
// otherwise the node is MUX iff it has a pair of equal grandchildren
return pNode1->p1 == Fraig_Not(pNode2->p1) ||
pNode1->p1 == Fraig_Not(pNode2->p2) ||
pNode1->p2 == Fraig_Not(pNode2->p1) ||
pNode1->p2 == Fraig_Not(pNode2->p2);
}
/**Function*************************************************************
Synopsis [Recognizes what nodes are control and data inputs of a MUX.]
Description [If the node is a MUX, returns the control variable C.
Assigns nodes T and E to be the then and else variables of the MUX.
Node C is never complemented. Nodes T and E can be complemented.
This function also recognizes EXOR/NEXOR gates as MUXes.]
SideEffects []
SeeAlso []
***********************************************************************/
Fraig_Node_t * Fraig_NodeRecognizeMux( Fraig_Node_t * pNode, Fraig_Node_t ** ppNodeT, Fraig_Node_t ** ppNodeE )
{
Fraig_Node_t * pNode1, * pNode2;
assert( !Fraig_IsComplement(pNode) );
assert( Fraig_NodeIsMuxType(pNode) );
// get children
pNode1 = Fraig_Regular(pNode->p1);
pNode2 = Fraig_Regular(pNode->p2);
// find the control variable
if ( pNode1->p1 == Fraig_Not(pNode2->p1) )
{
if ( Fraig_IsComplement(pNode1->p1) )
{ // pNode2->p1 is positive phase of C
*ppNodeT = Fraig_Not(pNode2->p2);
*ppNodeE = Fraig_Not(pNode1->p2);
return pNode2->p1;
}
else
{ // pNode1->p1 is positive phase of C
*ppNodeT = Fraig_Not(pNode1->p2);
*ppNodeE = Fraig_Not(pNode2->p2);
return pNode1->p1;
}
}
else if ( pNode1->p1 == Fraig_Not(pNode2->p2) )
{
if ( Fraig_IsComplement(pNode1->p1) )
{ // pNode2->p2 is positive phase of C
*ppNodeT = Fraig_Not(pNode2->p1);
*ppNodeE = Fraig_Not(pNode1->p2);
return pNode2->p2;
}
else
{ // pNode1->p1 is positive phase of C
*ppNodeT = Fraig_Not(pNode1->p2);
*ppNodeE = Fraig_Not(pNode2->p1);
return pNode1->p1;
}
}
else if ( pNode1->p2 == Fraig_Not(pNode2->p1) )
{
if ( Fraig_IsComplement(pNode1->p2) )
{ // pNode2->p1 is positive phase of C
*ppNodeT = Fraig_Not(pNode2->p2);
*ppNodeE = Fraig_Not(pNode1->p1);
return pNode2->p1;
}
else
{ // pNode1->p2 is positive phase of C
*ppNodeT = Fraig_Not(pNode1->p1);
*ppNodeE = Fraig_Not(pNode2->p2);
return pNode1->p2;
}
}
else if ( pNode1->p2 == Fraig_Not(pNode2->p2) )
{
if ( Fraig_IsComplement(pNode1->p2) )
{ // pNode2->p2 is positive phase of C
*ppNodeT = Fraig_Not(pNode2->p1);
*ppNodeE = Fraig_Not(pNode1->p1);
return pNode2->p2;
}
else
{ // pNode1->p2 is positive phase of C
*ppNodeT = Fraig_Not(pNode1->p1);
*ppNodeE = Fraig_Not(pNode2->p1);
return pNode1->p2;
}
}
assert( 0 ); // this is not MUX
return NULL;
}
/**Function*************************************************************
Synopsis [The internal AND operation for the two FRAIG nodes.]
Description [This procedure is the core of the FRAIG package, because
it performs the two-step canonicization of FRAIG nodes. The first step
involves the lookup in the structural hash table (which hashes two ANDs
into a node that has them as fanins, if such a node exists). If the node
is not found in the structural hash table, an attempt is made to find a
functionally equivalent node in another hash table (which hashes the
simulation info into the nodes, which has this simulation info). Some
tricks used on the way are described in the comments to the code and
in the paper "FRAIGs: Functionally reduced AND-INV graphs".]
SideEffects []
SeeAlso []
***********************************************************************/
Fraig_Node_t * Fraig_NodeAndCanon( Fraig_Man_t * pMan, Fraig_Node_t * p1, Fraig_Node_t * p2 )
{
Fraig_Node_t * pNodeNew, * pNodeOld, * pNodeRepr;
int fUseSatCheck;
// int RetValue;
// check for trivial cases
if ( p1 == p2 )
return p1;
if ( p1 == Fraig_Not(p2) )
return Fraig_Not(pMan->pConst1);
if ( Fraig_NodeIsConst(p1) )
{
if ( p1 == pMan->pConst1 )
return p2;
return Fraig_Not(pMan->pConst1);
}
if ( Fraig_NodeIsConst(p2) )
{
if ( p2 == pMan->pConst1 )
return p1;
return Fraig_Not(pMan->pConst1);
}
/*
// check for less trivial cases
if ( Fraig_IsComplement(p1) )
{
if ( RetValue = Fraig_NodeIsInSupergate( Fraig_Regular(p1), p2 ) )
{
if ( RetValue == -1 )
pMan->nImplies0++;
else
pMan->nImplies1++;
if ( RetValue == -1 )
return p2;
}
}
else
{
if ( RetValue = Fraig_NodeIsInSupergate( p1, p2 ) )
{
if ( RetValue == 1 )
pMan->nSimplifies1++;
else
pMan->nSimplifies0++;
if ( RetValue == 1 )
return p1;
return Fraig_Not(pMan->pConst1);
}
}
if ( Fraig_IsComplement(p2) )
{
if ( RetValue = Fraig_NodeIsInSupergate( Fraig_Regular(p2), p1 ) )
{
if ( RetValue == -1 )
pMan->nImplies0++;
else
pMan->nImplies1++;
if ( RetValue == -1 )
return p1;
}
}
else
{
if ( RetValue = Fraig_NodeIsInSupergate( p2, p1 ) )
{
if ( RetValue == 1 )
pMan->nSimplifies1++;
else
pMan->nSimplifies0++;
if ( RetValue == 1 )
return p2;
return Fraig_Not(pMan->pConst1);
}
}
*/
// perform level-one structural hashing
if ( Fraig_HashTableLookupS( pMan, p1, p2, &pNodeNew ) ) // the node with these children is found
{
// if the existent node is part of the cone of unused logic
// (that is logic feeding the node which is equivalent to the given node)
// return the canonical representative of this node
// determine the phase of the given node, with respect to its canonical form
pNodeRepr = Fraig_Regular(pNodeNew)->pRepr;
if ( pMan->fFuncRed && pNodeRepr )
return Fraig_NotCond( pNodeRepr, Fraig_IsComplement(pNodeNew) ^ Fraig_NodeComparePhase(Fraig_Regular(pNodeNew), pNodeRepr) );
// otherwise, the node is itself a canonical representative, return it
return pNodeNew;
}
// the same node is not found, but the new one is created
// if one level hashing is requested (without functionality hashing), return
if ( !pMan->fFuncRed )
return pNodeNew;
// check if the new node is unique using the simulation info
if ( pNodeNew->nOnes == 0 || pNodeNew->nOnes == (unsigned)pMan->nWordsRand * 32 )
{
pMan->nSatZeros++;
if ( !pMan->fDoSparse ) // if we do not do sparse functions, skip
return pNodeNew;
// check the sparse function simulation hash table
pNodeOld = Fraig_HashTableLookupF0( pMan, pNodeNew );
if ( pNodeOld == NULL ) // the node is unique (it is added to the table)
return pNodeNew;
}
else
{
// check the simulation hash table
pNodeOld = Fraig_HashTableLookupF( pMan, pNodeNew );
if ( pNodeOld == NULL ) // the node is unique
return pNodeNew;
}
assert( pNodeOld->pRepr == 0 );
// there is another node which looks the same according to simulation
// use SAT to resolve the ambiguity
fUseSatCheck = (pMan->nInspLimit == 0 || Fraig_ManReadInspects(pMan) < pMan->nInspLimit);
if ( fUseSatCheck && Fraig_NodeIsEquivalent( pMan, pNodeOld, pNodeNew, pMan->nBTLimit, 1000000 ) )
{
// set the node to be equivalent with this node
// to prevent loops, only set if the old node is not in the TFI of the new node
// the loop may happen in the following case: suppose
// NodeC = AND(NodeA, NodeB) and at the same time NodeA => NodeB
// in this case, NodeA and NodeC are functionally equivalent
// however, NodeA is a fanin of node NodeC (this leads to the loop)
// add the node to the list of equivalent nodes or dereference it
if ( pMan->fChoicing && !Fraig_CheckTfi( pMan, pNodeOld, pNodeNew ) )
{
// if the old node is not in the TFI of the new node and choicing
// is enabled, add the new node to the list of equivalent ones
pNodeNew->pNextE = pNodeOld->pNextE;
pNodeOld->pNextE = pNodeNew;
}
// set the canonical representative of this node
pNodeNew->pRepr = pNodeOld;
// return the equivalent node
return Fraig_NotCond( pNodeOld, Fraig_NodeComparePhase(pNodeOld, pNodeNew) );
}
// now we add another member to this simulation class
if ( pNodeNew->nOnes == 0 || pNodeNew->nOnes == (unsigned)pMan->nWordsRand * 32 )
{
Fraig_Node_t * pNodeTemp;
assert( pMan->fDoSparse );
pNodeTemp = Fraig_HashTableLookupF0( pMan, pNodeNew );
// assert( pNodeTemp == NULL );
// Fraig_HashTableInsertF0( pMan, pNodeNew );
}
else
{
pNodeNew->pNextD = pNodeOld->pNextD;
pNodeOld->pNextD = pNodeNew;
}
// return the new node
assert( pNodeNew->pRepr == 0 );
return pNodeNew;
}
/**Function*************************************************************
Synopsis [Perfoms the EXOR operation with functional hashing.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Fraig_Node_t * Fraig_NodeExor( Fraig_Man_t * p, Fraig_Node_t * p1, Fraig_Node_t * p2 )
{
return Fraig_NodeMux( p, p1, Fraig_Not(p2), p2 );
}
/**Function*************************************************************
Synopsis [Perfoms the OR operation with functional hashing.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Fraig_Node_t * Fraig_NodeOr( Fraig_Man_t * p, Fraig_Node_t * p1, Fraig_Node_t * p2 )
{
return Fraig_Not( Fraig_NodeAndCanon( p, Fraig_Not(p1), Fraig_Not(p2) ) );
}