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+/**CFile****************************************************************
+
+  FileName    [ivyBalance.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [And-Inverter Graph package.]
+
+  Synopsis    [Algebraic AIG balancing.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - May 11, 2006.]
+
+  Revision    [$Id: ivyBalance.c,v 1.00 2006/05/11 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "ivy.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+static void Ivy_NodeBalance( Ivy_Obj_t * pNode, int fUpdateLevel, Vec_Ptr_t * vFront, Vec_Ptr_t * vSpots );
+
+// this procedure returns 1 if the node cannot be expanded
+static inline int Ivy_NodeStopFanin( Ivy_Obj_t * pNode, int iFanin )
+{
+    if ( iFanin == 0 )
+        return Ivy_ObjFanin0(pNode)->Type != pNode->Type || Ivy_ObjRefs(Ivy_ObjFanin0(pNode)) > 1 || Ivy_ObjFaninC0(pNode);
+    else
+        return Ivy_ObjFanin1(pNode)->Type != pNode->Type || Ivy_ObjRefs(Ivy_ObjFanin1(pNode)) > 1 || Ivy_ObjFaninC1(pNode);
+}
+
+// this procedure returns 1 if the node cannot be recursively dereferenced
+static inline int Ivy_NodeBalanceDerefFanin( Ivy_Obj_t * pNode, int iFanin )
+{
+    if ( iFanin == 0 )
+        return Ivy_ObjFanin0(pNode)->Type == pNode->Type && Ivy_ObjRefs(Ivy_ObjFanin0(pNode)) == 0 && !Ivy_ObjFaninC0(pNode);
+    else
+        return Ivy_ObjFanin1(pNode)->Type == pNode->Type && Ivy_ObjRefs(Ivy_ObjFanin1(pNode)) == 0 && !Ivy_ObjFaninC1(pNode);
+}
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Performs algebraic balancing of the AIG.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Ivy_ManBalance( Ivy_Man_t * p, int fUpdateLevel )
+{
+    Vec_Int_t * vNodes;
+    Vec_Ptr_t * vFront, * vSpots;
+    Ivy_Obj_t * pNode;
+    int i;
+    vSpots = Vec_PtrAlloc( 50 );
+    vFront = Vec_PtrAlloc( 50 );
+    vNodes = Ivy_ManDfs( p );
+    Ivy_ManForEachNodeVec( p, vNodes, pNode, i )
+    {
+        if ( Ivy_ObjIsBuf(pNode) )
+            continue;
+        // fix the fanin buffer problem
+        Ivy_NodeFixBufferFanins( pNode );
+        // skip node if it became a buffer
+        if ( Ivy_ObjIsBuf(pNode) )
+            continue;
+        // skip nodes with one fanout if type of the node is the same as type of the fanout
+        // such nodes will be processed when the fanouts are processed
+        if ( Ivy_ObjRefs(pNode) == 1 && Ivy_ObjIsExor(pNode) == Ivy_ObjExorFanout(pNode) )
+            continue;
+        assert( Ivy_ObjRefs(pNode) > 0 );
+        // do not balance the node if both if its fanins have more than one fanout
+        if ( Ivy_NodeStopFanin(pNode, 0) && Ivy_NodeStopFanin(pNode, 1) )
+             continue;
+        // try balancing this node
+        Ivy_NodeBalance( pNode, fUpdateLevel, vFront, vSpots );
+    }
+    Vec_IntFree( vNodes );
+    Vec_PtrFree( vSpots );
+    Vec_PtrFree( vFront );
+    return 1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Dereferences MFFC of the node.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ivy_NodeBalanceDeref_rec( Ivy_Obj_t * pNode )
+{
+    Ivy_Obj_t * pFan;
+    // deref the first fanin
+    pFan = Ivy_ObjFanin0(pNode);
+    Ivy_ObjRefsDec( pFan );
+    if ( Ivy_NodeBalanceDerefFanin(pNode, 0) )
+        Ivy_NodeBalanceDeref_rec( pFan );
+    // deref the second fanin
+    pFan = Ivy_ObjFanin1(pNode);
+    Ivy_ObjRefsDec( pFan );
+    if ( Ivy_NodeBalanceDerefFanin(pNode, 1) )
+        Ivy_NodeBalanceDeref_rec( pFan );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Removes nodes inside supergate and determines frontier.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ivy_NodeBalanceCollect_rec( Ivy_Obj_t * pNode, Vec_Ptr_t * vSpots, Vec_Ptr_t * vFront )
+{
+    Ivy_Obj_t * pFanin;
+    // skip visited nodes
+    if ( Vec_PtrFind(vSpots, pNode) >= 0 )
+        return;
+    // collect node
+    Vec_PtrPush( vSpots, pNode );
+    // first fanin
+    pFanin = Ivy_ObjFanin0(pNode);
+    if ( Ivy_ObjRefs(pFanin) == 0 )
+        Ivy_NodeBalanceCollect_rec( pFanin, vSpots, vFront );
+    else if ( Ivy_ObjIsExor(pNode) && Vec_PtrFind(vFront, Ivy_ObjChild0(pNode)) >= 0 )
+        Vec_PtrRemove( vFront, Ivy_ObjChild0(pNode) );
+    else
+        Vec_PtrPushUnique( vFront, Ivy_ObjChild0(pNode) );
+    // second fanin
+    pFanin = Ivy_ObjFanin1(pNode);
+    if ( Ivy_ObjRefs(pFanin) == 0 )
+        Ivy_NodeBalanceCollect_rec( pFanin, vSpots, vFront );
+    else if ( Ivy_ObjIsExor(pNode) && Vec_PtrFind(vFront, Ivy_ObjChild1(pNode)) >= 0 )
+        Vec_PtrRemove( vFront, Ivy_ObjChild1(pNode) );
+    else
+        Vec_PtrPushUnique( vFront, Ivy_ObjChild1(pNode) );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Comparison procedure for two nodes by level.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Ivy_BalanceCompareByLevel( Ivy_Obj_t ** pp1, Ivy_Obj_t ** pp2 )
+{
+    int Level1 = Ivy_ObjLevel( *pp1 );
+    int Level2 = Ivy_ObjLevel( *pp2 );
+    if ( Level1 > Level2 )
+        return -1;
+    if ( Level1 < Level2 )
+        return 1;
+    return 0;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Removes nodes inside supergate and determines frontier.]
+
+  Description [Return 1 if the output needs to be complemented.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Ivy_NodeBalancePrepare( Ivy_Obj_t * pNode, Vec_Ptr_t * vFront, Vec_Ptr_t * vSpots )
+{
+    Ivy_Man_t * pMan = Ivy_ObjMan( pNode );
+    Ivy_Obj_t * pObj, * pNext;
+    int i, k, Counter = 0;
+    // dereference the cone
+    Ivy_NodeBalanceDeref_rec( pNode );
+    // collect the frontier and the internal nodes
+    Vec_PtrClear( vFront );
+    Vec_PtrClear( vSpots );
+    Ivy_NodeBalanceCollect_rec( pNode, vSpots, vFront );
+    // remove all the nodes
+    Vec_PtrForEachEntry( vSpots, pObj, i )
+    {
+        // skip the first entry (the node itself)
+        if ( i == 0 ) continue;
+        // collect the free entries
+        Vec_IntPush( pMan->vFree, pObj->Id );
+        Ivy_ObjDelete( pObj, 1 );
+    }
+    // sort nodes by level in decreasing order
+    qsort( (void *)Vec_PtrArray(vFront), Vec_PtrSize(vFront), sizeof(Ivy_Obj_t *), 
+            (int (*)(const void *, const void *))Ivy_BalanceCompareByLevel );
+    // check if there are nodes and their complements
+    Counter = 0;
+    Vec_PtrForEachEntry( vFront, pObj, i )
+    {
+        if ( i == Vec_PtrSize(vFront) - 1 )
+            break;
+        pNext = Vec_PtrEntry( vFront, i+1 );
+        if ( Ivy_Regular(pObj) == Ivy_Regular(pNext) )
+        {
+            assert( pObj == Ivy_Not(pNext) );
+            Vec_PtrWriteEntry( vFront, i, NULL );
+            Vec_PtrWriteEntry( vFront, i+1, NULL );
+            i++;
+            Counter++;
+        }
+    }
+    // if there are no complemented pairs, go ahead and balance
+    if ( Counter == 0 )
+        return 0;
+    // if there are complemented pairs and this is AND, create const 0
+    if ( Counter > 0 && Ivy_ObjIsAnd(pNode) )
+    {
+        Vec_PtrClear( vFront );
+        Vec_PtrPush( vFront, Ivy_ManConst0(pMan) );
+        return 0;
+    }
+    assert( Counter > 0 && Ivy_ObjIsExor(pNode) );
+    // remove the pairs
+    k = 0;
+    Vec_PtrForEachEntry( vFront, pObj, i )
+        if ( pObj ) 
+            Vec_PtrWriteEntry( vFront, k++, pObj );
+    Vec_PtrShrink( vFront, k );
+    // add constant zero node if nothing is left
+    if ( Vec_PtrSize(vFront) == 0 )
+        Vec_PtrPush( vFront, Ivy_ManConst0(pMan) );
+    // return 1 if the number of pairs is odd (need to complement the output)
+    return Counter & 1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Finds the left bound on the next candidate to be paired.]
+
+  Description [The nodes in the array are in the decreasing order of levels. 
+  The last node in the array has the smallest level. By default it would be paired 
+  with the next node on the left. However, it may be possible to pair it with some
+  other node on the left, in such a way that the new node is shared. This procedure
+  finds the index of the left-most node, which can be paired with the last node.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Ivy_NodeBalanceFindLeft( Vec_Ptr_t * vSuper )
+{
+    Ivy_Obj_t * pNodeRight, * pNodeLeft;
+    int Current;
+    // if two or less nodes, pair with the first
+    if ( Vec_PtrSize(vSuper) < 3 )
+        return 0;
+    // set the pointer to the one before the last
+    Current = Vec_PtrSize(vSuper) - 2;
+    pNodeRight = Vec_PtrEntry( vSuper, Current );
+    // go through the nodes to the left of this one
+    for ( Current--; Current >= 0; Current-- )
+    {
+        // get the next node on the left
+        pNodeLeft = Vec_PtrEntry( vSuper, Current );
+        // if the level of this node is different, quit the loop
+        if ( Ivy_Regular(pNodeLeft)->Level != Ivy_Regular(pNodeRight)->Level )
+            break;
+    }
+    Current++;    
+    // get the node, for which the equality holds
+    pNodeLeft = Vec_PtrEntry( vSuper, Current );
+    assert( Ivy_Regular(pNodeLeft)->Level == Ivy_Regular(pNodeRight)->Level );
+    return Current;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Moves closer to the end the node that is best for sharing.]
+
+  Description [If there is no node with sharing, randomly chooses one of 
+  the legal nodes.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ivy_NodeBalancePermute( Ivy_Man_t * pMan, Vec_Ptr_t * vSuper, int LeftBound, int fExor )
+{
+    Ivy_Obj_t * pNode1, * pNode2, * pNode3, * pGhost;
+    int RightBound, i;
+    // get the right bound
+    RightBound = Vec_PtrSize(vSuper) - 2;
+    assert( LeftBound <= RightBound );
+    if ( LeftBound == RightBound )
+        return;
+    // get the two last nodes
+    pNode1 = Vec_PtrEntry( vSuper, RightBound + 1 );
+    pNode2 = Vec_PtrEntry( vSuper, RightBound     );
+    // find the first node that can be shared
+    for ( i = RightBound; i >= LeftBound; i-- )
+    {
+        pNode3 = Vec_PtrEntry( vSuper, i );
+        pGhost = Ivy_ObjCreateGhost( pNode1, pNode3, fExor? IVY_EXOR : IVY_AND, IVY_INIT_NONE );
+        if ( Ivy_TableLookup( pGhost ) )
+        {
+            if ( pNode3 == pNode2 )
+                return;
+            Vec_PtrWriteEntry( vSuper, i,          pNode2 );
+            Vec_PtrWriteEntry( vSuper, RightBound, pNode3 );
+            return;
+        }
+    }
+/*
+    // we did not find the node to share, randomize choice
+    {
+        int Choice = rand() % (RightBound - LeftBound + 1);
+        pNode3 = Vec_PtrEntry( vSuper, LeftBound + Choice );
+        if ( pNode3 == pNode2 )
+            return;
+        Vec_PtrWriteEntry( vSuper, LeftBound + Choice, pNode2 );
+        Vec_PtrWriteEntry( vSuper, RightBound,         pNode3 );
+    }
+*/
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Inserts a new node in the order by levels.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ivy_NodeBalancePushUniqueOrderByLevel( Vec_Ptr_t * vFront, Ivy_Obj_t * pNode )
+{
+    Ivy_Obj_t * pNode1, * pNode2;
+    int i;
+    if ( Vec_PtrPushUnique(vFront, pNode) )
+        return;
+    // find the p of the node
+    for ( i = vFront->nSize-1; i > 0; i-- )
+    {
+        pNode1 = vFront->pArray[i  ];
+        pNode2 = vFront->pArray[i-1];
+        if ( Ivy_Regular(pNode1)->Level <= Ivy_Regular(pNode2)->Level )
+            break;
+        vFront->pArray[i  ] = pNode2;
+        vFront->pArray[i-1] = pNode1;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Balances one node.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Ivy_NodeBalance( Ivy_Obj_t * pNode, int fUpdateLevel, Vec_Ptr_t * vFront, Vec_Ptr_t * vSpots )
+{
+    Ivy_Man_t * pMan = Ivy_ObjMan( pNode );
+    Ivy_Obj_t * pFan0, * pFan1, * pNodeNew;
+    int fCompl, LeftBound;
+    // remove internal nodes and derive the frontier
+    fCompl = Ivy_NodeBalancePrepare( pNode, vFront, vSpots );
+    assert( Vec_PtrSize(vFront) > 0 );
+    // balance the nodes
+    while ( Vec_PtrSize(vFront) > 1 )
+    {
+        // find the left bound on the node to be paired
+        LeftBound = (!fUpdateLevel)? 0 : Ivy_NodeBalanceFindLeft( vFront );
+        // find the node that can be shared (if no such node, randomize choice)
+        Ivy_NodeBalancePermute( pMan, vFront, LeftBound, Ivy_ObjIsExor(pNode) );
+        // pull out the last two nodes
+        pFan0 = Vec_PtrPop(vFront);  assert( !Ivy_ObjIsConst1(Ivy_Regular(pFan0)) );
+        pFan1 = Vec_PtrPop(vFront);  assert( !Ivy_ObjIsConst1(Ivy_Regular(pFan1)) );
+        // create the new node
+        pNodeNew = Ivy_ObjCreate( Ivy_ObjCreateGhost(pFan0, pFan1, Ivy_ObjType(pNode), IVY_INIT_NONE) );
+        // add the new node to the frontier
+        Ivy_NodeBalancePushUniqueOrderByLevel( vFront, pNodeNew );
+    }
+    assert( Vec_PtrSize(vFront) == 1 );
+    // perform the replacement
+    Ivy_ObjReplace( pNode, Ivy_NotCond(Vec_PtrPop(vFront), fCompl), 1, 1 ); 
+}
+
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+