path: root/src/bdd/dsd/dsdProc.c

/**CFile****************************************************************

  FileName    [dsdProc.c]

  PackageName [DSD: Disjoint-support decomposition package.]

  Synopsis    [The core procedures of the package.]

  Author      [Alan Mishchenko]
  
  Affiliation [UC Berkeley]

  Date        [Ver. 8.0. Started - September 22, 2003.]

  Revision    [$Id: dsdProc.c,v 1.0 2002/22/09 00:00:00 alanmi Exp $]

***********************************************************************/

#include "dsdInt.h"


////////////////////////////////////////////////////////////////////////
///                    FUNCTION DECLARATIONS                         ///
////////////////////////////////////////////////////////////////////////

// the most important procedures
void dsdKernelDecompose( Dsd_Manager_t * pDsdMan, DdNode ** pbFuncs, int nFuncs );
static Dsd_Node_t * dsdKernelDecompose_rec( Dsd_Manager_t * pDsdMan, DdNode * F );

// additional procedures
static Dsd_Node_t * dsdKernelFindContainingComponent( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pWhere, DdNode * Var, int * fPolarity );
static int dsdKernelFindCommonComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t *** pCommon, Dsd_Node_t ** pLastDiffL, Dsd_Node_t ** pLastDiffH );
static void dsdKernelComputeSumOfComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t ** pCommon, int nCommon, DdNode ** pCompF, DdNode ** pCompS, int fExor );
static int dsdKernelCheckContainment( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t ** pLarge, Dsd_Node_t ** pSmall );

// list copying
static void dsdKernelCopyListPlusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize );
static void dsdKernelCopyListPlusOneMinusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize, int Skipped );

// debugging procedures
static int dsdKernelVerifyDecomposition( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pDE );

////////////////////////////////////////////////////////////////////////
///                       STATIC VARIABLES                           ///
////////////////////////////////////////////////////////////////////////

// the counter of marks
static int s_Mark;

// debugging flag
static int s_Show = 0;
// temporary var used for debugging
static int Depth = 0;

static int s_Loops1;
static int s_Loops2;
static int s_Loops3;
static int s_Pivot;
static int s_PivotNo;
static int s_Common;
static int s_CommonNo;

static int s_Case4Calls;
static int s_Case4CallsSpecial;

static int s_Case5;
static int s_Loops2Useless;


static int s_DecNodesTotal;
static int s_DecNodesUsed;

// statistical variables
static int   s_nDecBlocks;
static int   s_nLiterals;
static int   s_nExorGates; 
static int   s_nReusedBlocks;
static int   s_nCascades;
static float s_nArea;    
static float s_MaxDelay;
static long  s_Time;
static int   s_nInvertors;
static int   s_nPrimeBlocks;

static int HashSuccess = 0;
static int HashFailure = 0;

static int s_CacheEntries;


////////////////////////////////////////////////////////////////////////
///                     DECOMPOSITION FUNCTIONS                      ///
////////////////////////////////////////////////////////////////////////

/**Function*************************************************************

  Synopsis    [Performs DSD for the array of functions represented by BDDs.]

  Description [This function takes the DSD manager, which should be
  previously allocated by the call to Dsd_ManagerStart(). The resulting
  DSD tree is stored in the DSD manager (pDsdMan->pRoots, pDsdMan->nRoots).
  Access to the tree is through the APIs of the manager. The resulting
  tree is a shared DSD DAG for the functions given in the array. For one
  function the resulting DAG is always a tree. The root node pointers can 
  be complemented, as discussed in the literature referred to in "dsd.h".
  This procedure can be called repeatedly for different functions. There is
  no need to remove the decomposition tree after it is returned, because
  the next call to the DSD manager will "recycle" the tree. The user should
  not modify or dereference any data associated with the nodes of the 
  DSD trees (the user can only change the contents of a temporary
  mark associated with each node by the calling to Dsd_NodeSetMark()).
  All the decomposition trees and intermediate nodes will be removed when
  the DSD manager is deallocated at the end by calling Dsd_ManagerStop().]
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void Dsd_Decompose( Dsd_Manager_t * pDsdMan, DdNode ** pbFuncs, int nFuncs )
{
    DdManager * dd = pDsdMan->dd;
    int i;
    long clk;
    Dsd_Node_t * pTemp;
    int SumMaxGateSize = 0;
    int nDecOutputs = 0;
    int nCBFOutputs = 0;
/*
s_Loops1 = 0;
s_Loops2 = 0;
s_Loops3 = 0;
s_Case4Calls = 0;
s_Case4CallsSpecial = 0;
s_Case5 = 0;
s_Loops2Useless = 0;
*/
    // resize the number of roots in the manager
    if ( pDsdMan->nRootsAlloc < nFuncs )
    {
        if ( pDsdMan->nRootsAlloc > 0 )
            free( pDsdMan->pRoots );
        pDsdMan->nRootsAlloc = nFuncs;
        pDsdMan->pRoots = (Dsd_Node_t **) malloc( pDsdMan->nRootsAlloc * sizeof(Dsd_Node_t *) );
    }

    if ( pDsdMan->fVerbose )
        printf( "\nDecomposability statistics for individual outputs:\n" );

    // set the counter of decomposition nodes
    s_nDecBlocks = 0;

    // perform decomposition for all outputs
    clk = clock();
    pDsdMan->nRoots = 0;
    s_nCascades = 0;
    for ( i = 0; i < nFuncs; i++ )
    {
        int nLiteralsPrev;
        int nDecBlocksPrev;
        int nExorGatesPrev;
        int nReusedBlocksPres;
        int nCascades;
        int MaxBlock;
        int nPrimeBlocks;
        long clk;

        clk = clock();
        nLiteralsPrev     = s_nLiterals;
        nDecBlocksPrev    = s_nDecBlocks;
        nExorGatesPrev    = s_nExorGates;
        nReusedBlocksPres = s_nReusedBlocks;
        nPrimeBlocks      = s_nPrimeBlocks;

        pDsdMan->pRoots[ pDsdMan->nRoots++ ] = dsdKernelDecompose_rec( pDsdMan, pbFuncs[i] );

        Dsd_TreeNodeGetInfoOne( pDsdMan->pRoots[i], &nCascades, &MaxBlock );
        s_nCascades = ddMax( s_nCascades, nCascades );
        pTemp = Dsd_Regular(pDsdMan->pRoots[i]);
        if ( pTemp->Type != DSD_NODE_PRIME || pTemp->nDecs != Extra_bddSuppSize(dd,pTemp->S) )
            nDecOutputs++;
        if ( MaxBlock < 3 )
            nCBFOutputs++;
        SumMaxGateSize += MaxBlock;

        if ( pDsdMan->fVerbose )
        {
            printf("#%02d: ", i );                              
            printf("Ins=%2d. ", Cudd_SupportSize(dd,pbFuncs[i]) );                  
            printf("Gts=%3d. ", Dsd_TreeCountNonTerminalNodesOne( pDsdMan->pRoots[i] ) ); 
            printf("Pri=%3d. ", Dsd_TreeCountPrimeNodesOne( pDsdMan->pRoots[i] ) ); 
            printf("Max=%3d. ", MaxBlock ); 
            printf("Reuse=%2d. ", s_nReusedBlocks-nReusedBlocksPres ); 
            printf("Csc=%2d. ", nCascades ); 
            printf("T= %.2f s. ", (float)(clock()-clk)/(float)(CLOCKS_PER_SEC) ) ;
            printf("Bdd=%2d. ", Cudd_DagSize(pbFuncs[i]) ); 
            printf("\n");
            fflush( stdout );
        }
    }
    assert( pDsdMan->nRoots == nFuncs );

    if ( pDsdMan->fVerbose )
    {
        printf( "\n" );
        printf( "The cumulative decomposability statistics:\n" );
        printf( "  Total outputs                             = %5d\n", nFuncs );
        printf( "  Decomposable outputs                      = %5d\n", nDecOutputs );
        printf( "  Completely decomposable outputs           = %5d\n", nCBFOutputs );
        printf( "  The sum of max gate sizes                 = %5d\n", SumMaxGateSize );
        printf( "  Shared BDD size                           = %5d\n", Cudd_SharingSize( pbFuncs, nFuncs ) );
        printf( "  Decomposition entries                     = %5d\n", st_count( pDsdMan->Table ) );
        printf( "  Pure decomposition time                   =  %.2f sec\n", (float)(clock() - clk)/(float)(CLOCKS_PER_SEC) );
    }
/*
    printf( "s_Loops1 = %d.\n", s_Loops1 );
    printf( "s_Loops2 = %d.\n", s_Loops2 );
    printf( "s_Loops3 = %d.\n", s_Loops3 );
    printf( "s_Case4Calls = %d.\n", s_Case4Calls );
    printf( "s_Case4CallsSpecial = %d.\n", s_Case4CallsSpecial );
    printf( "s_Case5 = %d.\n", s_Case5 );
    printf( "s_Loops2Useless = %d.\n", s_Loops2Useless );
*/
}

/**Function*************************************************************

  Synopsis    [Performs decomposition for one function.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
Dsd_Node_t * Dsd_DecomposeOne( Dsd_Manager_t * pDsdMan, DdNode * bFunc )
{
    return dsdKernelDecompose_rec( pDsdMan, bFunc );
}

/**Function*************************************************************

  Synopsis    [The main function of this module. Recursive implementation of DSD.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
Dsd_Node_t * dsdKernelDecompose_rec( Dsd_Manager_t * pDsdMan, DdNode * bFunc0 )
{
    DdManager * dd = pDsdMan->dd;
    DdNode * bLow;
    DdNode * bLowR;
    DdNode * bHigh;

    int      VarInt;
    DdNode * bVarCur;
    Dsd_Node_t *     pVarCurDE; 
    // works only if var indices start from 0!!!
    DdNode * bSuppNew = NULL, * bTemp;

    int fContained;
    int nSuppLH;
    int nSuppL;
    int nSuppH;



    // various decomposition nodes
    Dsd_Node_t * pThis, * pL, * pH, * pLR, * pHR;

    Dsd_Node_t * pSmallR, * pLargeR;
    Dsd_Node_t * pTableEntry;


    // treat the complemented case
    DdNode * bF = Cudd_Regular(bFunc0);
    int  fCompF = (int)(bF != bFunc0);

    // check cache
    if ( st_lookup( pDsdMan->Table, (char*)bF, (char**)&pTableEntry ) )
    { // the entry is present 
        HashSuccess++;
        return Dsd_NotCond( pTableEntry, fCompF );
    }
    HashFailure++;
    Depth++;

    // proceed to consider "four cases"
    //////////////////////////////////////////////////////////////////////
    // TERMINAL CASES - CASES 1 and 2
    //////////////////////////////////////////////////////////////////////
    bLow    = cuddE(bF);
    bLowR   = Cudd_Regular(bLow);
    bHigh   = cuddT(bF);
    VarInt    = bF->index;
    bVarCur   = dd->vars[VarInt];
    pVarCurDE = pDsdMan->pInputs[VarInt]; 
    // works only if var indices start from 0!!!
    bSuppNew = NULL;

    if ( bLowR->index == CUDD_CONST_INDEX || bHigh->index == CUDD_CONST_INDEX )
    { // one of the cofactors in the constant
        if ( bHigh == b1 )  // bHigh cannot be equal to b0, because then it will be complemented
          if ( bLow == b0 ) // bLow cannot be equal to b1, because then the node will have bLow == bHigh
          /////////////////////////////////////////////////////////////////
          // bLow == 0, bHigh == 1, F = x'&0 + x&1 = x
          /////////////////////////////////////////////////////////////////
          { // create the elementary variable node
            assert(0); // should be already in the hash table
            pThis = Dsd_TreeNodeCreate( DSD_NODE_BUF, 1, s_nDecBlocks++ );
            pThis->pDecs[0] = NULL;
          }
          else // if ( bLow != constant )
          /////////////////////////////////////////////////////////////////
          // bLow != const, bHigh == 1, F = x'&bLow + x&1 = bLow + x  --- DSD_NODE_OR(x,bLow)
          /////////////////////////////////////////////////////////////////
          {
            pL  = dsdKernelDecompose_rec( pDsdMan, bLow );
            pLR = Dsd_Regular( pL );
            bSuppNew = Cudd_bddAnd( dd, bVarCur, pLR->S ); Cudd_Ref(bSuppNew);
            if ( pLR->Type == DSD_NODE_OR && pL == pLR ) // OR and no complement
            { // add to the components
                pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, pL->nDecs+1, s_nDecBlocks++ );
                dsdKernelCopyListPlusOne( pThis, pVarCurDE, pL->pDecs, pL->nDecs );
            }
            else // all other cases
            { // create a new 2-input OR-gate
                pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ );
                dsdKernelCopyListPlusOne( pThis, pVarCurDE, &pL, 1 );
            }
          }
        else // if ( bHigh != const ) // meaning that bLow should be a constant
        {
          pH = dsdKernelDecompose_rec( pDsdMan, bHigh );
          pHR = Dsd_Regular( pH );
          bSuppNew = Cudd_bddAnd( dd, bVarCur, pHR->S ); Cudd_Ref(bSuppNew);
          if ( bLow == b0 )
          /////////////////////////////////////////////////////////////////
          // Low == 0, High != 1, F = x'&0+x&High = (x'+High')'--- NOR(x',High')
          /////////////////////////////////////////////////////////////////
            if ( pHR->Type == DSD_NODE_OR && pH != pHR ) // DSD_NODE_OR and complement
            { // add to the components
               pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, pHR->nDecs+1, s_nDecBlocks++ );
              dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), pHR->pDecs, pHR->nDecs );
              pThis = Dsd_Not(pThis);
            }
            else // all other cases
            { // create a new 2-input NOR gate
               pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ );
              pH = Dsd_Not(pH);
              dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), &pH, 1 );
              pThis = Dsd_Not(pThis);
            }
          else // if ( bLow == b1 )
            /////////////////////////////////////////////////////////////////
          // Low == 1, High != 1, F = x'&1 + x&High = x' + High --- DSD_NODE_OR(x',High)
          /////////////////////////////////////////////////////////////////
            if ( pHR->Type == DSD_NODE_OR && pH == pHR ) // OR and no complement
            { // add to the components
                pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, pH->nDecs+1, s_nDecBlocks++ );
                dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), pH->pDecs, pH->nDecs );
            }
            else // all other cases
            { // create a new 2-input OR-gate
                pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ );
                dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), &pH, 1 );
            }
        }
        goto EXIT;
    }
    // else if ( bLow != const && bHigh != const )

    // the case of equal cofactors (up to complementation)
    if ( bLowR == bHigh )
    /////////////////////////////////////////////////////////////////
    // Low == G, High == G', F = x'&G + x&G' = (x(+)G) --- EXOR(x,Low)
    /////////////////////////////////////////////////////////////////
    {
        pL  = dsdKernelDecompose_rec( pDsdMan, bLow );
        pLR = Dsd_Regular( pL );
        bSuppNew = Cudd_bddAnd( dd, bVarCur, pLR->S ); Cudd_Ref(bSuppNew);
        if ( pLR->Type == DSD_NODE_EXOR ) // complemented or not - does not matter!
        { // add to the components
            pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, pLR->nDecs+1, s_nDecBlocks++ );
            dsdKernelCopyListPlusOne( pThis, pVarCurDE, pLR->pDecs, pLR->nDecs );
            if ( pL != pLR )
                pThis = Dsd_Not( pThis );
        }
        else // all other cases
        { // create a new 2-input EXOR-gate
            pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, 2, s_nDecBlocks++ );
            if ( pL != pLR ) // complemented
            {
                dsdKernelCopyListPlusOne( pThis, pVarCurDE, &pLR, 1 );
                pThis = Dsd_Not( pThis );
            }
            else // non-complemented
                dsdKernelCopyListPlusOne( pThis, pVarCurDE, &pL, 1 );
        }
        goto EXIT;
    }

    //////////////////////////////////////////////////////////////////////
    // solve subproblems
    //////////////////////////////////////////////////////////////////////
    pL   = dsdKernelDecompose_rec( pDsdMan, bLow );
    pH   = dsdKernelDecompose_rec( pDsdMan, bHigh );
    pLR  = Dsd_Regular( pL );
    pHR  = Dsd_Regular( pH );

    assert( pLR->Type == DSD_NODE_BUF || pLR->Type == DSD_NODE_OR || pLR->Type == DSD_NODE_EXOR || pLR->Type == DSD_NODE_PRIME );
    assert( pHR->Type == DSD_NODE_BUF || pHR->Type == DSD_NODE_OR || pHR->Type == DSD_NODE_EXOR || pHR->Type == DSD_NODE_PRIME );

/*
if ( Depth == 1 )
{
//    PRK(bLow,pDecTreeTotal->nInputs);
//    PRK(bHigh,pDecTreeTotal->nInputs);
if ( s_Show )
{
    PRD( pL );
    PRD( pH );
}
}
*/
    // compute the new support
    bTemp    = Cudd_bddAnd( dd, pLR->S, pHR->S );   Cudd_Ref( bTemp );
    nSuppL   = Extra_bddSuppSize( dd, pLR->S );
    nSuppH   = Extra_bddSuppSize( dd, pHR->S );
    nSuppLH  = Extra_bddSuppSize( dd, bTemp );
    bSuppNew = Cudd_bddAnd( dd, bTemp, bVarCur );   Cudd_Ref( bSuppNew );
    Cudd_RecursiveDeref( dd, bTemp );


    // several possibilities are possible
    // (1) support of one component contains another
    // (2) none of the supports is contained in another
    fContained = dsdKernelCheckContainment( pDsdMan, pLR, pHR, &pLargeR, &pSmallR );

    //////////////////////////////////////////////////////////////////////
    // CASE 3.b One of the cofactors in a constant (OR and EXOR)
    //////////////////////////////////////////////////////////////////////
    // the support of the larger component should contain the support of the smaller
    // it is possible to have PRIME function in this role
    // for example: F = ITE( a+b, c(+)d, e+f ), F0 = ITE( b, c(+)d, e+f ), F1 = c(+)d
    if ( fContained )
    {
        Dsd_Node_t * pSmall, * pLarge;
        int c, iCompLarge; // the number of the component is Large is equal to the whole of Small
        int fLowIsLarge;

        DdNode * bFTemp;     // the changed input function
        Dsd_Node_t * pDETemp, * pDENew;

        Dsd_Node_t * pComp = NULL;
        int  nComp;

        if ( pSmallR == pLR )
        { // Low is Small => High is Large
            pSmall = pL;
            pLarge = pH;
            fLowIsLarge = 0;
        }
        else
        { // vice versa
            pSmall = pH;
            pLarge = pL;
            fLowIsLarge = 1;
        }

        // treat the situation when the larger is PRIME
        if ( pLargeR->Type == DSD_NODE_PRIME ) //&& pLargeR->nDecs != pSmallR->nDecs )
        {
            // QUESTION: Is it possible for pLargeR->nDecs > 3 
            // and pSmall contained as one of input in pLarge?
            // Yes, for example F = a'c + a & MUX(b,c',d) = a'c + abc' + ab'd is non-decomposable
            // Consider the function H(a->xy) = F( xy, b, c, d )
            // H0 = H(x=0) = F(0,b,c,d) = c
            // H1 = F(x=1) = F(y,b,c,d) - non-decomposable
            //
            // QUESTION: Is it possible that pLarge is PRIME(3) and pSmall is OR(2),
            // which is not contained in PRIME as one input?
            // Yes, for example F = abcd + b'c'd' + a'c'd' = PRIME(ab, c, d)
            // F(a=0) = c'd' = NOT(OR(a,d))  F(a=1) = bcd + b'c'd' = PRIME(b,c,d)
            // To find decomposition, we have to prove that F(a=1)|b=0 = F(a=0)

            // Is it possible that (pLargeR->nDecs == pSmallR->nDecs) and yet this case holds?
            // Yes, consider the function such that F(a=0) = PRIME(a,b+c,d,e) and F(a=1) = OR(b,c,d,e)
            // They have the same number of inputs and it is possible that they will be the cofactors
            // as discribed in the previous example.

            // find the component, which when substituted for 0 or 1, produces the desired result
            int g, fFoundComp; // {0,1} depending on whether setting cofactor to 0 or 1 worked out

            DdNode * bLarge, * bSmall;
            if ( fLowIsLarge )
            {
                bLarge = bLow;
                bSmall = bHigh;
            }
            else
            {
                bLarge = bHigh;
                bSmall = bLow;
            }

            for ( g = 0; g < pLargeR->nDecs; g++ )
//            if ( g != c )
            {
                pDETemp = pLargeR->pDecs[g]; // cannot be complemented
                if ( Dsd_CheckRootFunctionIdentity( dd, bLarge, bSmall, pDETemp->G, b1 ) )
                {
                    fFoundComp = 1;
                    break;
                }

                s_Loops1++;

                if ( Dsd_CheckRootFunctionIdentity( dd, bLarge, bSmall, Cudd_Not(pDETemp->G), b1 ) )
                {
                    fFoundComp = 0;
                    break;
                }

                s_Loops1++;
            }

            if ( g != pLargeR->nDecs ) 
            { // decomposition is found
                if ( fFoundComp )
                    if ( fLowIsLarge )
                        bFTemp = Cudd_bddOr( dd, bVarCur, pLargeR->pDecs[g]->G );
                    else
                        bFTemp = Cudd_bddOr( dd, Cudd_Not(bVarCur), pLargeR->pDecs[g]->G );
                else
                    if ( fLowIsLarge )
                        bFTemp = Cudd_bddAnd( dd, Cudd_Not(bVarCur), pLargeR->pDecs[g]->G );
                    else
                        bFTemp = Cudd_bddAnd( dd, bVarCur, pLargeR->pDecs[g]->G );
                Cudd_Ref( bFTemp );

                pDENew = dsdKernelDecompose_rec( pDsdMan, bFTemp );
                pDENew = Dsd_Regular( pDENew );
                Cudd_RecursiveDeref( dd, bFTemp );

                // get the new gate
                pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, pLargeR->nDecs, s_nDecBlocks++ );
                dsdKernelCopyListPlusOneMinusOne( pThis, pDENew, pLargeR->pDecs, pLargeR->nDecs, g );
                goto EXIT;
            }
        }

        // try to find one component in the pLarger that is equal to the whole of pSmaller
        for ( c = 0; c < pLargeR->nDecs; c++ )
            if ( pLargeR->pDecs[c] == pSmall || pLargeR->pDecs[c] == Dsd_Not(pSmall) )
            {
                iCompLarge = c;
                break;
            }

        // assign the equal component
        if ( c != pLargeR->nDecs )  // the decomposition is possible!
        { 
            pComp  = pLargeR->pDecs[iCompLarge];
            nComp  = 1;
        }
        else // the decomposition is still possible
        { // for example F = OR(ab,c,d), F(a=0) = OR(c,d), F(a=1) = OR(b,c,d)
            // supp(F0) is contained in supp(F1), Polarity(F(a=0)) == Polarity(F(a=1))

            // try to find a group of common components
            if ( pLargeR->Type == pSmallR->Type &&
                (pLargeR->Type == DSD_NODE_EXOR || pSmallR->Type == DSD_NODE_OR&& ((pLarge==pLargeR) == (pSmall==pSmallR))) )
            {
                Dsd_Node_t ** pCommon, * pLastDiffL = NULL, * pLastDiffH = NULL; 
                int nCommon = dsdKernelFindCommonComponents( pDsdMan, pLargeR, pSmallR, &pCommon, &pLastDiffL, &pLastDiffH );
                // if all the components of pSmall are contained in pLarge,
                // then the decomposition exists
                if ( nCommon == pSmallR->nDecs )
                {
                    pComp = pSmallR;
                    nComp = pSmallR->nDecs;
                }
            }
        }

        if ( pComp ) // the decomposition is possible!
        {
//            Dsd_Node_t * pComp  = pLargeR->pDecs[iCompLarge];
            Dsd_Node_t * pCompR = Dsd_Regular( pComp );
            int fComp1 = (int)( pLarge != pLargeR );
            int fComp2 = (int)( pComp  != pCompR );
            int fComp3 = (int)( pSmall != pSmallR );

            DdNode * bFuncComp;  // the function of the given component
            DdNode * bFuncNew;   // the function of the input component

            if ( pLargeR->Type == DSD_NODE_OR ) // Figure 4 of Matsunaga's paper
            { 
                // the decomposition exists only if the polarity assignment 
                // along the paths is the same
                if ( (fComp1 ^ fComp2) == fComp3 )
                { // decomposition exists = consider 4 cases
                    // consideration of cases leads to the following conclusion
                    // fComp1 gives the polarity of the resulting DSD_NODE_OR gate
                    // fComp2 gives the polarity of the common component feeding into the DSD_NODE_OR gate
                    //
                    //                  |  fComp1              pL/  |pS
                    //                  <> .........<=>....... <>   |
                    //                  |                     /     |
                    //                [OR]                  [OR]    | fComp3
                    //                /  \  fComp2          / | \   |
                    //              <>    <> .......<=>... /..|..<> | 
                    //             /        \             /   |    \|
                    //          [OR]        [C]          S1   S2    C 
                    //          /  \
                    //        <>    \
                    //       /       \
                    //     [OR]      [x]
                    //     /  \
                    //    S1   S2
                    //


                    // at this point we have the function F (bFTemp) and the common component C (bFuncComp)
                    // to get the remainder, R, in the relationship F = R + C, supp(R) & supp(C) = 0
                    // we compute the following R = Exist( F - C, supp(C) )
                    bFTemp = (fComp1)? Cudd_Not( bF ): bF;
                    bFuncComp = (fComp2)? Cudd_Not( pCompR->G ): pCompR->G;
                    bFuncNew  = Cudd_bddAndAbstract( dd, bFTemp, Cudd_Not(bFuncComp), pCompR->S ); Cudd_Ref( bFuncNew );

                    // there is no need to copy the dec entry list first, because pComp is a component
                    // which will not be destroyed by the recursive call to decomposition
                    pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew );
                    assert( Dsd_IsComplement(pDENew) ); // follows from the consideration of cases
                    Cudd_RecursiveDeref( dd, bFuncNew );

                    // get the new gate
                    if ( nComp == 1 )
                    {
                        pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ );
                        pThis->pDecs[0] = pDENew;
                        pThis->pDecs[1] = pComp; // takes the complement
                    }
                    else
                    {  // pComp is not complemented
                        pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, nComp+1, s_nDecBlocks++ );
                        dsdKernelCopyListPlusOne( pThis, pDENew, pComp->pDecs, nComp );
                    }
                    
                    if ( fComp1 )
                        pThis = Dsd_Not( pThis );
                    goto EXIT;
                }
            }
            else if ( pLargeR->Type == DSD_NODE_EXOR ) // Figure 5 of Matsunaga's paper (with correction)
            { // decomposition always exists = consider 4 cases

                // consideration of cases leads to the following conclusion
                // fComp3 gives the COMPLEMENT of the polarity of the resulting EXOR gate
                // (if fComp3 is 0, the EXOR gate is complemented, and vice versa)
                //
                //                  |  fComp1              pL/  |pS
                //                  <> .........<=>....... /....|  fComp3
                //                  |                     /     |
                //                [XOR]                [XOR]    |
                //                /  \  fComp2==0       / | \   |
                //              /     \                /  |  \  | 
                //             /        \             /   |    \|
                //          [OR]        [C]          S1   S2    C 
                //          /  \
                //        <>    \
                //       /       \
                //    [XOR]      [x]
                //     /  \
                //    S1   S2
                //

                assert( fComp2 == 0 );
                // find the functionality of the lower gates
                bFTemp = (fComp3)? bF: Cudd_Not( bF );
                bFuncNew = Cudd_bddXor( dd, bFTemp, pComp->G );   Cudd_Ref( bFuncNew );

                pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew );
                assert( !Dsd_IsComplement(pDENew) ); // follows from the consideration of cases
                Cudd_RecursiveDeref( dd, bFuncNew ); 

                // get the new gate
                if ( nComp == 1 )
                {
                    pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, 2, s_nDecBlocks++ );
                    pThis->pDecs[0] = pDENew;
                    pThis->pDecs[1] = pComp; 
                }
                else
                {  // pComp is not complemented
                    pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, nComp+1, s_nDecBlocks++ );
                    dsdKernelCopyListPlusOne( pThis, pDENew, pComp->pDecs, nComp );
                }

                if ( !fComp3 )
                    pThis = Dsd_Not( pThis );
                goto EXIT;
            }
        }
    }

    // this case was added to fix the trivial bug found November 4, 2002 in Japan
    // by running the example provided by T. Sasao
    if ( nSuppLH == nSuppL + nSuppH ) // the supports of the components are disjoint
    {
        // create a new component of the type ITE( a, pH, pL )
        pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, 3, s_nDecBlocks++ );
        if ( dd->perm[pLR->S->index] < dd->perm[pHR->S->index] ) // pLR is higher in the varible order
        {
            pThis->pDecs[1] = pLR;
            pThis->pDecs[2] = pHR;
        }
        else  // pHR is higher in the varible order
        {
            pThis->pDecs[1] = pHR;
            pThis->pDecs[2] = pLR;
        }
        // add the first component
        pThis->pDecs[0] = pVarCurDE;
        goto EXIT;
    }


    //////////////////////////////////////////////////////////////////////
    // CASE 3.a Neither of the cofactors is a constant (OR, EXOR, PRIME)
    //////////////////////////////////////////////////////////////////////
    // the component types are identical 
    // and if they are OR, they are either both complemented or both not complemented
    // and if they are PRIME, their dec numbers should be the same
    if ( pLR->Type == pHR->Type && 
         pLR->Type != DSD_NODE_BUF &&           
        (pLR->Type != DSD_NODE_OR    || ( pL == pLR && pH == pHR || pL != pLR && pH != pHR ) ) &&
        (pLR->Type != DSD_NODE_PRIME || pLR->nDecs == pHR->nDecs)  )
    {
        // array to store common comps in pL and pH
        Dsd_Node_t ** pCommon, * pLastDiffL = NULL, * pLastDiffH = NULL; 
        int nCommon = dsdKernelFindCommonComponents( pDsdMan, pLR, pHR, &pCommon, &pLastDiffL, &pLastDiffH );
        if ( nCommon )
        {
            if ( pLR->Type == DSD_NODE_OR ) // Figure 2 of Matsunaga's paper
            { // at this point we have the function F and the group of common components C
                // to get the remainder, R, in the relationship F = R + C, supp(R) & supp(C) = 0
                // we compute the following R = Exist( F - C, supp(C) )

                // compute the sum total of the common components and the union of their supports
                DdNode * bCommF, * bCommS, * bFTemp, * bFuncNew;
                Dsd_Node_t * pDENew;

                dsdKernelComputeSumOfComponents( pDsdMan, pCommon, nCommon, &bCommF, &bCommS, 0 );
                Cudd_Ref( bCommF );
                Cudd_Ref( bCommS );
                bFTemp = ( pL != pLR )?    Cudd_Not(bF): bF;

                bFuncNew = Cudd_bddAndAbstract( dd, bFTemp, Cudd_Not(bCommF), bCommS ); Cudd_Ref( bFuncNew );
                Cudd_RecursiveDeref( dd, bCommF );
                Cudd_RecursiveDeref( dd, bCommS );

                // get the new gate

                // copy the components first, then call the decomposition
                // because decomposition will distroy the list used for copying
                pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, nCommon + 1, s_nDecBlocks++ );
                dsdKernelCopyListPlusOne( pThis, NULL, pCommon, nCommon );

                // call the decomposition recursively
                pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew );
//                assert( !Dsd_IsComplement(pDENew) ); // follows from the consideration of cases
                Cudd_RecursiveDeref( dd, bFuncNew );

                // add the first component
                pThis->pDecs[0] = pDENew;
                
                if ( pL != pLR )
                    pThis = Dsd_Not( pThis );
                goto EXIT;
            }
            else
            if ( pLR->Type == DSD_NODE_EXOR ) // Figure 3 of Matsunaga's paper
            {
                // compute the sum total of the common components and the union of their supports
                DdNode * bCommF, * bFuncNew;
                Dsd_Node_t * pDENew;
                int fCompExor;

                dsdKernelComputeSumOfComponents( pDsdMan, pCommon, nCommon, &bCommF, NULL, 1 );
                Cudd_Ref( bCommF );

                bFuncNew = Cudd_bddXor( dd, bF, bCommF ); Cudd_Ref( bFuncNew );
                Cudd_RecursiveDeref( dd, bCommF );

                // get the new gate

                // copy the components first, then call the decomposition
                // because decomposition will distroy the list used for copying
                pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, nCommon + 1, s_nDecBlocks++ );
                dsdKernelCopyListPlusOne( pThis, NULL, pCommon, nCommon );

                // call the decomposition recursively
                pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew );
                Cudd_RecursiveDeref( dd, bFuncNew );

                // remember the fact that it was complemented
                fCompExor = Dsd_IsComplement(pDENew);
                pDENew = Dsd_Regular(pDENew);

                // add the first component
                pThis->pDecs[0] = pDENew;

    
                if ( fCompExor )
                    pThis = Dsd_Not( pThis );
                goto EXIT;
            }
            else 
            if ( pLR->Type == DSD_NODE_PRIME && (nCommon == pLR->nDecs-1 || nCommon == pLR->nDecs) )
            {
                // for example the function F(a,b,c,d) = ITE(b,c,a(+)d) produces
                // two cofactors F(a=0) = PRIME(b,c,d) and F(a=1) = PRIME(b,c,d)
                // with exactly the same list of common components

                Dsd_Node_t * pDENew;
                DdNode * bFuncNew;
                int fCompComp = 0;    // this flag can be {0,1,2}
                // if it is 0 there is no identity
                // if it is 1/2, the cofactored functions are equal in the direct/complemented polarity

                if ( nCommon == pLR->nDecs )
                {    // all the components are the same
                    // find the formal input, in which pLow and pHigh differ (if such input exists)
                    int m;
                    Dsd_Node_t * pTempL, * pTempH;

                    s_Common++;
                    for ( m = 0; m < pLR->nDecs; m++ )
                    {
                        pTempL = pLR->pDecs[m]; // cannot be complemented
                        pTempH = pHR->pDecs[m]; // cannot be complemented

                        if ( Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh,          pTempL->G, Cudd_Not(pTempH->G) ) &&
                             Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, Cudd_Not(pTempL->G),         pTempH->G ) )
                        {
                             pLastDiffL = pTempL;
                             pLastDiffH = pTempH;
                             assert( pLastDiffL == pLastDiffH );
                             fCompComp = 2;
                             break;
                        }

                        s_Loops2++;
                        s_Loops2++;
/* 
                        if ( s_Loops2 % 10000  == 0 )
                        {
                            int i;
                            for ( i = 0; i < pLR->nDecs; i++ )
                                printf( " %d(s=%d)", pLR->pDecs[i]->Type,
                                    Extra_bddSuppSize(dd, pLR->pDecs[i]->S) );
                            printf( "\n" );
                        }
*/

                    }
//                    if ( pLR->nDecs == Extra_bddSuppSize(dd, pLR->S) )
//                        s_Loops2Useless += pLR->nDecs * 2;

                    if ( fCompComp )
                    { // put the equal components into pCommon, so that they could be copied into the new dec entry
                        nCommon = 0;
                        for ( m = 0; m < pLR->nDecs; m++ )
                            if ( pLR->pDecs[m] != pLastDiffL )
                                 pCommon[nCommon++] = pLR->pDecs[m];
                        assert( nCommon = pLR->nDecs-1 );
                    }
                }
                else
                {  // the differing components are known - check that they have compatible PRIME function

                    s_CommonNo++;

                    // find the numbers of different components
                    assert( pLastDiffL );
                    assert( pLastDiffH );
                    // also, they cannot be complemented, because the decomposition type is PRIME

                    if ( Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, Cudd_Not(pLastDiffL->G), Cudd_Not(pLastDiffH->G) ) &&
                         Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh,          pLastDiffL->G,           pLastDiffH->G ) )
                        fCompComp = 1;
                    else if ( Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh,          pLastDiffL->G, Cudd_Not(pLastDiffH->G) ) &&
                              Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, Cudd_Not(pLastDiffL->G),         pLastDiffH->G ) )
                        fCompComp = 2;

                    s_Loops3 += 4;
                }

                if ( fCompComp )
                {
                    if ( fCompComp == 1 ) // it is true that bLow(G=0) == bHigh(H=0) && bLow(G=1) == bHigh(H=1)
                        bFuncNew = Cudd_bddIte( dd, bVarCur, pLastDiffH->G, pLastDiffL->G ); 
                    else // it is true that bLow(G=0) == bHigh(H=1) && bLow(G=1) == bHigh(H=0)
                        bFuncNew = Cudd_bddIte( dd, bVarCur, Cudd_Not(pLastDiffH->G), pLastDiffL->G ); 
                    Cudd_Ref( bFuncNew );

                    // get the new gate

                    // copy the components first, then call the decomposition
                    // because decomposition will distroy the list used for copying
                    pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, pLR->nDecs, s_nDecBlocks++ );
                    dsdKernelCopyListPlusOne( pThis, NULL, pCommon, nCommon );

                    // create a new component
                    pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew );
                    Cudd_RecursiveDeref( dd, bFuncNew );
                    // the BDD of the argument function in PRIME decomposition, should be regular
                    pDENew = Dsd_Regular(pDENew);

                    // add the first component
                    pThis->pDecs[0] = pDENew;
                    goto EXIT;
                }
            } // end of PRIME type
        } // end of existing common components
    } // end of CASE 3.a

// if ( Depth != 1) 
// {

//CASE4:
    //////////////////////////////////////////////////////////////////////
    // CASE 4
    //////////////////////////////////////////////////////////////////////
    {
    // estimate the number of entries in the list
    int nEntriesMax = pDsdMan->nInputs - dd->perm[VarInt];

    // create the new decomposition entry
    int nEntries = 0;

    DdNode * SuppL, * SuppH, * SuppL_init, * SuppH_init;
    Dsd_Node_t *pHigher, *pLower, * pTemp, * pDENew;


    int levTopSuppL;
    int levTopSuppH;
    int levTop;

    pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, nEntriesMax, s_nDecBlocks++ );
    pThis->pDecs[ nEntries++ ] = pVarCurDE;
    // other entries will be added to this list one-by-one during analysis

    // count how many times does it happen that the decomposition entries are
    s_Case4Calls++;
 
    // consider the simplest case: when the supports are equal 
    // and at least one of the components
    // is the PRIME without decompositions, or 
    // when both of them are without decomposition
    if ( (((pLR->Type == DSD_NODE_PRIME && nSuppL == pLR->nDecs) || (pHR->Type == DSD_NODE_PRIME && nSuppH == pHR->nDecs)) && pLR->S == pHR->S)  ||
          ((pLR->Type == DSD_NODE_PRIME && nSuppL == pLR->nDecs) && (pHR->Type == DSD_NODE_PRIME && nSuppH == pHR->nDecs)) )
    {

         s_Case4CallsSpecial++;
         // walk through both supports and create the decomposition list composed of simple entries
         SuppL = pLR->S;
         SuppH = pHR->S;
         do
         {
             // determine levels
             levTopSuppL = cuddI(dd,SuppL->index);
             levTopSuppH = cuddI(dd,SuppH->index);

             // skip the topmost variable in both supports
             if ( levTopSuppL <= levTopSuppH )
             {
                 levTop = levTopSuppL;
                 SuppL  = cuddT(SuppL);
             }
             else
                 levTop = levTopSuppH;

             if ( levTopSuppH <= levTopSuppL )
                 SuppH = cuddT(SuppH);

             // set the new decomposition entry
             pThis->pDecs[ nEntries++ ] = pDsdMan->pInputs[ dd->invperm[levTop] ];
         }
         while ( SuppL != b1 || SuppH != b1 );
    }
    else
    {

        // compare two different decomposition lists
        SuppL_init = pLR->S;
        SuppH_init = pHR->S;
        // start references (because these supports will change)
        SuppL = pLR->S;  Cudd_Ref( SuppL );
        SuppH = pHR->S;  Cudd_Ref( SuppH );
        while ( SuppL != b1 || SuppH != b1 )
        {
            // determine the top level in cofactors and
            // whether they have the same top level
            int TopLevL  = cuddI(dd,SuppL->index);
            int TopLevH  = cuddI(dd,SuppH->index);
            int TopLevel = TopLevH;
            int fEqualLevel = 0;

            DdNode * bVarTop;
            DdNode * bSuppSubract;


            if ( TopLevL < TopLevH )
            {
                pHigher = pLR;
                pLower  = pHR;
                TopLevel = TopLevL;
            }
            else if ( TopLevL > TopLevH )
            {
                pHigher = pHR;
                pLower  = pLR;
            }
            else
                fEqualLevel = 1;
            assert( TopLevel != CUDD_CONST_INDEX );


            // find the currently top variable in the decomposition lists
            bVarTop = dd->vars[dd->invperm[TopLevel]];

            if ( !fEqualLevel )
            {
                // find the lower support
                DdNode * bSuppLower = (TopLevL < TopLevH)? SuppH_init: SuppL_init; 

                // find the first component in pHigher 
                // whose support does not overlap with supp(Lower) 
                // and remember the previous component
                int fPolarity;            
                Dsd_Node_t * pPrev = NULL;       // the pointer to the component proceeding pCur
                Dsd_Node_t * pCur  = pHigher;    // the first component not contained in supp(Lower)
                while ( Extra_bddSuppOverlapping( dd, pCur->S, bSuppLower ) )
                {    // get the next component
                    pPrev = pCur;
                    pCur  = dsdKernelFindContainingComponent( pDsdMan, pCur, bVarTop, &fPolarity );
                };

                // look for the possibility to subtract more than one component
                if ( pPrev == NULL || pPrev->Type == DSD_NODE_PRIME )
                { // if there is no previous component, or if the previous component is PRIME
                  // there is no way to subtract more than one component

                    // add the new decomposition entry (it is already regular)
                    pThis->pDecs[ nEntries++ ] = pCur;
                    // assign the support to be subtracted from both components
                    bSuppSubract = pCur->S;
                }
                else // all other types
                {
                    // go through the decomposition list of pPrev and find components 
                    // whose support does not overlap with supp(Lower) 

                    static Dsd_Node_t * pNonOverlap[MAXINPUTS];
                    int i, nNonOverlap = 0;
                    for ( i = 0; i < pPrev->nDecs; i++ )
                    {
                        pTemp = Dsd_Regular( pPrev->pDecs[i] );
                        if ( !Extra_bddSuppOverlapping( dd, pTemp->S, bSuppLower ) )
                            pNonOverlap[ nNonOverlap++ ] = pPrev->pDecs[i];
                    }
                    assert( nNonOverlap > 0 );

                    if ( nNonOverlap == 1 )
                    { // one one component was found, which is the original one
                        assert( Dsd_Regular(pNonOverlap[0]) == pCur);
                        // add the new decomposition entry
                        pThis->pDecs[ nEntries++ ] = pCur;
                        // assign the support to be subtracted from both components
                        bSuppSubract = pCur->S;
                    }
                    else // more than one components was found
                    {
                        // find the OR (EXOR) of the non-overlapping components
                        DdNode * bCommF;
                        dsdKernelComputeSumOfComponents( pDsdMan, pNonOverlap, nNonOverlap, &bCommF, NULL, (int)(pPrev->Type==DSD_NODE_EXOR) );
                        Cudd_Ref( bCommF );

                        // create a new gated 
                        pDENew = dsdKernelDecompose_rec( pDsdMan, bCommF );
                        Cudd_RecursiveDeref(dd, bCommF);
                        // make it regular... it must be regular already
                        assert( !Dsd_IsComplement(pDENew) );

                        // add the new decomposition entry
                        pThis->pDecs[ nEntries++ ] = pDENew;
                        // assign the support to be subtracted from both components
                        bSuppSubract = pDENew->S;
                    }
                }
                
                // subtract its support from the support of upper component
                if ( TopLevL < TopLevH )
                {
                    SuppL = Cudd_bddExistAbstract( dd, bTemp = SuppL, bSuppSubract ); Cudd_Ref( SuppL );
                    Cudd_RecursiveDeref(dd, bTemp);
                }
                else
                {
                    SuppH = Cudd_bddExistAbstract( dd, bTemp = SuppH, bSuppSubract ); Cudd_Ref( SuppH );
                    Cudd_RecursiveDeref(dd, bTemp);
                }
            } // end of if ( !fEqualLevel )
            else // if ( fEqualLevel ) -- they have the same top level var
            {
                static Dsd_Node_t * pMarkedLeft[MAXINPUTS]; // the pointers to the marked blocks
                static char pMarkedPols[MAXINPUTS]; // polarities of the marked blocks
                int nMarkedLeft = 0;

                int fPolarity = 0;
                Dsd_Node_t * pTempL = pLR;

                int fPolarityCurH = 0;
                Dsd_Node_t * pPrevH = NULL, * pCurH = pHR;

                int fPolarityCurL = 0;
                Dsd_Node_t * pPrevL = NULL, * pCurL = pLR; // = pMarkedLeft[0];
                int index = 1;

                // set the new mark
                s_Mark++;

                // go over the dec list of pL, mark all components that contain the given variable
                assert( Extra_bddSuppContainVar( dd, pLR->S, bVarTop ) );
                assert( Extra_bddSuppContainVar( dd, pHR->S, bVarTop ) );
                do {
                    pTempL->Mark = s_Mark;
                    pMarkedLeft[ nMarkedLeft ] = pTempL;
                    pMarkedPols[ nMarkedLeft ] = fPolarity;
                    nMarkedLeft++;
                } while ( pTempL = dsdKernelFindContainingComponent( pDsdMan, pTempL, bVarTop, &fPolarity ) );

                // go over the dec list of pH, and find the component that is marked and the previos one
                // (such component always exists, because they have common variables)
                while ( pCurH->Mark != s_Mark )
                {
                    pPrevH = pCurH;
                    pCurH  = dsdKernelFindContainingComponent( pDsdMan, pCurH, bVarTop, &fPolarityCurH );
                    assert( pCurH );
                }

                // go through the first list once again and find 
                // the component proceeding the one marked found in the second list
                while ( pCurL != pCurH )
                {
                    pPrevL = pCurL;
                    pCurL  = pMarkedLeft[index];
                    fPolarityCurL = pMarkedPols[index];
                    index++;
                }

                // look for the possibility to subtract more than one component
                if ( !pPrevL || !pPrevH || pPrevL->Type != pPrevH->Type || pPrevL->Type == DSD_NODE_PRIME || fPolarityCurL != fPolarityCurH )
                { // there is no way to extract more than one
                    pThis->pDecs[ nEntries++ ] = pCurH;
                    // assign the support to be subtracted from both components
                    bSuppSubract = pCurH->S;
                }
                else 
                {
                    // find the equal components in two decomposition lists
                    Dsd_Node_t ** pCommon, * pLastDiffL = NULL, * pLastDiffH = NULL; 
                    int nCommon = dsdKernelFindCommonComponents( pDsdMan, pPrevL, pPrevH, &pCommon, &pLastDiffL, &pLastDiffH );
        
                    if ( nCommon == 0 || nCommon == 1 )
                    { // one one component was found, which is the original one
    //                    assert( Dsd_Regular(pCommon[0]) == pCurL);
                        // add the new decomposition entry
                        pThis->pDecs[ nEntries++ ] = pCurL;
                        // assign the support to be subtracted from both components
                        bSuppSubract = pCurL->S;
                    }
                    else // more than one components was found
                    {
                        // find the OR (EXOR) of the non-overlapping components
                        DdNode * bCommF;
                        dsdKernelComputeSumOfComponents( pDsdMan, pCommon, nCommon, &bCommF, NULL, (int)(pPrevL->Type==DSD_NODE_EXOR) );
                        Cudd_Ref( bCommF );

                        pDENew = dsdKernelDecompose_rec( pDsdMan, bCommF );
                        assert( !Dsd_IsComplement(pDENew) ); // cannot be complemented because of construction
                        Cudd_RecursiveDeref( dd, bCommF );

                        // add the new decomposition entry
                        pThis->pDecs[ nEntries++ ] = pDENew;

                        // assign the support to be subtracted from both components
                        bSuppSubract = pDENew->S;
                    }
                }

                SuppL = Cudd_bddExistAbstract( dd, bTemp = SuppL, bSuppSubract ), Cudd_Ref( SuppL );
                Cudd_RecursiveDeref(dd, bTemp);

                SuppH = Cudd_bddExistAbstract( dd, bTemp = SuppH, bSuppSubract ), Cudd_Ref( SuppH );
                Cudd_RecursiveDeref(dd, bTemp);

            } // end of if ( fEqualLevel ) 

        } // end of decomposition list comparison
        Cudd_RecursiveDeref( dd, SuppL );
        Cudd_RecursiveDeref( dd, SuppH );

    }

    // check that the estimation of the number of entries was okay
    assert( nEntries <= nEntriesMax );

//    if ( nEntries != Extra_bddSuppSize(dd, bSuppNew) )
//        s_Case5++;

    // update the number of entries in the new decomposition list
    pThis->nDecs = nEntries;
    }
//}
EXIT:

    {
    // if the component created is complemented, it represents a function without complement
    // therefore, as it is, without complement, it should recieve the complemented function
    Dsd_Node_t * pThisR = Dsd_Regular( pThis );
    assert( pThisR->G == NULL );
    assert( pThisR->S == NULL );

    if ( pThisR == pThis ) // set regular function
        pThisR->G = bF; 
    else // set complemented function
        pThisR->G = Cudd_Not(bF);    
    Cudd_Ref(bF);           // reference the function in the component

    assert( bSuppNew );
    pThisR->S = bSuppNew;   // takes the reference from the new support
    if ( st_insert( pDsdMan->Table, (char*)bF, (char*)pThis ) )
    {
        assert( 0 );
    }
    s_CacheEntries++;


/*
    if ( dsdKernelVerifyDecomposition(dd, pThis) == 0 )
    {
        // write the function, for which verification does not work
        cout << endl << "Internal verification failed!"" );

        // create the variable mask
        static int s_pVarMask[MAXINPUTS];
        int nInputCounter = 0;

        Cudd_SupportArray( dd, bF, s_pVarMask );
        int k; 
        for ( k = 0; k < dd->size; k++ )
            if ( s_pVarMask[k] )
                nInputCounter++;

        cout << endl << "The problem function is "" );

        DdNode * zNewFunc = Cudd_zddIsopCover( dd, bF, bF ); Cudd_Ref( zNewFunc );
        cuddWriteFunctionSop( stdout, dd, zNewFunc, -1, dd->size, "1", s_pVarMask );
        Cudd_RecursiveDerefZdd( dd, zNewFunc );
    }
*/

    }

    Depth--;
    return Dsd_NotCond( pThis, fCompF );
}


////////////////////////////////////////////////////////////////////////
///                        OTHER FUNCTIONS                           ///
////////////////////////////////////////////////////////////////////////

/**Function*************************************************************

  Synopsis    [Finds the corresponding decomposition entry.]

  Description [This function returns the non-complemented pointer to the 
  DecEntry of that component which contains the given variable in its 
  support, or NULL if no such component exists]
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
Dsd_Node_t * dsdKernelFindContainingComponent( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pWhere, DdNode * Var, int * fPolarity )

{
    Dsd_Node_t * pTemp;
    int i;

//    assert( !Dsd_IsComplement( pWhere ) );
//    assert( Extra_bddSuppContainVar( pDsdMan->dd, pWhere->S, Var ) );

    if ( pWhere->nDecs == 1 )
        return NULL;

    for( i = 0; i < pWhere->nDecs; i++ )
    {
        pTemp = Dsd_Regular( pWhere->pDecs[i] );
        if ( Extra_bddSuppContainVar( pDsdMan->dd, pTemp->S, Var ) )
        {
            *fPolarity = (int)( pTemp != pWhere->pDecs[i] );
            return pTemp;
        }
    }
    assert( 0 );
    return NULL;
}

/**Function*************************************************************

  Synopsis    [Find the common decomposition components.]

  Description [This function determines the common components. It counts 
  the number of common components in the decomposition lists of pL and pH
  and returns their number and the lists of common components. It assumes 
  that pL and pH are regular pointers. It retuns also the pointers to the 
  last different components encountered in pL and pH.]
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int dsdKernelFindCommonComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t *** pCommon, Dsd_Node_t ** pLastDiffL, Dsd_Node_t ** pLastDiffH )
{
    static Dsd_Node_t * Common[MAXINPUTS];
    int nCommon = 0;

    // pointers to the current decomposition entries
    Dsd_Node_t * pLcur;
    Dsd_Node_t * pHcur;

    // the pointers to their supports
    DdNode * bSLcur;
    DdNode * bSHcur;

    // the top variable in the supports
    int TopVar;

    // the indices running through the components
    int iCurL = 0;
    int iCurH = 0;
    while ( iCurL < pL->nDecs && iCurH < pH->nDecs )
    { // both did not run out

        pLcur = Dsd_Regular(pL->pDecs[iCurL]);
        pHcur = Dsd_Regular(pH->pDecs[iCurH]);

        bSLcur = pLcur->S;
        bSHcur = pHcur->S;

        // find out what component is higher in the BDD
        if ( pDsdMan->dd->perm[bSLcur->index] < pDsdMan->dd->perm[bSHcur->index] )
            TopVar = bSLcur->index;
        else
            TopVar = bSHcur->index;

        if ( TopVar == bSLcur->index && TopVar == bSHcur->index ) 
        {
            // the components may be equal - should match exactly!
            if ( pL->pDecs[iCurL] == pH->pDecs[iCurH] )
                Common[nCommon++] = pL->pDecs[iCurL];
            else
            {
                *pLastDiffL = pL->pDecs[iCurL];
                *pLastDiffH = pH->pDecs[iCurH];
            }

            // skip both
            iCurL++;
            iCurH++;
        }
        else if ( TopVar == bSLcur->index )
        {  // the components cannot be equal
            // skip the top-most one
            *pLastDiffL = pL->pDecs[iCurL++];
        }
        else // if ( TopVar == bSHcur->index )
        {  // the components cannot be equal
            // skip the top-most one
            *pLastDiffH = pH->pDecs[iCurH++];
        }
    }

    // if one of the lists still has components, write the first one down
    if ( iCurL < pL->nDecs )
        *pLastDiffL = pL->pDecs[iCurL];

    if ( iCurH < pH->nDecs )
        *pLastDiffH = pH->pDecs[iCurH];

    // return the pointer to the array
    *pCommon = Common;
    // return the number of common components
    return nCommon;            
}

/**Function*************************************************************

  Synopsis    [Computes the sum (OR or EXOR) of the functions of the components.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void dsdKernelComputeSumOfComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t ** pCommon, int nCommon, DdNode ** pCompF, DdNode ** pCompS, int fExor )
{
    DdManager * dd = pDsdMan->dd;
    DdNode * bF, * bS, * bFadd, * bTemp;
    Dsd_Node_t * pDE, * pDER;
    int i;

    // start the function
    bF = b0; Cudd_Ref( bF );
    // start the support
    if ( pCompS )
        bS = b1, Cudd_Ref( bS );

    assert( nCommon > 0 );
    for ( i = 0; i < nCommon; i++ )
    {
        pDE  = pCommon[i];
        pDER = Dsd_Regular( pDE );
        bFadd = (pDE != pDER)? Cudd_Not(pDER->G): pDER->G;
        // add to the function
        if ( fExor )
            bF = Cudd_bddXor( dd, bTemp = bF, bFadd );
        else
            bF = Cudd_bddOr( dd, bTemp = bF, bFadd );
        Cudd_Ref( bF );
        Cudd_RecursiveDeref( dd, bTemp );
        if ( pCompS )
        {
            // add to the support
            bS = Cudd_bddAnd( dd, bTemp = bS, pDER->S );  Cudd_Ref( bS );
            Cudd_RecursiveDeref( dd, bTemp );
        }
    }
    // return the function
    Cudd_Deref( bF );
    *pCompF = bF;

    // return the support
    if ( pCompS )
        Cudd_Deref( bS ), *pCompS = bS;
}

/**Function*************************************************************

  Synopsis    [Checks support containment of the decomposition components.]

  Description [This function returns 1 if support of one component is contained 
  in that of another. In this case, pLarge (pSmall) is assigned to point to the 
  larger (smaller) support. If the supports are identical return 0, and does not 
  assign the components.]
]
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int dsdKernelCheckContainment( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t ** pLarge, Dsd_Node_t ** pSmall )
{
    DdManager * dd = pDsdMan->dd;
    DdNode * bSuppLarge, * bSuppSmall;
    int RetValue;
    
    RetValue = Extra_bddSuppCheckContainment( dd, pL->S, pH->S, &bSuppLarge, &bSuppSmall );

    if ( RetValue == 0 ) 
        return 0;

    if ( pH->S == bSuppLarge )
    {
        *pLarge = pH;
        *pSmall = pL;
    }
    else // if ( pL->S == bSuppLarge )
    {
        *pLarge = pL;
        *pSmall = pH;
    }
    return 1;
}

/**Function*************************************************************

  Synopsis    [Copies the list of components plus one.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void dsdKernelCopyListPlusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize )
{
    int i;
    assert( nListSize+1 == p->nDecs );
    p->pDecs[0] = First;
    for( i = 0; i < nListSize; i++ )
        p->pDecs[i+1] = ppList[i];
}

/**Function*************************************************************

  Synopsis    [Copies the list of components plus one, and skips one.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
void dsdKernelCopyListPlusOneMinusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize, int iSkipped )
{
    int i, Counter;
    assert( nListSize == p->nDecs );
    p->pDecs[0] = First;
    for( i = 0, Counter = 1; i < nListSize; i++ )
        if ( i != iSkipped )
            p->pDecs[Counter++] = ppList[i];
}

/**Function*************************************************************

  Synopsis    [Debugging procedure to compute the functionality of the decomposed structure.]

  Description []
               
  SideEffects []

  SeeAlso     []

***********************************************************************/
int dsdKernelVerifyDecomposition( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pDE )
{
    DdManager * dd = pDsdMan->dd;
    Dsd_Node_t * pR    = Dsd_Regular(pDE);
    int fCompP = (int)( pDE != pR );
    int RetValue;

    DdNode * bRes;
    if ( pR->Type == DSD_NODE_CONST1 )
        bRes = b1;
    else if ( pR->Type == DSD_NODE_BUF )
        bRes = pR->G;
    else if ( pR->Type == DSD_NODE_OR || pR->Type == DSD_NODE_EXOR )
        dsdKernelComputeSumOfComponents( pDsdMan, pR->pDecs, pR->nDecs, &bRes, NULL, (int)(pR->Type == DSD_NODE_EXOR) );
    else if ( pR->Type == DSD_NODE_PRIME )
    {
        int i;
        static DdNode * bGVars[MAXINPUTS];
        // transform the function of this block, so that it depended on inputs
        // corresponding to the formal inputs
        DdNode * bNewFunc = Dsd_TreeGetPrimeFunctionOld( dd, pR, 1 );  Cudd_Ref( bNewFunc );

        // compose this function with the inputs
        // create the elementary permutation
        for ( i = 0; i < dd->size; i++ )
            bGVars[i] = dd->vars[i];

        // assign functions to be composed
        for ( i = 0; i < pR->nDecs; i++ )
            bGVars[dd->invperm[i]] = pR->pDecs[i]->G;

        // perform the composition
        bRes = Cudd_bddVectorCompose( dd, bNewFunc, bGVars );       Cudd_Ref( bRes );
        Cudd_RecursiveDeref( dd, bNewFunc );

        /////////////////////////////////////////////////////////
        RetValue = (int)( bRes == pR->G );//|| bRes == Cudd_Not(pR->G) );
        /////////////////////////////////////////////////////////
        Cudd_Deref( bRes );
    }
    else
    {
        assert(0);
    }

    Cudd_Ref( bRes );
    RetValue = (int)( bRes == pR->G );//|| bRes == Cudd_Not(pR->G) );
    Cudd_RecursiveDeref( dd, bRes );
    return RetValue;
}

////////////////////////////////////////////////////////////////////////
///                           END OF FILE                            ///
////////////////////////////////////////////////////////////////////////