src/bdd/dsd/dsdProc.c File Reference

#include "dsdInt.h"

Include dependency graph for dsdProc.c:

Go to the source code of this file.

Functions
void	dsdKernelDecompose (Dsd_Manager_t *pDsdMan, DdNode **pbFuncs, int nFuncs)
static Dsd_Node_t *	dsdKernelDecompose_rec (Dsd_Manager_t *pDsdMan, DdNode *F)
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)
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)
static int	dsdKernelVerifyDecomposition (Dsd_Manager_t *pDsdMan, Dsd_Node_t *pDE)
void	Dsd_Decompose (Dsd_Manager_t *pDsdMan, DdNode **pbFuncs, int nFuncs)
Dsd_Node_t *	Dsd_DecomposeOne (Dsd_Manager_t *pDsdMan, DdNode *bFunc)
Variables
static int	s_Mark
static int	s_Show = 0
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
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

---

Function Documentation

void Dsd_Decompose	(	Dsd_Manager_t *	pDsdMan,
		DdNode **	pbFuncs,
		int	nFuncs
	)

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 []

Definition at line 120 of file dsdProc.c.

{
        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 );
*/
}

Dsd_Node_t* Dsd_DecomposeOne	(	Dsd_Manager_t *	pDsdMan,
		DdNode *	bFunc
	)

Function*************************************************************

Synopsis [Performs decomposition for one function.]

Description []

SideEffects []

SeeAlso []

Definition at line 237 of file dsdProc.c.

{
    return dsdKernelDecompose_rec( pDsdMan, bFunc );
}

int dsdKernelCheckContainment	(	Dsd_Manager_t *	pDsdMan,
		Dsd_Node_t *	pL,
		Dsd_Node_t *	pH,
		Dsd_Node_t **	pLarge,
		Dsd_Node_t **	pSmall
	)			[static]

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 []

Definition at line 1488 of file dsdProc.c.

{
        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;
}

void dsdKernelComputeSumOfComponents	(	Dsd_Manager_t *	pDsdMan,
		Dsd_Node_t **	pCommon,
		int	nCommon,
		DdNode **	pCompF,
		DdNode **	pCompS,
		int	fExor
	)			[static]

Function*************************************************************

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

Description []

SideEffects []

SeeAlso []

Definition at line 1431 of file dsdProc.c.

{
        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;
}

void dsdKernelCopyListPlusOne	(	Dsd_Node_t *	p,
		Dsd_Node_t *	First,
		Dsd_Node_t **	ppList,
		int	nListSize
	)			[static]

Function*************************************************************

Synopsis [Copies the list of components plus one.]

Description []

SideEffects []

SeeAlso []

Definition at line 1523 of file dsdProc.c.

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

void dsdKernelCopyListPlusOneMinusOne	(	Dsd_Node_t *	p,
		Dsd_Node_t *	First,
		Dsd_Node_t **	ppList,
		int	nListSize,
		int	iSkipped
	)			[static]

Function*************************************************************

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

Description []

SideEffects []

SeeAlso []

Definition at line 1543 of file dsdProc.c.

{
        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];
}

void dsdKernelDecompose	(	Dsd_Manager_t *	pDsdMan,
		DdNode **	pbFuncs,
		int	nFuncs
	)

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

] FUNCTION DECLARATIONS ///

Dsd_Node_t * dsdKernelDecompose_rec	(	Dsd_Manager_t *	pDsdMan,
		DdNode *	bFunc0
	)			[static]

Function*************************************************************

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

Description []

SideEffects []

SeeAlso []

Definition at line 253 of file dsdProc.c.

{
        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 );
}

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]

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 []

Definition at line 1346 of file dsdProc.c.

{
        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;                 
}

Dsd_Node_t * dsdKernelFindContainingComponent	(	Dsd_Manager_t *	pDsdMan,
		Dsd_Node_t *	pWhere,
		DdNode *	Var,
		int *	fPolarity
	)			[static]

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 []

Definition at line 1306 of file dsdProc.c.

{
        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;
}

int dsdKernelVerifyDecomposition	(	Dsd_Manager_t *	pDsdMan,
		Dsd_Node_t *	pDE
	)			[static]

Function*************************************************************

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

Description []

SideEffects []

SeeAlso []

Definition at line 1564 of file dsdProc.c.

{
        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;
}

---

Variable Documentation

int Depth = 0 [static]

Definition at line 53 of file dsdProc.c.

int HashFailure = 0 [static]

Definition at line 86 of file dsdProc.c.

int HashSuccess = 0 [static]

Definition at line 85 of file dsdProc.c.

int s_CacheEntries [static]

Definition at line 88 of file dsdProc.c.

int s_Case4Calls [static]

Definition at line 63 of file dsdProc.c.

int s_Case4CallsSpecial [static]

Definition at line 64 of file dsdProc.c.

int s_Case5 [static]

Definition at line 66 of file dsdProc.c.

int s_Common [static]

Definition at line 60 of file dsdProc.c.

int s_CommonNo [static]

Definition at line 61 of file dsdProc.c.

int s_DecNodesTotal [static]

Definition at line 70 of file dsdProc.c.

int s_DecNodesUsed [static]

Definition at line 71 of file dsdProc.c.

int s_Loops1 [static]

Definition at line 55 of file dsdProc.c.

int s_Loops2 [static]

Definition at line 56 of file dsdProc.c.

int s_Loops2Useless [static]

Definition at line 67 of file dsdProc.c.

int s_Loops3 [static]

Definition at line 57 of file dsdProc.c.

int s_Mark [static]

STATIC VARIABLES ///

Definition at line 48 of file dsdProc.c.

float s_MaxDelay [static]

Definition at line 80 of file dsdProc.c.

float s_nArea [static]

Definition at line 79 of file dsdProc.c.

int s_nCascades [static]

Definition at line 78 of file dsdProc.c.

int s_nDecBlocks [static]

Definition at line 74 of file dsdProc.c.

int s_nExorGates [static]

Definition at line 76 of file dsdProc.c.

int s_nInvertors [static]

Definition at line 82 of file dsdProc.c.

int s_nLiterals [static]

Definition at line 75 of file dsdProc.c.

int s_nPrimeBlocks [static]

Definition at line 83 of file dsdProc.c.

int s_nReusedBlocks [static]

Definition at line 77 of file dsdProc.c.

int s_Pivot [static]

Definition at line 58 of file dsdProc.c.

int s_PivotNo [static]

Definition at line 59 of file dsdProc.c.

int s_Show = 0 [static]

Definition at line 51 of file dsdProc.c.

long s_Time [static]

Definition at line 81 of file dsdProc.c.