#include "dsdInt.h"

Functions
ABC_NAMESPACE_IMPL_START void	dsdKernelDecompose (Dsd_Manager_t pDsdMan, DdNode *pbFuncs, int nFuncs)
	FUNCTION DECLARATIONS ///. More...

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)
	OTHER FUNCTIONS ///. More...

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)
	DECOMPOSITION FUNCTIONS ///. More...

Dsd_Node_t *	Dsd_DecomposeOne (Dsd_Manager_t pDsdMan, DdNode bFunc)

Variables
static int	s_Mark
	STATIC VARIABLES ///. More...

static int	Depth = 0

static int	s_Loops1

static int	s_Loops2

static int	s_Loops3

static int	s_Common

static int	s_CommonNo

static int	s_Case4Calls

static int	s_Case4CallsSpecial

static int	s_nDecBlocks

static int	s_nLiterals

static int	s_nExorGates

static int	s_nReusedBlocks

static int	s_nCascades

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 113 of file dsdProc.c.

 {
     DdManager * dd = pDsdMan->dd;
     int i;
     abctime 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 )
             ABC_FREE( pDsdMan->pRoots );
         pDsdMan->nRootsAlloc = nFuncs;
         pDsdMan->pRoots = (Dsd_Node_t **) ABC_ALLOC( char, 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 = Abc_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;
         abctime clk;
 
         clk = Abc_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)(Abc_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)(Abc_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 230 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 1483 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 1425 of file dsdProc.c.

 {
     DdManager * dd = pDsdMan->dd;
     DdNode * bF, * bFadd, * bTemp;
         DdNode * bS = NULL; // Suppress "might be used uninitialized"
     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 1518 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 1538 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];
 }

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

FUNCTION DECLARATIONS ///.

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

]

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 246 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 = -1; // the number of the component is Large is equal to the whole of Small; suppress "might be used uninitialized"
         int fLowIsLarge;
 
         DdNode * bFTemp;     // the changed input function
         Dsd_Node_t * pDETemp, * pDENew;
 
         Dsd_Node_t * pComp = NULL;
         int  nComp = -1; // Suppress "might be used uninitialized"
 
         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 = -1; // {0,1} depending on whether setting cofactor to 0 or 1 worked out; suppress "might be used uninitialized"
 
             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 = NULL; // Suppress "might be used uninitialized"
         Dsd_Node_t *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 1340 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 1300 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 1559 of file dsdProc.c.

 {
     DdManager * dd = pDsdMan->dd;
     Dsd_Node_t * pR    = Dsd_Regular(pDE);
     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 56 of file dsdProc.c.

int HashFailure = 0

static

Definition at line 79 of file dsdProc.c.

int HashSuccess = 0

static

Definition at line 78 of file dsdProc.c.

int s_CacheEntries

static

Definition at line 81 of file dsdProc.c.

int s_Case4Calls

static

Definition at line 64 of file dsdProc.c.

int s_Case4CallsSpecial

static

Definition at line 65 of file dsdProc.c.

int s_Common

static

Definition at line 61 of file dsdProc.c.

int s_CommonNo

static

Definition at line 62 of file dsdProc.c.

int s_Loops1

static

Definition at line 58 of file dsdProc.c.

int s_Loops2

static

Definition at line 59 of file dsdProc.c.

int s_Loops3

static

Definition at line 60 of file dsdProc.c.

int s_Mark

static

STATIC VARIABLES ///.

Definition at line 51 of file dsdProc.c.

int s_nCascades

static

Definition at line 75 of file dsdProc.c.

int s_nDecBlocks

static

Definition at line 71 of file dsdProc.c.

int s_nExorGates

static

Definition at line 73 of file dsdProc.c.

int s_nLiterals

static

Definition at line 72 of file dsdProc.c.

int s_nPrimeBlocks

static

Definition at line 76 of file dsdProc.c.

int s_nReusedBlocks

static

Definition at line 74 of file dsdProc.c.

Functions

Variables

Function Documentation

Variable Documentation