Changes to be able to compile ABC without CUDD.

1 files changed, 2342 insertions, 0 deletions

diff --git a/src/bdd/extrab/extraBddMisc.c b/src/bdd/extrab/extraBddMisc.c
new file mode 100644
index 00000000..a2ba4036
--- /dev/null
+++ b/src/bdd/extrab/extraBddMisc.c
@@ -0,0 +1,2342 @@
+/**CFile****************************************************************
+
+  FileName    [extraBddMisc.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [extra]
+
+  Synopsis    [DD-based utilities.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - June 20, 2005.]
+
+  Revision    [$Id: extraBddMisc.c,v 1.4 2005/10/04 00:19:54 alanmi Exp $]
+
+***********************************************************************/
+
+#include "extraBdd.h"
+
+ABC_NAMESPACE_IMPL_START
+
+
+/*---------------------------------------------------------------------------*/
+/* Constant declarations                                                     */
+/*---------------------------------------------------------------------------*/
+
+/*---------------------------------------------------------------------------*/
+/* Stucture declarations                                                     */
+/*---------------------------------------------------------------------------*/
+
+/*---------------------------------------------------------------------------*/
+/* Type declarations                                                         */
+/*---------------------------------------------------------------------------*/
+
+/*---------------------------------------------------------------------------*/
+/* Variable declarations                                                     */
+/*---------------------------------------------------------------------------*/
+
+/*---------------------------------------------------------------------------*/
+/* Macro declarations                                                        */
+/*---------------------------------------------------------------------------*/
+
+
+/**AutomaticStart*************************************************************/
+
+/*---------------------------------------------------------------------------*/
+/* Static function prototypes                                                */
+/*---------------------------------------------------------------------------*/
+
+// file "extraDdTransfer.c"
+static DdNode * extraTransferPermuteRecur( DdManager * ddS, DdManager * ddD, DdNode * f, st__table * table, int * Permute );
+static DdNode * extraTransferPermute( DdManager * ddS, DdManager * ddD, DdNode * f, int * Permute );
+static DdNode * cuddBddPermuteRecur ARGS( ( DdManager * manager, DdHashTable * table, DdNode * node, int *permut ) );
+
+static DdNode * extraBddAndPermute( DdHashTable * table, DdManager * ddF, DdNode * bF, DdManager * ddG, DdNode * bG, int * pPermute );
+
+// file "cuddUtils.c"
+static void ddSupportStep(DdNode *f, int *support);
+static void ddClearFlag(DdNode *f);
+
+static DdNode* extraZddPrimes( DdManager *dd, DdNode* F );
+
+/**AutomaticEnd***************************************************************/
+
+/*---------------------------------------------------------------------------*/
+/* Definition of exported functions                                          */
+/*---------------------------------------------------------------------------*/
+
+/**Function********************************************************************
+
+  Synopsis    [Convert a {A,B}DD from a manager to another with variable remapping.]
+
+  Description [Convert a {A,B}DD from a manager to another one. The orders of the
+  variables in the two managers may be different. Returns a
+  pointer to the {A,B}DD in the destination manager if successful; NULL
+  otherwise. The i-th entry in the array Permute tells what is the index
+  of the i-th variable from the old manager in the new manager.]
+
+  SideEffects [None]
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_TransferPermute( DdManager * ddSource, DdManager * ddDestination, DdNode * f, int * Permute )
+{
+    DdNode * bRes;
+    do
+    {
+        ddDestination->reordered = 0;
+        bRes = extraTransferPermute( ddSource, ddDestination, f, Permute );
+    }
+    while ( ddDestination->reordered == 1 );
+    return ( bRes );
+
+}                               /* end of Extra_TransferPermute */
+
+/**Function********************************************************************
+
+  Synopsis    [Transfers the BDD from one manager into another level by level.]
+
+  Description [Transfers the BDD from one manager into another while
+  preserving the correspondence between variables level by level.]
+
+  SideEffects [None]
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_TransferLevelByLevel( DdManager * ddSource, DdManager * ddDestination, DdNode * f )
+{
+    DdNode * bRes;
+    int * pPermute;
+    int nMin, nMax, i;
+
+    nMin = ddMin(ddSource->size, ddDestination->size);
+    nMax = ddMax(ddSource->size, ddDestination->size);
+    pPermute = ABC_ALLOC( int, nMax );
+    // set up the variable permutation
+    for ( i = 0; i < nMin; i++ )
+        pPermute[ ddSource->invperm[i] ] = ddDestination->invperm[i];
+    if ( ddSource->size > ddDestination->size )
+    {
+        for (      ; i < nMax; i++ )
+            pPermute[ ddSource->invperm[i] ] = -1;
+    }
+    bRes = Extra_TransferPermute( ddSource, ddDestination, f, pPermute );
+    ABC_FREE( pPermute );
+    return bRes;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Remaps the function to depend on the topmost variables on the manager.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddRemapUp(
+  DdManager * dd,
+  DdNode * bF )
+{
+    int * pPermute;
+    DdNode * bSupp, * bTemp, * bRes;
+    int Counter;
+
+    pPermute = ABC_ALLOC( int, dd->size );
+
+    // get support
+    bSupp = Cudd_Support( dd, bF );    Cudd_Ref( bSupp );
+
+    // create the variable map
+    // to remap the DD into the upper part of the manager
+    Counter = 0;
+    for ( bTemp = bSupp; bTemp != dd->one; bTemp = cuddT(bTemp) )
+        pPermute[bTemp->index] = dd->invperm[Counter++];
+
+    // transfer the BDD and remap it
+    bRes = Cudd_bddPermute( dd, bF, pPermute );  Cudd_Ref( bRes );
+
+    // remove support
+    Cudd_RecursiveDeref( dd, bSupp );
+
+    // return
+    Cudd_Deref( bRes );
+    ABC_FREE( pPermute );
+    return bRes;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Moves the BDD by the given number of variables up or down.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     [Extra_bddShift]
+
+******************************************************************************/
+DdNode * Extra_bddMove( 
+  DdManager * dd,   /* the DD manager */
+  DdNode * bF,
+  int nVars) 
+{
+    DdNode * res;
+    DdNode * bVars;
+    if ( nVars == 0 )
+        return bF;
+    if ( Cudd_IsConstant(bF) )
+        return bF;
+    assert( nVars <= dd->size );
+    if ( nVars > 0 )
+        bVars = dd->vars[nVars];
+    else
+        bVars = Cudd_Not(dd->vars[-nVars]);
+
+    do {
+        dd->reordered = 0;
+        res = extraBddMove( dd, bF, bVars );
+    } while (dd->reordered == 1);
+    return(res);
+
+} /* end of Extra_bddMove */
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Extra_StopManager( DdManager * dd )
+{
+    int RetValue;
+    // check for remaining references in the package
+    RetValue = Cudd_CheckZeroRef( dd );
+    if ( RetValue > 10 )
+//    if ( RetValue )
+        printf( "\nThe number of referenced nodes = %d\n\n", RetValue );
+//  Cudd_PrintInfo( dd, stdout );
+    Cudd_Quit( dd );
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Outputs the BDD in a readable format.]
+
+  Description []
+
+  SideEffects [None]
+
+  SeeAlso     []
+
+******************************************************************************/
+void Extra_bddPrint( DdManager * dd, DdNode * F )
+{
+    DdGen * Gen;
+    int * Cube;
+    CUDD_VALUE_TYPE Value;
+    int nVars = dd->size;
+    int fFirstCube = 1;
+    int i;
+
+    if ( F == NULL )
+    {
+        printf("NULL");
+        return;
+    }
+    if ( F == b0 )
+    {
+        printf("Constant 0");
+        return;
+    }
+    if ( F == b1 )
+    {
+        printf("Constant 1");
+        return;
+    }
+
+    Cudd_ForeachCube( dd, F, Gen, Cube, Value )
+    {
+        if ( fFirstCube )
+            fFirstCube = 0;
+        else
+//          Output << " + ";
+            printf( " + " );
+
+        for ( i = 0; i < nVars; i++ )
+            if ( Cube[i] == 0 )
+                printf( "[%d]'", i );
+//              printf( "%c'", (char)('a'+i) );
+            else if ( Cube[i] == 1 )
+                printf( "[%d]", i );
+//              printf( "%c", (char)('a'+i) );
+    }
+
+//  printf("\n");
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Outputs the BDD in a readable format.]
+
+  Description []
+
+  SideEffects [None]
+
+  SeeAlso     []
+
+******************************************************************************/
+void Extra_bddPrintSupport( DdManager * dd, DdNode * F )
+{
+    DdNode * bSupp;
+    bSupp = Cudd_Support( dd, F );   Cudd_Ref( bSupp );
+    Extra_bddPrint( dd, bSupp );
+    Cudd_RecursiveDeref( dd, bSupp );
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Returns the size of the support.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Extra_bddSuppSize( DdManager * dd, DdNode * bSupp )
+{
+    int Counter = 0;
+    while ( bSupp != b1 )
+    {
+        assert( !Cudd_IsComplement(bSupp) );
+        assert( cuddE(bSupp) == b0 );
+
+        bSupp = cuddT(bSupp);
+        Counter++;
+    }
+    return Counter;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Returns 1 if the support contains the given BDD variable.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Extra_bddSuppContainVar( DdManager * dd, DdNode * bS, DdNode * bVar )   
+{ 
+    for( ; bS != b1; bS = cuddT(bS) )
+        if ( bS->index == bVar->index )
+            return 1;
+    return 0;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Returns 1 if two supports represented as BDD cubes are overlapping.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Extra_bddSuppOverlapping( DdManager * dd, DdNode * S1, DdNode * S2 )
+{
+    while ( S1->index != CUDD_CONST_INDEX && S2->index != CUDD_CONST_INDEX )
+    {
+        // if the top vars are the same, they intersect
+        if ( S1->index == S2->index )
+            return 1;
+        // if the top vars are different, skip the one, which is higher
+        if ( dd->perm[S1->index] < dd->perm[S2->index] )
+            S1 = cuddT(S1);
+        else
+            S2 = cuddT(S2);
+    }
+    return 0;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Returns the number of different vars in two supports.]
+
+  Description [Counts the number of variables that appear in one support and 
+  does not appear in other support. If the number exceeds DiffMax, returns DiffMax.]
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Extra_bddSuppDifferentVars( DdManager * dd, DdNode * S1, DdNode * S2, int DiffMax )
+{
+    int Result = 0;
+    while ( S1->index != CUDD_CONST_INDEX && S2->index != CUDD_CONST_INDEX )
+    {
+        // if the top vars are the same, this var is the same
+        if ( S1->index == S2->index )
+        {
+            S1 = cuddT(S1);
+            S2 = cuddT(S2);
+            continue;
+        }
+        // the top var is different
+        Result++;
+
+        if ( Result >= DiffMax )
+            return DiffMax;
+
+        // if the top vars are different, skip the one, which is higher
+        if ( dd->perm[S1->index] < dd->perm[S2->index] )
+            S1 = cuddT(S1);
+        else
+            S2 = cuddT(S2);
+    }
+
+    // consider the remaining variables
+    if ( S1->index != CUDD_CONST_INDEX )
+        Result += Extra_bddSuppSize(dd,S1);
+    else if ( S2->index != CUDD_CONST_INDEX )
+        Result += Extra_bddSuppSize(dd,S2);
+
+    if ( Result >= DiffMax )
+        return DiffMax;
+    return Result;
+}
+
+
+/**Function********************************************************************
+
+  Synopsis    [Checks the support containment.]
+
+  Description [This function returns 1 if one support is contained in another.
+  In this case, bLarge (bSmall) is assigned to point to the larger (smaller) support.
+  If the supports are identical, return 0 and does not assign the supports!]
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Extra_bddSuppCheckContainment( DdManager * dd, DdNode * bL, DdNode * bH, DdNode ** bLarge, DdNode ** bSmall )
+{
+    DdNode * bSL = bL;
+    DdNode * bSH = bH;
+    int fLcontainsH = 1;
+    int fHcontainsL = 1;
+    int TopVar;
+    
+    if ( bSL == bSH )
+        return 0;
+
+    while ( bSL != b1 || bSH != b1 )
+    {
+        if ( bSL == b1 )
+        { // Low component has no vars; High components has some vars
+            fLcontainsH = 0;
+            if ( fHcontainsL == 0 )
+                return 0;
+            else
+                break;
+        }
+
+        if ( bSH == b1 )
+        { // similarly
+            fHcontainsL = 0;
+            if ( fLcontainsH == 0 )
+                return 0;
+            else
+                break;
+        }
+
+        // determine the topmost var of the supports by comparing their levels
+        if ( dd->perm[bSL->index] < dd->perm[bSH->index] )
+            TopVar = bSL->index;
+        else
+            TopVar = bSH->index;
+
+        if ( TopVar == bSL->index && TopVar == bSH->index ) 
+        { // they are on the same level
+            // it does not tell us anything about their containment
+            // skip this var
+            bSL = cuddT(bSL);
+            bSH = cuddT(bSH);
+        }
+        else if ( TopVar == bSL->index ) // and TopVar != bSH->index
+        { // Low components is higher and contains more vars
+            // it is not possible that High component contains Low
+            fHcontainsL = 0;
+            // skip this var
+            bSL = cuddT(bSL);
+        }
+        else // if ( TopVar == bSH->index ) // and TopVar != bSL->index
+        { // similarly
+            fLcontainsH = 0;
+            // skip this var
+            bSH = cuddT(bSH);
+        }
+
+        // check the stopping condition
+        if ( !fHcontainsL && !fLcontainsH )
+            return 0;
+    }
+    // only one of them can be true at the same time
+    assert( !fHcontainsL || !fLcontainsH );
+    if ( fHcontainsL )
+    {
+        *bLarge = bH;
+        *bSmall = bL;
+    }
+    else // fLcontainsH
+    {
+        *bLarge = bL;
+        *bSmall = bH;
+    }
+    return 1;
+}
+
+
+/**Function********************************************************************
+
+  Synopsis    [Finds variables on which the DD depends and returns them as am array.]
+
+  Description [Finds the variables on which the DD depends. Returns an array 
+  with entries set to 1 for those variables that belong to the support; 
+  NULL otherwise. The array is allocated by the user and should have at least
+  as many entries as the maximum number of variables in BDD and ZDD parts of 
+  the manager.]
+
+  SideEffects [None]
+
+  SeeAlso     [Cudd_Support Cudd_VectorSupport Cudd_ClassifySupport]
+
+******************************************************************************/
+int * 
+Extra_SupportArray(
+  DdManager * dd, /* manager */
+  DdNode * f,     /* DD whose support is sought */
+  int * support ) /* array allocated by the user */
+{
+    int i, size;
+
+    /* Initialize support array for ddSupportStep. */
+    size = ddMax(dd->size, dd->sizeZ);
+    for (i = 0; i < size; i++) 
+        support[i] = 0;
+    
+    /* Compute support and clean up markers. */
+    ddSupportStep(Cudd_Regular(f),support);
+    ddClearFlag(Cudd_Regular(f));
+
+    return(support);
+
+} /* end of Extra_SupportArray */
+
+/**Function********************************************************************
+
+  Synopsis    [Finds the variables on which a set of DDs depends.]
+
+  Description [Finds the variables on which a set of DDs depends.
+  The set must contain either BDDs and ADDs, or ZDDs.
+  Returns a BDD consisting of the product of the variables if
+  successful; NULL otherwise.]
+
+  SideEffects [None]
+
+  SeeAlso     [Cudd_Support Cudd_ClassifySupport]
+
+******************************************************************************/
+int *
+Extra_VectorSupportArray( 
+  DdManager * dd, /* manager */ 
+  DdNode ** F, /* array of DDs whose support is sought */ 
+  int n, /* size of the array */  
+  int * support ) /* array allocated by the user */
+{
+    int i, size;
+
+    /* Allocate and initialize support array for ddSupportStep. */
+    size = ddMax( dd->size, dd->sizeZ );
+    for ( i = 0; i < size; i++ )
+        support[i] = 0;
+
+    /* Compute support and clean up markers. */
+    for ( i = 0; i < n; i++ )
+        ddSupportStep( Cudd_Regular(F[i]), support );
+    for ( i = 0; i < n; i++ )
+        ddClearFlag( Cudd_Regular(F[i]) );
+
+    return support;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Find any cube belonging to the on-set of the function.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode *  Extra_bddFindOneCube( DdManager * dd, DdNode * bF )
+{
+    char * s_Temp;
+    DdNode * bCube, * bTemp;
+    int v;
+
+    // get the vector of variables in the cube
+    s_Temp = ABC_ALLOC( char, dd->size );
+    Cudd_bddPickOneCube( dd, bF, s_Temp );
+
+    // start the cube
+    bCube = b1; Cudd_Ref( bCube );
+    for ( v = 0; v < dd->size; v++ )
+        if ( s_Temp[v] == 0 )
+        {
+//          Cube &= !s_XVars[v];
+            bCube = Cudd_bddAnd( dd, bTemp = bCube, Cudd_Not(dd->vars[v]) ); Cudd_Ref( bCube );
+            Cudd_RecursiveDeref( dd, bTemp );
+        }
+        else if ( s_Temp[v] == 1 )
+        {
+//          Cube &=  s_XVars[v];
+            bCube = Cudd_bddAnd( dd, bTemp = bCube,          dd->vars[v]  ); Cudd_Ref( bCube );
+            Cudd_RecursiveDeref( dd, bTemp );
+        }
+    Cudd_Deref(bCube);
+    ABC_FREE( s_Temp );
+    return bCube;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Returns one cube contained in the given BDD.]
+
+  Description [This function returns the cube with the smallest 
+  bits-to-integer value.]
+
+  SideEffects []
+
+******************************************************************************/
+DdNode * Extra_bddGetOneCube( DdManager * dd, DdNode * bFunc )
+{
+    DdNode * bFuncR, * bFunc0, * bFunc1;
+    DdNode * bRes0,  * bRes1,  * bRes;
+
+    bFuncR = Cudd_Regular(bFunc);
+    if ( cuddIsConstant(bFuncR) )
+        return bFunc;
+
+    // cofactor
+    if ( Cudd_IsComplement(bFunc) )
+    {
+        bFunc0 = Cudd_Not( cuddE(bFuncR) );
+        bFunc1 = Cudd_Not( cuddT(bFuncR) );
+    }
+    else
+    {
+        bFunc0 = cuddE(bFuncR);
+        bFunc1 = cuddT(bFuncR);
+    }
+
+    // try to find the cube with the negative literal
+    bRes0 = Extra_bddGetOneCube( dd, bFunc0 );  Cudd_Ref( bRes0 );
+
+    if ( bRes0 != b0 )
+    {
+        bRes = Cudd_bddAnd( dd, bRes0, Cudd_Not(dd->vars[bFuncR->index]) ); Cudd_Ref( bRes );
+        Cudd_RecursiveDeref( dd, bRes0 );
+    }
+    else
+    {
+        Cudd_RecursiveDeref( dd, bRes0 );
+        // try to find the cube with the positive literal
+        bRes1 = Extra_bddGetOneCube( dd, bFunc1 );  Cudd_Ref( bRes1 );
+        assert( bRes1 != b0 );
+        bRes = Cudd_bddAnd( dd, bRes1, dd->vars[bFuncR->index] ); Cudd_Ref( bRes );
+        Cudd_RecursiveDeref( dd, bRes1 );
+    }
+
+    Cudd_Deref( bRes );
+    return bRes;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the reordering-sensitive step of Extra_bddMove().]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddComputeRangeCube( DdManager * dd, int iStart, int iStop )
+{
+    DdNode * bTemp, * bProd;
+    int i;
+    assert( iStart <= iStop );
+    assert( iStart >= 0 && iStart <= dd->size );
+    assert( iStop >= 0  && iStop  <= dd->size );
+    bProd = b1;         Cudd_Ref( bProd );
+    for ( i = iStart; i < iStop; i++ )
+    {
+        bProd = Cudd_bddAnd( dd, bTemp = bProd, dd->vars[i] );      Cudd_Ref( bProd );
+        Cudd_RecursiveDeref( dd, bTemp ); 
+    }
+    Cudd_Deref( bProd );
+    return bProd;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Computes the cube of BDD variables corresponding to bits it the bit-code]
+
+  Description [Returns a bdd composed of elementary bdds found in array BddVars[] such 
+  that the bdd vars encode the number Value of bit length CodeWidth (if fMsbFirst is 1, 
+  the most significant bit is encoded with the first bdd variable). If the variables 
+  BddVars are not specified, takes the first CodeWidth variables of the manager]
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddBitsToCube( DdManager * dd, int Code, int CodeWidth, DdNode ** pbVars, int fMsbFirst )
+{
+    int z;
+    DdNode * bTemp, * bVar, * bVarBdd, * bResult;
+
+    bResult = b1;   Cudd_Ref( bResult );
+    for ( z = 0; z < CodeWidth; z++ )
+    {
+        bVarBdd = (pbVars)? pbVars[z]: dd->vars[z];
+        if ( fMsbFirst )
+            bVar = Cudd_NotCond( bVarBdd, (Code & (1 << (CodeWidth-1-z)))==0 );
+        else
+            bVar = Cudd_NotCond( bVarBdd, (Code & (1 << (z)))==0 );
+        bResult = Cudd_bddAnd( dd, bTemp = bResult, bVar );     Cudd_Ref( bResult );
+        Cudd_RecursiveDeref( dd, bTemp );
+    }
+    Cudd_Deref( bResult );
+
+    return bResult;
+}  /* end of Extra_bddBitsToCube */
+
+/**Function********************************************************************
+
+  Synopsis    [Finds the support as a negative polarity cube.]
+
+  Description [Finds the variables on which a DD depends. Returns a BDD 
+  consisting of the product of the variables in the negative polarity 
+  if successful; NULL otherwise.]
+
+  SideEffects [None]
+
+  SeeAlso     [Cudd_VectorSupport Cudd_Support]
+
+******************************************************************************/
+DdNode * Extra_bddSupportNegativeCube( DdManager * dd, DdNode * f )
+{
+    int *support;
+    DdNode *res, *tmp, *var;
+    int i, j;
+    int size;
+
+    /* Allocate and initialize support array for ddSupportStep. */
+    size = ddMax( dd->size, dd->sizeZ );
+    support = ABC_ALLOC( int, size );
+    if ( support == NULL )
+    {
+        dd->errorCode = CUDD_MEMORY_OUT;
+        return ( NULL );
+    }
+    for ( i = 0; i < size; i++ )
+    {
+        support[i] = 0;
+    }
+
+    /* Compute support and clean up markers. */
+    ddSupportStep( Cudd_Regular( f ), support );
+    ddClearFlag( Cudd_Regular( f ) );
+
+    /* Transform support from array to cube. */
+    do
+    {
+        dd->reordered = 0;
+        res = DD_ONE( dd );
+        cuddRef( res );
+        for ( j = size - 1; j >= 0; j-- )
+        {                        /* for each level bottom-up */
+            i = ( j >= dd->size ) ? j : dd->invperm[j];
+            if ( support[i] == 1 )
+            {
+                var = cuddUniqueInter( dd, i, dd->one, Cudd_Not( dd->one ) );
+                //////////////////////////////////////////////////////////////////
+                var = Cudd_Not(var);
+                //////////////////////////////////////////////////////////////////
+                cuddRef( var );
+                tmp = cuddBddAndRecur( dd, res, var );
+                if ( tmp == NULL )
+                {
+                    Cudd_RecursiveDeref( dd, res );
+                    Cudd_RecursiveDeref( dd, var );
+                    res = NULL;
+                    break;
+                }
+                cuddRef( tmp );
+                Cudd_RecursiveDeref( dd, res );
+                Cudd_RecursiveDeref( dd, var );
+                res = tmp;
+            }
+        }
+    }
+    while ( dd->reordered == 1 );
+
+    ABC_FREE( support );
+    if ( res != NULL )
+        cuddDeref( res );
+    return ( res );
+
+}                                /* end of Extra_SupportNeg */
+
+/**Function********************************************************************
+
+  Synopsis    [Returns 1 if the BDD is the BDD of elementary variable.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Extra_bddIsVar( DdNode * bFunc )
+{
+    bFunc = Cudd_Regular( bFunc );
+    if ( cuddIsConstant(bFunc) )
+        return 0;
+    return cuddIsConstant( cuddT(bFunc) ) && cuddIsConstant( Cudd_Regular(cuddE(bFunc)) );
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Creates AND composed of the first nVars of the manager.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddCreateAnd( DdManager * dd, int nVars )
+{
+    DdNode * bFunc, * bTemp;
+    int i;
+    bFunc = Cudd_ReadOne(dd); Cudd_Ref( bFunc );
+    for ( i = 0; i < nVars; i++ )
+    {
+        bFunc = Cudd_bddAnd( dd, bTemp = bFunc, Cudd_bddIthVar(dd,i) );  Cudd_Ref( bFunc );
+        Cudd_RecursiveDeref( dd, bTemp );
+    }
+    Cudd_Deref( bFunc );
+    return bFunc;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Creates OR composed of the first nVars of the manager.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddCreateOr( DdManager * dd, int nVars )
+{
+    DdNode * bFunc, * bTemp;
+    int i;
+    bFunc = Cudd_ReadLogicZero(dd); Cudd_Ref( bFunc );
+    for ( i = 0; i < nVars; i++ )
+    {
+        bFunc = Cudd_bddOr( dd, bTemp = bFunc, Cudd_bddIthVar(dd,i) );  Cudd_Ref( bFunc );
+        Cudd_RecursiveDeref( dd, bTemp );
+    }
+    Cudd_Deref( bFunc );
+    return bFunc;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Creates EXOR composed of the first nVars of the manager.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddCreateExor( DdManager * dd, int nVars )
+{
+    DdNode * bFunc, * bTemp;
+    int i;
+    bFunc = Cudd_ReadLogicZero(dd); Cudd_Ref( bFunc );
+    for ( i = 0; i < nVars; i++ )
+    {
+        bFunc = Cudd_bddXor( dd, bTemp = bFunc, Cudd_bddIthVar(dd,i) );  Cudd_Ref( bFunc );
+        Cudd_RecursiveDeref( dd, bTemp );
+    }
+    Cudd_Deref( bFunc );
+    return bFunc;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Computes the set of primes as a ZDD.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_zddPrimes( DdManager * dd, DdNode * F )
+{
+    DdNode    *res;
+    do {
+        dd->reordered = 0;
+        res = extraZddPrimes(dd, F);
+        if ( dd->reordered == 1 )
+            printf("\nReordering in Extra_zddPrimes()\n");
+    } while (dd->reordered == 1);
+    return(res);
+
+} /* end of Extra_zddPrimes */
+
+/**Function********************************************************************
+
+  Synopsis    [Permutes the variables of the array of BDDs.]
+
+  Description [Given a permutation in array permut, creates a new BDD
+  with permuted variables. There should be an entry in array permut
+  for each variable in the manager. The i-th entry of permut holds the
+  index of the variable that is to substitute the i-th variable.
+  The DDs in the resulting array are already referenced.]
+
+  SideEffects [None]
+
+  SeeAlso     [Cudd_addPermute Cudd_bddSwapVariables]
+
+******************************************************************************/
+void Extra_bddPermuteArray( DdManager * manager, DdNode ** bNodesIn, DdNode ** bNodesOut, int nNodes, int *permut )
+{
+    DdHashTable *table;
+    int i, k;
+    do
+    {
+        manager->reordered = 0;
+        table = cuddHashTableInit( manager, 1, 2 );
+
+        /* permute the output functions one-by-one */
+        for ( i = 0; i < nNodes; i++ )
+        {
+            bNodesOut[i] = cuddBddPermuteRecur( manager, table, bNodesIn[i], permut );
+            if ( bNodesOut[i] == NULL )
+            {
+                /* deref the array of the already computed outputs */
+                for ( k = 0; k < i; k++ )
+                    Cudd_RecursiveDeref( manager, bNodesOut[k] );
+                break;
+            }
+            cuddRef( bNodesOut[i] );
+        }
+        /* Dispose of local cache. */
+        cuddHashTableQuit( table );
+    }
+    while ( manager->reordered == 1 );
+}    /* end of Extra_bddPermuteArray */
+
+
+/**Function********************************************************************
+
+  Synopsis    [Computes the positive polarty cube composed of the first vars in the array.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddComputeCube( DdManager * dd, DdNode ** bXVars, int nVars )
+{
+    DdNode * bRes;
+    DdNode * bTemp;
+    int i;
+
+    bRes = b1; Cudd_Ref( bRes );
+    for ( i = 0; i < nVars; i++ )
+    {
+        bRes = Cudd_bddAnd( dd, bTemp = bRes, bXVars[i] );  Cudd_Ref( bRes );
+        Cudd_RecursiveDeref( dd, bTemp );
+    }
+
+    Cudd_Deref( bRes );
+    return bRes;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Changes the polarity of vars listed in the cube.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * Extra_bddChangePolarity( 
+  DdManager * dd,   /* the DD manager */
+  DdNode * bFunc,
+  DdNode * bVars) 
+{
+    DdNode  *res;
+    do {
+        dd->reordered = 0;
+        res = extraBddChangePolarity( dd, bFunc, bVars );
+    } while (dd->reordered == 1);
+    return(res);
+
+} /* end of Extra_bddChangePolarity */
+
+
+/**Function*************************************************************
+
+  Synopsis    [Checks if the given variable belongs to the cube.]
+
+  Description [Return -1 if the var does not appear in the cube.
+  Otherwise, returns polarity (0 or 1) of the var in the cube.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Extra_bddVarIsInCube( DdNode * bCube, int iVar )
+{
+    DdNode * bCube0, * bCube1;
+    while ( Cudd_Regular(bCube)->index != CUDD_CONST_INDEX )
+    {
+        bCube0 = Cudd_NotCond( cuddE(Cudd_Regular(bCube)), Cudd_IsComplement(bCube) );
+        bCube1 = Cudd_NotCond( cuddT(Cudd_Regular(bCube)), Cudd_IsComplement(bCube) );
+        // make sure it is a cube
+        assert( (Cudd_IsComplement(bCube0) && Cudd_Regular(bCube0)->index == CUDD_CONST_INDEX) || // bCube0 == 0
+                (Cudd_IsComplement(bCube1) && Cudd_Regular(bCube1)->index == CUDD_CONST_INDEX) ); // bCube1 == 0
+        // quit if it is the last one
+        if ( Cudd_Regular(bCube)->index == iVar )
+            return (int)(Cudd_IsComplement(bCube0) && Cudd_Regular(bCube0)->index == CUDD_CONST_INDEX);
+        // get the next cube
+        if ( (Cudd_IsComplement(bCube0) && Cudd_Regular(bCube0)->index == CUDD_CONST_INDEX) )
+            bCube = bCube1;
+        else
+            bCube = bCube0;
+    }
+    return -1;
+}
+ 
+/**Function*************************************************************
+
+  Synopsis    [Computes the AND of two BDD with different orders.]
+
+  Description [Derives the result of Boolean AND of bF and bG in ddF.
+  The array pPermute gives the mapping of variables of ddG into that of ddF.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+DdNode * Extra_bddAndPermute( DdManager * ddF, DdNode * bF, DdManager * ddG, DdNode * bG, int * pPermute )
+{
+    DdHashTable * table;
+    DdNode * bRes;
+    do
+    {
+        ddF->reordered = 0;
+        table = cuddHashTableInit( ddF, 2, 256 );
+        if (table == NULL) return NULL;
+        bRes = extraBddAndPermute( table, ddF, bF, ddG, bG, pPermute );  
+        if ( bRes ) cuddRef( bRes );
+        cuddHashTableQuit( table );
+        if ( bRes ) cuddDeref( bRes );
+//if ( ddF->reordered == 1 )
+//printf( "Reordering happened\n" );
+    }
+    while ( ddF->reordered == 1 );
+//printf( "|F| =%6d  |G| =%6d  |H| =%6d  |F|*|G| =%9d\n", 
+//       Cudd_DagSize(bF), Cudd_DagSize(bG), Cudd_DagSize(bRes), 
+//       Cudd_DagSize(bF) * Cudd_DagSize(bG) );
+    return ( bRes );
+}
+
+/*---------------------------------------------------------------------------*/
+/* Definition of internal functions                                          */
+/*---------------------------------------------------------------------------*/
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the reordering-sensitive step of Extra_bddMove().]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * extraBddMove( 
+  DdManager * dd,    /* the DD manager */
+  DdNode * bF,
+  DdNode * bDist) 
+{
+    DdNode * bRes;
+
+    if ( Cudd_IsConstant(bF) )
+        return bF;
+
+    if ( (bRes = cuddCacheLookup2(dd, extraBddMove, bF, bDist)) )
+        return bRes;
+    else
+    {
+        DdNode * bRes0, * bRes1;             
+        DdNode * bF0, * bF1;             
+        DdNode * bFR = Cudd_Regular(bF); 
+        int VarNew;
+        
+        if ( Cudd_IsComplement(bDist) )
+            VarNew = bFR->index - Cudd_Not(bDist)->index;
+        else
+            VarNew = bFR->index + bDist->index;
+        assert( VarNew < dd->size );
+
+        // cofactor the functions
+        if ( bFR != bF ) // bFunc is complemented 
+        {
+            bF0 = Cudd_Not( cuddE(bFR) );
+            bF1 = Cudd_Not( cuddT(bFR) );
+        }
+        else
+        {
+            bF0 = cuddE(bFR);
+            bF1 = cuddT(bFR);
+        }
+
+        bRes0 = extraBddMove( dd, bF0, bDist );
+        if ( bRes0 == NULL ) 
+            return NULL;
+        cuddRef( bRes0 );
+
+        bRes1 = extraBddMove( dd, bF1, bDist );
+        if ( bRes1 == NULL ) 
+        {
+            Cudd_RecursiveDeref( dd, bRes0 );
+            return NULL;
+        }
+        cuddRef( bRes1 );
+
+        /* only bRes0 and bRes1 are referenced at this point */
+        bRes = cuddBddIteRecur( dd, dd->vars[VarNew], bRes1, bRes0 );
+        if ( bRes == NULL ) 
+        {
+            Cudd_RecursiveDeref( dd, bRes0 );
+            Cudd_RecursiveDeref( dd, bRes1 );
+            return NULL;
+        }
+        cuddRef( bRes );
+        Cudd_RecursiveDeref( dd, bRes0 );
+        Cudd_RecursiveDeref( dd, bRes1 );
+
+        /* insert the result into cache */
+        cuddCacheInsert2( dd, extraBddMove, bF, bDist, bRes );
+        cuddDeref( bRes );
+        return bRes;
+    }
+} /* end of extraBddMove */
+
+
+/**Function********************************************************************
+
+  Synopsis    [Finds three cofactors of the cover w.r.t. to the topmost variable.]
+
+  Description [Finds three cofactors of the cover w.r.t. to the topmost variable.
+  Does not check the cover for being a constant. Assumes that ZDD variables encoding 
+  positive and negative polarities are adjacent in the variable order. Is different 
+  from cuddZddGetCofactors3() in that it does not compute the cofactors w.r.t. the 
+  given variable but takes the cofactors with respent to the topmost variable. 
+  This function is more efficient when used in recursive procedures because it does 
+  not require referencing of the resulting cofactors (compare cuddZddProduct() 
+  and extraZddPrimeProduct()).]
+
+  SideEffects [None]
+
+  SeeAlso     [cuddZddGetCofactors3]
+
+******************************************************************************/
+void 
+extraDecomposeCover( 
+  DdManager* dd,    /* the manager */
+  DdNode*  zC,      /* the cover */
+  DdNode** zC0,     /* the pointer to the negative var cofactor */ 
+  DdNode** zC1,     /* the pointer to the positive var cofactor */ 
+  DdNode** zC2 )    /* the pointer to the cofactor without var */ 
+{
+    if ( (zC->index & 1) == 0 ) 
+    { /* the top variable is present in positive polarity and maybe in negative */
+
+        DdNode *Temp = cuddE( zC );
+        *zC1  = cuddT( zC );
+        if ( cuddIZ(dd,Temp->index) == cuddIZ(dd,zC->index) + 1 )
+        {   /* Temp is not a terminal node 
+             * top var is present in negative polarity */
+            *zC2 = cuddE( Temp );
+            *zC0 = cuddT( Temp );
+        }
+        else
+        {   /* top var is not present in negative polarity */
+            *zC2 = Temp;
+            *zC0 = dd->zero;
+        }
+    }
+    else 
+    { /* the top variable is present only in negative */
+        *zC1 = dd->zero;
+        *zC2 = cuddE( zC );
+        *zC0 = cuddT( zC );
+    }
+} /* extraDecomposeCover */
+
+
+
+/**Function********************************************************************
+
+  Synopsis    [Counts the total number of cubes in the ISOPs of the functions.]
+
+  Description [Returns -1 if the number of cubes exceeds the limit.]
+
+  SideEffects [None]
+
+  SeeAlso     [Extra_TransferPermute]
+
+******************************************************************************/
+static DdNode * extraBddCountCubes( DdManager * dd, DdNode * L, DdNode * U, st__table *table, int * pnCubes, int Limit )
+{
+    DdNode      *one = DD_ONE(dd);
+    DdNode      *zero = Cudd_Not(one);
+    int         v, top_l, top_u;
+    DdNode      *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
+    DdNode      *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
+    DdNode      *Isub0, *Isub1, *Id;
+    DdNode      *x;
+    DdNode      *term0, *term1, *sum;
+    DdNode      *Lv, *Uv, *Lnv, *Unv;
+    DdNode      *r;
+    int         index;
+    int         Count0 = 0, Count1 = 0, Count2 = 0;
+
+    statLine(dd);
+    if (L == zero)
+    {
+        *pnCubes = 0;
+        return(zero);
+    }
+    if (U == one)
+    {
+        *pnCubes = 1;
+        return(one);
+    }
+
+    /* Check cache */
+    r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
+    if (r)
+    {
+        int nCubes = 0;
+        if ( st__lookup( table, (char *)r, (char **)&nCubes ) )
+            *pnCubes = nCubes;
+        else assert( 0 );
+        return r;
+    }
+
+    top_l = dd->perm[Cudd_Regular(L)->index];
+    top_u = dd->perm[Cudd_Regular(U)->index];
+    v = ddMin(top_l, top_u);
+
+    /* Compute cofactors */
+    if (top_l == v) {
+        index = Cudd_Regular(L)->index;
+        Lv = Cudd_T(L);
+        Lnv = Cudd_E(L);
+        if (Cudd_IsComplement(L)) {
+            Lv = Cudd_Not(Lv);
+            Lnv = Cudd_Not(Lnv);
+        }
+    }
+    else {
+        index = Cudd_Regular(U)->index;
+        Lv = Lnv = L;
+    }
+
+    if (top_u == v) {
+        Uv = Cudd_T(U);
+        Unv = Cudd_E(U);
+        if (Cudd_IsComplement(U)) {
+            Uv = Cudd_Not(Uv);
+            Unv = Cudd_Not(Unv);
+        }
+    }
+    else {
+        Uv = Unv = U;
+    }
+
+    Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
+    if (Lsub0 == NULL)
+        return(NULL);
+    Cudd_Ref(Lsub0);
+    Usub0 = Unv;
+    Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
+    if (Lsub1 == NULL) {
+        Cudd_RecursiveDeref(dd, Lsub0);
+        return(NULL);
+    }
+    Cudd_Ref(Lsub1);
+    Usub1 = Uv;
+
+    Isub0 = extraBddCountCubes(dd, Lsub0, Usub0, table, &Count0, Limit);
+    if (Isub0 == NULL) {
+        Cudd_RecursiveDeref(dd, Lsub0);
+        Cudd_RecursiveDeref(dd, Lsub1);
+        return(NULL);
+    }
+    Cudd_Ref(Isub0);
+    Isub1 = extraBddCountCubes(dd, Lsub1, Usub1, table, &Count1, Limit);
+    if (Isub1 == NULL) {
+        Cudd_RecursiveDeref(dd, Lsub0);
+        Cudd_RecursiveDeref(dd, Lsub1);
+        Cudd_RecursiveDeref(dd, Isub0);
+        return(NULL);
+    }
+    Cudd_Ref(Isub1);
+    Cudd_RecursiveDeref(dd, Lsub0);
+    Cudd_RecursiveDeref(dd, Lsub1);
+
+    Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
+    if (Lsuper0 == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        return(NULL);
+    }
+    Cudd_Ref(Lsuper0);
+    Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
+    if (Lsuper1 == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Lsuper0);
+        return(NULL);
+    }
+    Cudd_Ref(Lsuper1);
+    Usuper0 = Unv;
+    Usuper1 = Uv;
+
+    /* Ld = Lsuper0 + Lsuper1 */
+    Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
+    Ld = Cudd_NotCond(Ld, Ld != NULL);
+    if (Ld == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Lsuper0);
+        Cudd_RecursiveDeref(dd, Lsuper1);
+        return(NULL);
+    }
+    Cudd_Ref(Ld);
+    Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
+    if (Ud == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Lsuper0);
+        Cudd_RecursiveDeref(dd, Lsuper1);
+        Cudd_RecursiveDeref(dd, Ld);
+        return(NULL);
+    }
+    Cudd_Ref(Ud);
+    Cudd_RecursiveDeref(dd, Lsuper0);
+    Cudd_RecursiveDeref(dd, Lsuper1);
+
+    Id = extraBddCountCubes(dd, Ld, Ud, table, &Count2, Limit);
+    if (Id == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Ld);
+        Cudd_RecursiveDeref(dd, Ud);
+        return(NULL);
+    }
+    Cudd_Ref(Id);
+    Cudd_RecursiveDeref(dd, Ld);
+    Cudd_RecursiveDeref(dd, Ud);
+
+    x = cuddUniqueInter(dd, index, one, zero);
+    if (x == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Id);
+        return(NULL);
+    }
+    Cudd_Ref(x);
+    term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
+    if (term0 == NULL) {
+        Cudd_RecursiveDeref(dd, Isub0);
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Id);
+        Cudd_RecursiveDeref(dd, x);
+        return(NULL);
+    }
+    Cudd_Ref(term0);
+    Cudd_RecursiveDeref(dd, Isub0);
+    term1 = cuddBddAndRecur(dd, x, Isub1);
+    if (term1 == NULL) {
+        Cudd_RecursiveDeref(dd, Isub1);
+        Cudd_RecursiveDeref(dd, Id);
+        Cudd_RecursiveDeref(dd, x);
+        Cudd_RecursiveDeref(dd, term0);
+        return(NULL);
+    }
+    Cudd_Ref(term1);
+    Cudd_RecursiveDeref(dd, x);
+    Cudd_RecursiveDeref(dd, Isub1);
+    /* sum = term0 + term1 */
+    sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
+    sum = Cudd_NotCond(sum, sum != NULL);
+    if (sum == NULL) {
+        Cudd_RecursiveDeref(dd, Id);
+        Cudd_RecursiveDeref(dd, term0);
+        Cudd_RecursiveDeref(dd, term1);
+        return(NULL);
+    }
+    Cudd_Ref(sum);
+    Cudd_RecursiveDeref(dd, term0);
+    Cudd_RecursiveDeref(dd, term1);
+    /* r = sum + Id */
+    r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
+    r = Cudd_NotCond(r, r != NULL);
+    if (r == NULL) {
+        Cudd_RecursiveDeref(dd, Id);
+        Cudd_RecursiveDeref(dd, sum);
+        return(NULL);
+    }
+    Cudd_Ref(r);
+    Cudd_RecursiveDeref(dd, sum);
+    Cudd_RecursiveDeref(dd, Id);
+
+    cuddCacheInsert2(dd, cuddBddIsop, L, U, r);
+    *pnCubes = Count0 + Count1 + Count2;
+    if ( st__add_direct( table, (char *)r, (char *)(ABC_PTRINT_T)*pnCubes ) == st__OUT_OF_MEM )
+    {
+        Cudd_RecursiveDeref( dd, r );
+        return NULL;
+    }
+    if ( *pnCubes > Limit )
+    {
+        Cudd_RecursiveDeref( dd, r );
+        return NULL;
+    }
+    //printf( "%d ", *pnCubes );
+    Cudd_Deref(r);
+    return r;
+} 
+int Extra_bddCountCubes( DdManager * dd, DdNode ** pFuncs, int nFuncs, int fMode, int nLimit, int * pGuide )
+{
+    DdNode * pF0, * pF1; 
+    int i, Count, Count0, Count1, CounterAll = 0;
+    st__table *table = st__init_table( st__ptrcmp, st__ptrhash );
+    unsigned int saveLimit = dd->maxLive;
+    dd->maxLive = dd->keys - dd->dead + 1000000; // limit on intermediate BDD nodes
+    for ( i = 0; i < nFuncs; i++ )
+    {
+        if ( !pFuncs[i] )
+            continue;
+        pF1 = pF0 = NULL;
+        Count0 = Count1 = nLimit;
+        if ( fMode == -1 || fMode == 1 ) // both or pos
+            pF1 = extraBddCountCubes( dd, pFuncs[i], pFuncs[i], table, &Count1, nLimit );
+        pFuncs[i] = Cudd_Not( pFuncs[i] );
+        if ( fMode == -1 || fMode == 0 ) // both or neg
+            pF0 = extraBddCountCubes( dd, pFuncs[i], pFuncs[i], table, &Count0, Count1 );
+        pFuncs[i] = Cudd_Not( pFuncs[i] );
+        if ( !pF1 && !pF0 )
+            break;
+        if ( !pF0 )                  pGuide[i] = 1, Count = Count1; // use pos
+        else if ( !pF1 )             pGuide[i] = 0, Count = Count0; // use neg
+        else if ( Count1 <= Count0 ) pGuide[i] = 1, Count = Count1; // use pos
+        else                         pGuide[i] = 0, Count = Count0; // use neg
+        CounterAll += Count;
+        //printf( "Output %5d has %5d cubes (%d)  (%5d and %5d)\n", nOuts++, Count, pGuide[i], Count1, Count0 );
+    }
+    dd->maxLive = saveLimit;
+    st__free_table( table );
+    return i == nFuncs ? CounterAll : -1;
+}   /* end of Extra_bddCountCubes */
+
+/*---------------------------------------------------------------------------*/
+/* Definition of static Functions                                            */
+/*---------------------------------------------------------------------------*/
+
+/**Function********************************************************************
+
+  Synopsis    [Convert a BDD from a manager to another one.]
+
+  Description [Convert a BDD from a manager to another one. Returns a
+  pointer to the BDD in the destination manager if successful; NULL
+  otherwise.]
+
+  SideEffects [None]
+
+  SeeAlso     [Extra_TransferPermute]
+
+******************************************************************************/
+DdNode * extraTransferPermute( DdManager * ddS, DdManager * ddD, DdNode * f, int * Permute )
+{
+    DdNode *res;
+    st__table *table = NULL;
+    st__generator *gen = NULL;
+    DdNode *key, *value;
+
+    table = st__init_table( st__ptrcmp, st__ptrhash );
+    if ( table == NULL )
+        goto failure;
+    res = extraTransferPermuteRecur( ddS, ddD, f, table, Permute );
+    if ( res != NULL )
+        cuddRef( res );
+
+    /* Dereference all elements in the table and dispose of the table.
+       ** This must be done also if res is NULL to avoid leaks in case of
+       ** reordering. */
+    gen = st__init_gen( table );
+    if ( gen == NULL )
+        goto failure;
+    while ( st__gen( gen, ( const char ** ) &key, ( char ** ) &value ) )
+    {
+        Cudd_RecursiveDeref( ddD, value );
+    }
+    st__free_gen( gen );
+    gen = NULL;
+    st__free_table( table );
+    table = NULL;
+
+    if ( res != NULL )
+        cuddDeref( res );
+    return ( res );
+
+  failure:
+    if ( table != NULL )
+        st__free_table( table );
+    if ( gen != NULL )
+        st__free_gen( gen );
+    return ( NULL );
+
+}                               /* end of extraTransferPermute */
+
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the recursive step of Extra_TransferPermute.]
+
+  Description [Performs the recursive step of Extra_TransferPermute.
+  Returns a pointer to the result if successful; NULL otherwise.]
+
+  SideEffects [None]
+
+  SeeAlso     [extraTransferPermute]
+
+******************************************************************************/
+static DdNode * 
+extraTransferPermuteRecur( 
+  DdManager * ddS, 
+  DdManager * ddD, 
+  DdNode * f, 
+  st__table * table, 
+  int * Permute )
+{
+    DdNode *ft, *fe, *t, *e, *var, *res;
+    DdNode *one, *zero;
+    int index;
+    int comple = 0;
+
+    statLine( ddD );
+    one = DD_ONE( ddD );
+    comple = Cudd_IsComplement( f );
+
+    /* Trivial cases. */
+    if ( Cudd_IsConstant( f ) )
+        return ( Cudd_NotCond( one, comple ) );
+
+
+    /* Make canonical to increase the utilization of the cache. */
+    f = Cudd_NotCond( f, comple );
+    /* Now f is a regular pointer to a non-constant node. */
+
+    /* Check the cache. */
+    if ( st__lookup( table, ( char * ) f, ( char ** ) &res ) )
+        return ( Cudd_NotCond( res, comple ) );
+
+    if ( ddS->TimeStop && Abc_Clock() > ddS->TimeStop )
+        return NULL;
+    if ( ddD->TimeStop && Abc_Clock() > ddD->TimeStop )
+        return NULL;
+
+    /* Recursive step. */
+    if ( Permute )
+        index = Permute[f->index];
+    else
+        index = f->index;
+
+    ft = cuddT( f );
+    fe = cuddE( f );
+
+    t = extraTransferPermuteRecur( ddS, ddD, ft, table, Permute );
+    if ( t == NULL )
+    {
+        return ( NULL );
+    }
+    cuddRef( t );
+
+    e = extraTransferPermuteRecur( ddS, ddD, fe, table, Permute );
+    if ( e == NULL )
+    {
+        Cudd_RecursiveDeref( ddD, t );
+        return ( NULL );
+    }
+    cuddRef( e );
+
+    zero = Cudd_Not(ddD->one);
+    var = cuddUniqueInter( ddD, index, one, zero );
+    if ( var == NULL )
+    {
+        Cudd_RecursiveDeref( ddD, t );
+        Cudd_RecursiveDeref( ddD, e );
+        return ( NULL );
+    }
+    res = cuddBddIteRecur( ddD, var, t, e );
+
+    if ( res == NULL )
+    {
+        Cudd_RecursiveDeref( ddD, t );
+        Cudd_RecursiveDeref( ddD, e );
+        return ( NULL );
+    }
+    cuddRef( res );
+    Cudd_RecursiveDeref( ddD, t );
+    Cudd_RecursiveDeref( ddD, e );
+
+    if ( st__add_direct( table, ( char * ) f, ( char * ) res ) ==
+         st__OUT_OF_MEM )
+    {
+        Cudd_RecursiveDeref( ddD, res );
+        return ( NULL );
+    }
+    return ( Cudd_NotCond( res, comple ) );
+
+}                               /* end of extraTransferPermuteRecur */
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the recursive step of Cudd_Support.]
+
+  Description [Performs the recursive step of Cudd_Support. Performs a
+  DFS from f. The support is accumulated in supp as a side effect. Uses
+  the LSB of the then pointer as visited flag.]
+
+  SideEffects [None]
+
+  SeeAlso     [ddClearFlag]
+
+******************************************************************************/
+static void
+ddSupportStep(
+  DdNode * f,
+  int * support)
+{
+    if (cuddIsConstant(f) || Cudd_IsComplement(f->next)) {
+    return;
+    }
+
+    support[f->index] = 1;
+    ddSupportStep(cuddT(f),support);
+    ddSupportStep(Cudd_Regular(cuddE(f)),support);
+    /* Mark as visited. */
+    f->next = Cudd_Not(f->next);
+    return;
+
+} /* end of ddSupportStep */
+
+
+/**Function********************************************************************
+
+  Synopsis    [Performs a DFS from f, clearing the LSB of the next
+  pointers.]
+
+  Description []
+
+  SideEffects [None]
+
+  SeeAlso     [ddSupportStep ddDagInt]
+
+******************************************************************************/
+static void
+ddClearFlag(
+  DdNode * f)
+{
+    if (!Cudd_IsComplement(f->next)) {
+    return;
+    }
+    /* Clear visited flag. */
+    f->next = Cudd_Regular(f->next);
+    if (cuddIsConstant(f)) {
+    return;
+    }
+    ddClearFlag(cuddT(f));
+    ddClearFlag(Cudd_Regular(cuddE(f)));
+    return;
+
+} /* end of ddClearFlag */
+
+
+/**Function********************************************************************
+
+  Synopsis    [Composed three subcovers into one ZDD.]
+
+  Description []
+
+  SideEffects [None]
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode *
+extraComposeCover( 
+  DdManager* dd,    /* the manager */
+  DdNode* zC0,     /* the pointer to the negative var cofactor */ 
+  DdNode* zC1,     /* the pointer to the positive var cofactor */ 
+  DdNode* zC2,     /* the pointer to the cofactor without var */ 
+  int TopVar)    /* the index of the positive ZDD var */
+{
+    DdNode * zRes, * zTemp;
+    /* compose with-neg-var and without-var using the neg ZDD var */
+    zTemp = cuddZddGetNode( dd, 2*TopVar + 1, zC0, zC2 );
+    if ( zTemp == NULL ) 
+    {
+        Cudd_RecursiveDerefZdd(dd, zC0);
+        Cudd_RecursiveDerefZdd(dd, zC1);
+        Cudd_RecursiveDerefZdd(dd, zC2);
+        return NULL;
+    }
+    cuddRef( zTemp );
+    cuddDeref( zC0 );
+    cuddDeref( zC2 );
+
+    /* compose with-pos-var and previous result using the pos ZDD var */
+    zRes = cuddZddGetNode( dd, 2*TopVar, zC1, zTemp );
+    if ( zRes == NULL ) 
+    {
+        Cudd_RecursiveDerefZdd(dd, zC1);
+        Cudd_RecursiveDerefZdd(dd, zTemp);
+        return NULL;
+    }
+    cuddDeref( zC1 );
+    cuddDeref( zTemp );
+    return zRes;
+} /* extraComposeCover */
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the recursive step of prime computation.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode* extraZddPrimes( DdManager *dd, DdNode* F )
+{
+    DdNode *zRes;
+
+    if ( F == Cudd_Not( dd->one ) )
+        return dd->zero;
+    if ( F == dd->one )
+        return dd->one;
+
+    /* check cache */
+    zRes = cuddCacheLookup1Zdd(dd, extraZddPrimes, F);
+    if (zRes)
+        return(zRes);
+    {
+        /* temporary variables */
+        DdNode *bF01, *zP0, *zP1;
+        /* three components of the prime set */
+        DdNode *zResE, *zResP, *zResN;
+        int fIsComp = Cudd_IsComplement( F );
+
+        /* find cofactors of F */
+        DdNode * bF0 = Cudd_NotCond( Cudd_E( F ), fIsComp );
+        DdNode * bF1 = Cudd_NotCond( Cudd_T( F ), fIsComp );
+
+        /* find the intersection of cofactors */
+        bF01 = cuddBddAndRecur( dd, bF0, bF1 );
+        if ( bF01 == NULL ) return NULL;
+        cuddRef( bF01 );
+
+        /* solve the problems for cofactors */
+        zP0 = extraZddPrimes( dd, bF0 );
+        if ( zP0 == NULL )
+        {
+            Cudd_RecursiveDeref( dd, bF01 );
+            return NULL;
+        }
+        cuddRef( zP0 );
+
+        zP1 = extraZddPrimes( dd, bF1 );
+        if ( zP1 == NULL )
+        {
+            Cudd_RecursiveDeref( dd, bF01 );
+            Cudd_RecursiveDerefZdd( dd, zP0 );
+            return NULL;
+        }
+        cuddRef( zP1 );
+
+        /* check for local unateness */
+        if ( bF01 == bF0 )       /* unate increasing */
+        {
+            /* intersection is useless */
+            cuddDeref( bF01 );
+            /* the primes of intersection are the primes of F0 */
+            zResE = zP0;
+            /* there are no primes with negative var */
+            zResN = dd->zero;
+            cuddRef( zResN );
+            /* primes with positive var are primes of F1 that are not primes of F01 */
+            zResP = cuddZddDiff( dd, zP1, zP0 );
+            if ( zResP == NULL )  
+            {
+                Cudd_RecursiveDerefZdd( dd, zResE );
+                Cudd_RecursiveDerefZdd( dd, zResN );
+                Cudd_RecursiveDerefZdd( dd, zP1 );
+                return NULL;
+            }
+            cuddRef( zResP );
+            Cudd_RecursiveDerefZdd( dd, zP1 );
+        }
+        else if ( bF01 == bF1 ) /* unate decreasing */
+        {
+            /* intersection is useless */
+            cuddDeref( bF01 );
+            /* the primes of intersection are the primes of F1 */
+            zResE = zP1;
+            /* there are no primes with positive var */
+            zResP = dd->zero;
+            cuddRef( zResP );
+            /* primes with negative var are primes of F0 that are not primes of F01 */
+            zResN = cuddZddDiff( dd, zP0, zP1 );
+            if ( zResN == NULL )  
+            {
+                Cudd_RecursiveDerefZdd( dd, zResE );
+                Cudd_RecursiveDerefZdd( dd, zResP );
+                Cudd_RecursiveDerefZdd( dd, zP0 );
+                return NULL;
+            }
+            cuddRef( zResN );
+            Cudd_RecursiveDerefZdd( dd, zP0 );
+        }
+        else /* not unate */
+        {
+            /* primes without the top var are primes of F10 */
+            zResE = extraZddPrimes( dd, bF01 );
+            if ( zResE == NULL )  
+            {
+                Cudd_RecursiveDerefZdd( dd, bF01 );
+                Cudd_RecursiveDerefZdd( dd, zP0 );
+                Cudd_RecursiveDerefZdd( dd, zP1 );
+                return NULL;
+            }
+            cuddRef( zResE );
+            Cudd_RecursiveDeref( dd, bF01 );
+
+            /* primes with the negative top var are those of P0 that are not in F10 */
+            zResN = cuddZddDiff( dd, zP0, zResE );
+            if ( zResN == NULL )  
+            {
+                Cudd_RecursiveDerefZdd( dd, zResE );
+                Cudd_RecursiveDerefZdd( dd, zP0 );
+                Cudd_RecursiveDerefZdd( dd, zP1 );
+                return NULL;
+            }
+            cuddRef( zResN );
+            Cudd_RecursiveDerefZdd( dd, zP0 );
+
+            /* primes with the positive top var are those of P1 that are not in F10 */
+            zResP = cuddZddDiff( dd, zP1, zResE );
+            if ( zResP == NULL )  
+            {
+                Cudd_RecursiveDerefZdd( dd, zResE );
+                Cudd_RecursiveDerefZdd( dd, zResN );
+                Cudd_RecursiveDerefZdd( dd, zP1 );
+                return NULL;
+            }
+            cuddRef( zResP );
+            Cudd_RecursiveDerefZdd( dd, zP1 );
+        }
+
+        zRes = extraComposeCover( dd, zResN, zResP, zResE, Cudd_Regular(F)->index );
+        if ( zRes == NULL ) return NULL;
+
+        /* insert the result into cache */
+        cuddCacheInsert1(dd, extraZddPrimes, F, zRes);
+        return zRes;
+    }
+} /* end of extraZddPrimes */
+
+/**Function********************************************************************
+
+  Synopsis    [Implements the recursive step of Cudd_bddPermute.]
+
+  Description [ Recursively puts the BDD in the order given in the array permut.
+  Checks for trivial cases to terminate recursion, then splits on the
+  children of this node.  Once the solutions for the children are
+  obtained, it puts into the current position the node from the rest of
+  the BDD that should be here. Then returns this BDD.
+  The key here is that the node being visited is NOT put in its proper
+  place by this instance, but rather is switched when its proper position
+  is reached in the recursion tree.<p>
+  The DdNode * that is returned is the same BDD as passed in as node,
+  but in the new order.]
+
+  SideEffects [None]
+
+  SeeAlso     [Cudd_bddPermute cuddAddPermuteRecur]
+
+******************************************************************************/
+static DdNode *
+cuddBddPermuteRecur( DdManager * manager /* DD manager */ ,
+                     DdHashTable * table /* computed table */ ,
+                     DdNode * node /* BDD to be reordered */ ,
+                     int *permut /* permutation array */  )
+{
+    DdNode *N, *T, *E;
+    DdNode *res;
+    int index;
+
+    statLine( manager );
+    N = Cudd_Regular( node );
+
+    /* Check for terminal case of constant node. */
+    if ( cuddIsConstant( N ) )
+    {
+        return ( node );
+    }
+
+    /* If problem already solved, look up answer and return. */
+    if ( N->ref != 1 && ( res = cuddHashTableLookup1( table, N ) ) != NULL )
+    {
+        return ( Cudd_NotCond( res, N != node ) );
+    }
+
+    /* Split and recur on children of this node. */
+    T = cuddBddPermuteRecur( manager, table, cuddT( N ), permut );
+    if ( T == NULL )
+        return ( NULL );
+    cuddRef( T );
+    E = cuddBddPermuteRecur( manager, table, cuddE( N ), permut );
+    if ( E == NULL )
+    {
+        Cudd_IterDerefBdd( manager, T );
+        return ( NULL );
+    }
+    cuddRef( E );
+
+    /* Move variable that should be in this position to this position
+       ** by retrieving the single var BDD for that variable, and calling
+       ** cuddBddIteRecur with the T and E we just created.
+     */
+    index = permut[N->index];
+    res = cuddBddIteRecur( manager, manager->vars[index], T, E );
+    if ( res == NULL )
+    {
+        Cudd_IterDerefBdd( manager, T );
+        Cudd_IterDerefBdd( manager, E );
+        return ( NULL );
+    }
+    cuddRef( res );
+    Cudd_IterDerefBdd( manager, T );
+    Cudd_IterDerefBdd( manager, E );
+
+    /* Do not keep the result if the reference count is only 1, since
+       ** it will not be visited again.
+     */
+    if ( N->ref != 1 )
+    {
+        ptrint fanout = ( ptrint ) N->ref;
+        cuddSatDec( fanout );
+        if ( !cuddHashTableInsert1( table, N, res, fanout ) )
+        {
+            Cudd_IterDerefBdd( manager, res );
+            return ( NULL );
+        }
+    }
+    cuddDeref( res );
+    return ( Cudd_NotCond( res, N != node ) );
+
+}                                /* end of cuddBddPermuteRecur */
+
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the reordering-sensitive step of Extra_bddChangePolarity().]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+DdNode * extraBddChangePolarity( 
+  DdManager * dd,    /* the DD manager */
+  DdNode * bFunc, 
+  DdNode * bVars) 
+{
+    DdNode * bRes;
+
+    if ( bVars == b1 )
+        return bFunc;
+    if ( Cudd_IsConstant(bFunc) )
+        return bFunc;
+
+    if ( (bRes = cuddCacheLookup2(dd, extraBddChangePolarity, bFunc, bVars)) )
+        return bRes;
+    else
+    {
+        DdNode * bFR = Cudd_Regular(bFunc); 
+        int LevelF   = dd->perm[bFR->index];
+        int LevelV   = dd->perm[bVars->index];
+
+        if ( LevelV < LevelF )
+            bRes = extraBddChangePolarity( dd, bFunc, cuddT(bVars) );
+        else // if ( LevelF <= LevelV )
+        {
+            DdNode * bRes0, * bRes1;             
+            DdNode * bF0, * bF1;             
+            DdNode * bVarsNext;
+
+            // cofactor the functions
+            if ( bFR != bFunc ) // bFunc is complemented 
+            {
+                bF0 = Cudd_Not( cuddE(bFR) );
+                bF1 = Cudd_Not( cuddT(bFR) );
+            }
+            else
+            {
+                bF0 = cuddE(bFR);
+                bF1 = cuddT(bFR);
+            }
+
+            if ( LevelF == LevelV )
+                bVarsNext = cuddT(bVars);
+            else
+                bVarsNext = bVars;
+
+            bRes0 = extraBddChangePolarity( dd, bF0, bVarsNext );
+            if ( bRes0 == NULL ) 
+                return NULL;
+            cuddRef( bRes0 );
+
+            bRes1 = extraBddChangePolarity( dd, bF1, bVarsNext );
+            if ( bRes1 == NULL ) 
+            {
+                Cudd_RecursiveDeref( dd, bRes0 );
+                return NULL;
+            }
+            cuddRef( bRes1 );
+
+            if ( LevelF == LevelV )
+            { // swap the cofactors
+                DdNode * bTemp;
+                bTemp = bRes0;
+                bRes0 = bRes1;
+                bRes1 = bTemp;
+            }
+
+            /* only aRes0 and aRes1 are referenced at this point */
+
+            /* consider the case when Res0 and Res1 are the same node */
+            if ( bRes0 == bRes1 )
+                bRes = bRes1;
+            /* consider the case when Res1 is complemented */
+            else if ( Cudd_IsComplement(bRes1) ) 
+            {
+                bRes = cuddUniqueInter(dd, bFR->index, Cudd_Not(bRes1), Cudd_Not(bRes0));
+                if ( bRes == NULL ) 
+                {
+                    Cudd_RecursiveDeref(dd,bRes0);
+                    Cudd_RecursiveDeref(dd,bRes1);
+                    return NULL;
+                }
+                bRes = Cudd_Not(bRes);
+            } 
+            else 
+            {
+                bRes = cuddUniqueInter( dd, bFR->index, bRes1, bRes0 );
+                if ( bRes == NULL ) 
+                {
+                    Cudd_RecursiveDeref(dd,bRes0);
+                    Cudd_RecursiveDeref(dd,bRes1);
+                    return NULL;
+                }
+            }
+            cuddDeref( bRes0 );
+            cuddDeref( bRes1 );
+        }
+            
+        /* insert the result into cache */
+        cuddCacheInsert2(dd, extraBddChangePolarity, bFunc, bVars, bRes);
+        return bRes;
+    }
+} /* end of extraBddChangePolarity */
+
+
+
+static int Counter = 0;
+
+/**Function*************************************************************
+
+  Synopsis    [Computes the AND of two BDD with different orders.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+DdNode * extraBddAndPermute( DdHashTable * table, DdManager * ddF, DdNode * bF, DdManager * ddG, DdNode * bG, int * pPermute )
+{
+    DdNode * bF0, * bF1, * bG0, * bG1, * bRes0, * bRes1, * bRes, * bVar;
+    int LevF, LevG, Lev;
+
+    // if F == 0, return 0 
+    if ( bF == Cudd_Not(ddF->one) )
+        return Cudd_Not(ddF->one);
+    // if G == 0, return 0 
+    if ( bG == Cudd_Not(ddG->one) )
+        return Cudd_Not(ddF->one);
+    // if G == 1, return F
+    if ( bG == ddG->one )
+        return bF;
+    // cannot use F == 1, because the var order of G has to be changed
+
+    // check cache
+    if ( //(Cudd_Regular(bF)->ref != 1 || Cudd_Regular(bG)->ref != 1) && 
+         (bRes = cuddHashTableLookup2(table, bF, bG)) )
+        return bRes;
+    Counter++;
+
+    if ( ddF->TimeStop && Abc_Clock() > ddF->TimeStop )
+        return NULL;
+    if ( ddG->TimeStop && Abc_Clock() > ddG->TimeStop )
+        return NULL;
+
+    // find the topmost variable in F and G using var order of F
+    LevF = cuddI( ddF, Cudd_Regular(bF)->index );
+    LevG = cuddI( ddF, pPermute ? pPermute[Cudd_Regular(bG)->index] : Cudd_Regular(bG)->index );
+    Lev  = Abc_MinInt( LevF, LevG );
+    assert( Lev < ddF->size );
+    bVar = ddF->vars[ddF->invperm[Lev]];
+
+    // cofactor
+    bF0 = (Lev < LevF) ? bF : Cudd_NotCond( cuddE(Cudd_Regular(bF)), Cudd_IsComplement(bF) );
+    bF1 = (Lev < LevF) ? bF : Cudd_NotCond( cuddT(Cudd_Regular(bF)), Cudd_IsComplement(bF) );
+    bG0 = (Lev < LevG) ? bG : Cudd_NotCond( cuddE(Cudd_Regular(bG)), Cudd_IsComplement(bG) );
+    bG1 = (Lev < LevG) ? bG : Cudd_NotCond( cuddT(Cudd_Regular(bG)), Cudd_IsComplement(bG) );
+
+    // call for cofactors
+    bRes0 = extraBddAndPermute( table, ddF, bF0, ddG, bG0, pPermute );
+    if ( bRes0 == NULL ) 
+        return NULL;
+    cuddRef( bRes0 );
+    // call for cofactors
+    bRes1 = extraBddAndPermute( table, ddF, bF1, ddG, bG1, pPermute );
+    if ( bRes1 == NULL ) 
+    {
+        Cudd_IterDerefBdd( ddF, bRes0 );
+        return NULL;
+    }
+    cuddRef( bRes1 );
+
+    // compose the result
+    bRes = cuddBddIteRecur( ddF, bVar, bRes1, bRes0 );
+    if ( bRes == NULL )
+    {
+        Cudd_IterDerefBdd( ddF, bRes0 );
+        Cudd_IterDerefBdd( ddF, bRes1 );
+        return NULL;
+    }
+    cuddRef( bRes );
+    Cudd_IterDerefBdd( ddF, bRes0 );
+    Cudd_IterDerefBdd( ddF, bRes1 );
+
+    // cache the result
+//    if ( Cudd_Regular(bF)->ref != 1 || Cudd_Regular(bG)->ref != 1 )
+    {
+        ptrint fanout = (ptrint)Cudd_Regular(bF)->ref * Cudd_Regular(bG)->ref;
+        cuddSatDec(fanout);
+        cuddHashTableInsert2( table, bF, bG, bRes, fanout );
+    }
+    cuddDeref( bRes );
+    return bRes;
+} 
+
+/**Function*************************************************************
+
+  Synopsis    [Testbench.]
+
+  Description [This procedure takes BDD manager ddF and two BDDs
+  in this manager (bF and bG).  It creates a new manager ddG,
+  transfers bG into it and then reorders it, resulting in bG2.
+  Then it tries to compute the product of bF and bG2 in ddF.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Extra_TestAndPerm( DdManager * ddF, DdNode * bF, DdNode * bG )
+{
+    DdManager * ddG;
+    DdNode * bG2, * bRes1, * bRes2;
+    abctime clk;
+    // disable variable ordering in ddF
+    Cudd_AutodynDisable( ddF );
+
+    // create new BDD manager
+    ddG = Cudd_Init( ddF->size, 0, CUDD_UNIQUE_SLOTS, CUDD_CACHE_SLOTS, 0 );
+    // transfer BDD into it
+    Cudd_ShuffleHeap( ddG, ddF->invperm );
+    bG2 = Extra_TransferLevelByLevel( ddF, ddG, bG );   Cudd_Ref( bG2 );
+    // reorder the new manager
+    Cudd_ReduceHeap( ddG, CUDD_REORDER_SYMM_SIFT, 1 );
+
+    // compute the result
+clk = Abc_Clock();
+    bRes1 = Cudd_bddAnd( ddF, bF, bG );                 Cudd_Ref( bRes1 );
+Abc_PrintTime( 1, "Runtime of Cudd_bddAnd  ", Abc_Clock() - clk );
+
+    // compute the result
+Counter = 0;
+clk = Abc_Clock();
+    bRes2 = Extra_bddAndPermute( ddF, bF, ddG, bG2, NULL );      Cudd_Ref( bRes2 );
+Abc_PrintTime( 1, "Runtime of new procedure", Abc_Clock() - clk );
+printf( "Recursive calls = %d\n", Counter );
+printf( "|F| =%6d  |G| =%6d  |H| =%6d  |F|*|G| =%9d  ", 
+       Cudd_DagSize(bF), Cudd_DagSize(bG), Cudd_DagSize(bRes2), 
+       Cudd_DagSize(bF) * Cudd_DagSize(bG) );
+
+    if ( bRes1 == bRes2 )
+        printf( "Result verified.\n\n" );
+    else
+        printf( "Result is incorrect.\n\n" );
+
+    Cudd_RecursiveDeref( ddF, bRes1 );
+    Cudd_RecursiveDeref( ddF, bRes2 );
+    // quit the new manager
+    Cudd_RecursiveDeref( ddG, bG2 );
+    Extra_StopManager( ddG );
+
+    // re-enable variable ordering in ddF
+    Cudd_AutodynEnable( ddF, CUDD_REORDER_SYMM_SIFT );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Writes ZDD into a PLA file.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Extra_zddDumpPla( DdManager * dd, DdNode * F, int nVars, char * pFileName )
+{
+    DdGen *gen;
+    char * pCube;
+    int * pPath, i;
+    FILE * pFile = fopen( pFileName, "wb" );
+    if ( pFile == NULL )
+    {
+        printf( "Cannot open file \"%s\" for writing.\n", pFileName );
+        return;
+    }
+    fprintf( pFile, "# PLA file dumped by Extra_zddDumpPla() in ABC\n" );
+    fprintf( pFile, ".i %d\n", nVars );
+    fprintf( pFile, ".o 1\n" );
+    pCube = ABC_CALLOC( char, dd->sizeZ );
+    Cudd_zddForeachPath( dd, F, gen, pPath )
+    {
+        for ( i = 0; i < nVars; i++ )
+            pCube[i] = '-';
+        for ( i = 0; i < nVars; i++ )
+            if ( pPath[2*i] == 1 || pPath[2*i+1] == 1 )
+                pCube[i] = '0' + (pPath[2*i] == 1);
+        fprintf( pFile, "%s 1\n", pCube );           
+    }
+    fprintf( pFile, ".e\n\n" );
+    fclose( pFile );
+    ABC_FREE( pCube );
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+