extraBddCas.c File Reference

#include "extraBdd.h"

Go to the source code of this file.

Data Structures
struct	_HashEntry_cof
struct	_HashEntry_mint
struct	traventry

Macros
#define	_TABLESIZE_COF   51113
#define	_TABLESIZE_MINT   15113

Functions
static DdNode *	CreateTheCodes_rec (DdManager *dd, DdNode *bEncoded, int Level, DdNode **pCVars)
static void	EvaluateEncodings_rec (DdManager *dd, DdNode *bVarsCol, int nVarsCol, int nMulti, int Level)
static DdNode *	ComputeVarSetAndCountMinterms (DdManager *dd, DdNode *bVars, DdNode *bVarTop, unsigned *Cost)
static DdNode *	ComputeVarSetAndCountMinterms2 (DdManager *dd, DdNode *bVars, DdNode *bVarTop, unsigned *Cost)
unsigned	Extra_CountCofactorMinterms (DdManager *dd, DdNode *bFunc, DdNode *bVarsCof, DdNode *bVarsAll)
static unsigned	Extra_CountMintermsSimple (DdNode *bFunc, unsigned max)
static void	CountNodeVisits_rec (DdManager *dd, DdNode *aFunc, st__table *Visited)
static void	CollectNodesAndComputePaths_rec (DdManager *dd, DdNode *aFunc, DdNode *bCube, st__table *Visited, st__table *CutNodes)
DdNode *	Extra_bddEncodingBinary (DdManager *dd, DdNode **pbFuncs, int nFuncs, DdNode **pbVars, int nVars)
DdNode *	Extra_bddEncodingNonStrict (DdManager *dd, DdNode **pbColumns, int nColumns, DdNode *bVarsCol, DdNode **pCVars, int nMulti, int *pSimple)
st__table *	Extra_bddNodePathsUnderCut (DdManager *dd, DdNode *bFunc, int CutLevel)
int	Extra_bddNodePathsUnderCutArray (DdManager *dd, DdNode **paNodes, DdNode **pbCubes, int nNodes, DdNode **paNodesRes, DdNode **pbCubesRes, int CutLevel)
void	extraCollectNodes (DdNode *Func, st__table *tNodes)
st__table *	Extra_CollectNodes (DdNode *Func)
void	extraProfileUpdateTopLevel (st__table *tNodeTopRef, int TopLevelNew, DdNode *node)
int	Extra_ProfileWidth (DdManager *dd, DdNode *Func, int *pProfile, int CutLevel)

Variables
_HashEntry_cof	HHTable1 [_TABLESIZE_COF]
_HashEntry_mint	HHTable2 [_TABLESIZE_MINT]
static unsigned	s_Signature = 1
static int	s_CutLevel = 0
static int	s_MaxDepth = 5
static int	s_nVarsBest
static int	s_VarOrderBest [32]
static int	s_VarOrderCur [32]
static DdNode *	s_Field [8][256]
static DdNode *	s_Encoded
static DdNode *	s_VarAll
static int	s_MultiStart
static DdNode **	s_pbTemp
static int	s_BackTracks
static int	s_BackTrackLimit = 100
static DdNode *	s_Terminal
static int	s_EncodingVarsLevel

Macro Definition Documentation

#define _TABLESIZE_COF   51113

CFile****************************************************************

FileName [extraBddCas.c]

PackageName [extra]

Synopsis [Procedures related to LUT cascade synthesis.]

Author [Alan Mishchenko]

Affiliation [UC Berkeley]

Date [Ver. 2.0. Started - September 1, 2003.]

Revision [

Id:

extraBddCas.c,v 1.0 2003/05/21 18:03:50 alanmi Exp

]

Definition at line 37 of file extraBddCas.c.

#define _TABLESIZE_MINT   15113

Definition at line 46 of file extraBddCas.c.

Function Documentation

void CollectNodesAndComputePaths_rec ( DdManager *  dd, DdNode *  aFunc, DdNode *  bCube, st__table *  Visited, st__table *  CutNodes  )

static

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

Synopsis [Revisits the nodes and computes the paths.]

Description [This function visits the nodes above the cut having the goal of summing all the incomming BDD edges; when this function comes across the node below the cut, it saves this node in the CutNode table.]

SideEffects []

SeeAlso []

Definition at line 1159 of file extraBddCas.c.

{   
    // find the node in the visited table
    DdNode * bTemp;
    traventry * p;
    char **slot;
    if ( st__find_or_add(Visited, (char*)aFunc, &slot) )
    { // the node is found
        // get the pointer to the traversal entry
        p = (traventry*) *slot;

        // make sure that the counter of incoming edges is positive
        assert( p->nEdges > 0 );

        // add the cube to the currently accumulated cubes
        p->bSum = Cudd_bddOr( dd, bTemp = p->bSum, bCube );  Cudd_Ref( p->bSum );
        Cudd_RecursiveDeref( dd, bTemp );

        // decrement the number of visits
        p->nEdges--;

        // if more visits to this node are expected, return
        if ( p->nEdges ) 
            return;
        else // if ( p->nEdges == 0 )
        { // this is the last visit - propagate the cube

            // check where this node is
            if ( cuddI(dd,aFunc->index) < s_CutLevel )
            { // the node is above the cut
                DdNode * bCube0, * bCube1;

                // get the top-most variable
                DdNode * bVarTop = dd->vars[aFunc->index];

                // compute the propagated cubes
                bCube0 = Cudd_bddAnd( dd, p->bSum, Cudd_Not( bVarTop ) );   Cudd_Ref( bCube0 );
                bCube1 = Cudd_bddAnd( dd, p->bSum,           bVarTop   );   Cudd_Ref( bCube1 );

                // call recursively
                CollectNodesAndComputePaths_rec( dd, cuddE(aFunc), bCube0, Visited, CutNodes );
                CollectNodesAndComputePaths_rec( dd, cuddT(aFunc), bCube1, Visited, CutNodes );

                // dereference the cubes
                Cudd_RecursiveDeref( dd, bCube0 );
                Cudd_RecursiveDeref( dd, bCube1 );
                return;
            }
            else
            { // the node is below the cut
                // add this node to the cut node table, if it is not yet there

//              DdNode * bNode;
//              bNode = Cudd_addBddPattern( dd, aFunc );  Cudd_Ref( bNode );
                if ( st__find_or_add(CutNodes, (char*)aFunc, &slot) )
                { // the node exists - should never happen
                    assert( 0 );
                }
                *slot = (char*) p->bSum;   Cudd_Ref( p->bSum );
                // the table takes the reference of bNode
                return;
            }
        }
    }

    // the node does not exist in the visited table - should never happen
    assert(0);

} /* end of CollectNodesAndComputePaths_rec */

DdNode * ComputeVarSetAndCountMinterms ( DdManager *  dd, DdNode *  bVars, DdNode *  bVarTop, unsigned *  Cost  )

static

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

Synopsis [Computes the current set of variables and counts the number of minterms.]

Description []

SideEffects []

SeeAlso []

Definition at line 852 of file extraBddCas.c.

{
    DdNode * bVarsRes;

    // get the resulting set of variables
    bVarsRes = Cudd_bddAnd( dd, bVars, bVarTop );  Cudd_Ref( bVarsRes );

    // increment signature before calling Cudd_CountCofactorMinterms()
    s_Signature++;
    *Cost = Extra_CountCofactorMinterms( dd, s_Encoded, bVarsRes, s_VarAll );

    Cudd_Deref( bVarsRes );
//  s_CountCalls++;
    return bVarsRes;
}

DdNode * ComputeVarSetAndCountMinterms2 ( DdManager *  dd, DdNode *  bVars, DdNode *  bVarTop, unsigned *  Cost  )

static

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

Synopsis [Computes the current set of variables and counts the number of minterms.]

Description [The old implementation, which is approximately 4 times slower.]

SideEffects []

SeeAlso []

Definition at line 882 of file extraBddCas.c.

{
    DdNode * bVarsRes;
    DdNode * bCof, * bFun;

    bVarsRes = Cudd_bddAnd( dd, bVars, bVarTop );             Cudd_Ref( bVarsRes );

    bCof  = Cudd_Cofactor( dd, s_Encoded,  bVarsRes );        Cudd_Ref( bCof );
    bFun  = Cudd_bddExistAbstract( dd, bCof, s_VarAll );      Cudd_Ref( bFun );
    *Cost = (unsigned)Cudd_CountMinterm( dd, bFun, s_MultiStart );
    Cudd_RecursiveDeref( dd, bFun );
    Cudd_RecursiveDeref( dd, bCof );

    Cudd_Deref( bVarsRes );
//  s_CountCalls++;
    return bVarsRes;
}

void CountNodeVisits_rec ( DdManager *  dd, DdNode *  aFunc, st__table *  Visited  )

static

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

Synopsis [Visits the nodes.]

Description [Visits the nodes above the cut and the nodes pointed to below the cut; collects the visited nodes, counts how many times each node is visited, and sets the path-sum to be the constant zero BDD.]

SideEffects []

SeeAlso []

Definition at line 1113 of file extraBddCas.c.

{
    traventry * p;
    char **slot;
    if ( st__find_or_add(Visited, (char*)aFunc, &slot) )
    { // the entry already exists
        p = (traventry*) *slot;
        // increment the counter of incoming edges
        p->nEdges++;
        return; 
    }
    // this node has not been visited
    assert( !Cudd_IsComplement(aFunc) );

    // create the new traversal entry
    p = (traventry *) ABC_ALLOC( char, sizeof(traventry) );
    // set the initial sum of edges to zero BDD
    p->bSum = b0;   Cudd_Ref( b0 );
    // set the starting number of incoming edges
    p->nEdges = 1;
    // set this entry into the slot
    *slot = (char*)p;

    // recur if the node is above the cut
    if ( cuddI(dd,aFunc->index) < s_CutLevel )
    {
        CountNodeVisits_rec( dd, cuddE(aFunc), Visited );
        CountNodeVisits_rec( dd, cuddT(aFunc), Visited );
    }
} /* end of CountNodeVisits_rec */

DdNode * CreateTheCodes_rec ( DdManager *  dd, DdNode *  bEncoded, int  Level, DdNode **  pCVars  )

static

AutomaticStart

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

Synopsis [Computes the non-strict codes when evaluation is finished.]

Description [The information about the best code is stored in s_VarOrderBest, which has s_nVarsBest entries.]

SideEffects [None]

Definition at line 599 of file extraBddCas.c.

{
    DdNode * bRes;
    if ( Level == s_nVarsBest )
    { // the terminal case, when we need to remap the encoded function 
        // from the preliminary encoded variables to the new ones
        st__table * CutNodes;
        int nCols;
//      double nMints;
/*
#ifdef _DEBUG

        {
        DdNode * bTemp;
        // make sure that the given number of variables is enough
        bTemp  = Cudd_bddExistAbstract( dd, bEncoded, s_VarAll );           Cudd_Ref( bTemp );
//      nMints = Cudd_CountMinterm( dd, bTemp, s_MultiStart );
        nMints = Extra_CountMintermsSimple( bTemp, (1<<s_MultiStart) );
        if ( nMints > Extra_Power2( s_MultiStart-Level ) ) 
        {  // the number of minterms is too large to encode the columns 
           // using the given minimum number of encoding variables
            assert( 0 );
        }
        Cudd_RecursiveDeref( dd, bTemp );
        }
#endif
*/
        // get the columns to be re-encoded
        CutNodes = Extra_bddNodePathsUnderCut( dd, bEncoded, s_EncodingVarsLevel );
        // LUT size is the cut level because because the temporary encoding variables 
        // are above the functional variables - this is not true!!!
        // the temporary variables are below!

        // put the entries from the table into the temporary array
        { 
            st__generator * gen;
            DdNode * bColumn, * bCode;
            nCols = 0;
            st__foreach_item( CutNodes, gen, (const char**)&bCode, (char**)&bColumn )
            {
                if ( bCode == b0 )
                { // the unused part of the columns
                    Cudd_RecursiveDeref( dd, bColumn );
                    Cudd_RecursiveDeref( dd, bCode );
                    continue;
                }
                else
                {
                    s_pbTemp[ nCols ] = bColumn; // takes ref
                    Cudd_RecursiveDeref( dd, bCode );
                    nCols++;
                }
            }
            st__free_table( CutNodes );
//          assert( nCols == (int)nMints );
        }

        // encode the columns
        if ( s_MultiStart-Level == 0 ) // we reached the bottom level of recursion
        {
            assert( nCols       == 1 );
//          assert( (int)nMints == 1 );
            bRes = s_pbTemp[0];     Cudd_Ref( bRes );
        }
        else
        {
            bRes = Extra_bddEncodingBinary( dd, s_pbTemp, nCols, pCVars+Level, s_MultiStart-Level ); Cudd_Ref( bRes );
        }

        // deref the columns
        {
            int i;
            for ( i = 0; i < nCols; i++ )
                Cudd_RecursiveDeref( dd, s_pbTemp[i] );
        }
    }
    else
    {
        // cofactor the problem as specified in the best solution
        DdNode * bCof0,  * bCof1;
        DdNode * bRes0,  * bRes1;
        DdNode * bProd0, * bProd1;
        DdNode * bTemp;
        DdNode * bVarNext = dd->vars[ s_VarOrderBest[Level] ];

        bCof0  = Cudd_Cofactor( dd, bEncoded,  Cudd_Not( bVarNext ) );   Cudd_Ref( bCof0 );
        bCof1  = Cudd_Cofactor( dd, bEncoded,            bVarNext   );   Cudd_Ref( bCof1 );

        // call recursively
        bRes0 = CreateTheCodes_rec( dd, bCof0, Level+1, pCVars );  Cudd_Ref( bRes0 );
        bRes1 = CreateTheCodes_rec( dd, bCof1, Level+1, pCVars );  Cudd_Ref( bRes1 );

        Cudd_RecursiveDeref( dd, bCof0 );
        Cudd_RecursiveDeref( dd, bCof1 );

        // compose the result using the identity (bVarNext <=> pCVars[Level])  - this is wrong!
        // compose the result as follows: x'y'F0 + xyF1
        bProd0 = Cudd_bddAnd( dd, Cudd_Not(bVarNext), Cudd_Not(pCVars[Level]) );   Cudd_Ref( bProd0 );
        bProd1 = Cudd_bddAnd( dd,          bVarNext ,          pCVars[Level]  );   Cudd_Ref( bProd1 );

        bProd0 = Cudd_bddAnd( dd, bTemp = bProd0, bRes0 );   Cudd_Ref( bProd0 );
        Cudd_RecursiveDeref( dd, bTemp );
        Cudd_RecursiveDeref( dd, bRes0 );

        bProd1 = Cudd_bddAnd( dd, bTemp = bProd1, bRes1 );   Cudd_Ref( bProd1 );
        Cudd_RecursiveDeref( dd, bTemp );
        Cudd_RecursiveDeref( dd, bRes1 );

        bRes = Cudd_bddOr( dd, bProd0, bProd1 );             Cudd_Ref( bRes );

        Cudd_RecursiveDeref( dd, bProd0 );
        Cudd_RecursiveDeref( dd, bProd1 );
    }
    Cudd_Deref( bRes );
    return bRes;
}

void EvaluateEncodings_rec ( DdManager *  dd, DdNode *  bVarsCol, int  nVarsCol, int  nMulti, int  Level  )

static

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

Synopsis [Computes the current set of variables and counts the number of minterms.]

Description [Old implementation.]

SideEffects []

SeeAlso []

Definition at line 730 of file extraBddCas.c.

{
    int i, k;
    int nEntries = (1<<(Level-1)); // the number of entries in the field of the previous level
    DdNode * bVars0, * bVars1; // the cofactors
    unsigned nMint0, nMint1;   // the number of minterms
    DdNode * bTempV;
    DdNode * bVarTop;
    int fBreak;


    // there is no need to search above this level
    if ( Level > s_MaxDepth )
        return;

    // if there are no variables left, quit the research
    if ( bVarsCol == b1 )
        return;

    if ( s_BackTracks > s_BackTrackLimit )
        return;

    s_BackTracks++;

    // otherwise, go through the remaining variables
    for ( bTempV = bVarsCol; bTempV != b1; bTempV = cuddT(bTempV) )
    {
        // the currently tested variable
        bVarTop = dd->vars[bTempV->index];

        // put it into the array
        s_VarOrderCur[Level-1] = bTempV->index;

        // go through the entries and fill them out by cofactoring
        fBreak = 0;
        for ( i = 0; i < nEntries; i++ )
        {
            bVars0 = ComputeVarSetAndCountMinterms( dd, s_Field[Level-1][i], Cudd_Not(bVarTop), &nMint0 );
            Cudd_Ref( bVars0 );

            if ( nMint0 > Extra_Power2( nMulti-1 ) ) 
            {
                // there is no way to encode - dereference and return
                Cudd_RecursiveDeref( dd, bVars0 );
                fBreak = 1;
                break;
            }

            bVars1 = ComputeVarSetAndCountMinterms( dd, s_Field[Level-1][i], bVarTop, &nMint1 );
            Cudd_Ref( bVars1 );

            if ( nMint1 > Extra_Power2( nMulti-1 ) ) 
            {
                // there is no way to encode - dereference and return
                Cudd_RecursiveDeref( dd, bVars0 );
                Cudd_RecursiveDeref( dd, bVars1 );
                fBreak = 1;
                break;
            }

            // otherwise, add these two cofactors
            s_Field[Level][2*i + 0] = bVars0; // takes ref
            s_Field[Level][2*i + 1] = bVars1; // takes ref
        } 

        if ( !fBreak )
        {
            DdNode * bVarsRem;
            // if we ended up here, it means that the cofactors w.r.t. variable bVarTop satisfy the condition
            // save this situation
            if ( s_nVarsBest < Level )
            {
                s_nVarsBest = Level;
                // copy the variable assignment
                for ( k = 0; k < Level; k++ )
                    s_VarOrderBest[k] = s_VarOrderCur[k];
            }

            // call recursively
            // get the new variable set
            if ( nMulti-1 > 0 )
            {
                bVarsRem = Cudd_bddExistAbstract( dd, bVarsCol, bVarTop );   Cudd_Ref( bVarsRem );
                EvaluateEncodings_rec( dd, bVarsRem, nVarsCol-1, nMulti-1, Level+1 );
                Cudd_RecursiveDeref( dd, bVarsRem );
            }
        }

        // deref the contents of the array
        for ( k = 0; k < i; k++ )
        {
            Cudd_RecursiveDeref( dd, s_Field[Level][2*k + 0] );
            Cudd_RecursiveDeref( dd, s_Field[Level][2*k + 1] );
        }

        // if the solution is found, there is no need to continue
        if ( s_nVarsBest == s_MaxDepth )
            return;

        // if the solution is found, there is no need to continue
        if ( s_nVarsBest == s_MultiStart )
            return;
    }
    // at this point, we have tried all possible directions in the space of variables
}

DdNode* Extra_bddEncodingBinary	(	DdManager *	dd,
		DdNode **	pbFuncs,
		int	nFuncs,
		DdNode **	pbVars,
		int	nVars
	)

AutomaticEnd Function********************************************************************

Synopsis [Performs the binary encoding of the set of function using the given vars.]

Description [Performs a straight binary encoding of the set of functions using the variable cubes formed from the given set of variables. ]

SideEffects []

SeeAlso []

Definition at line 138 of file extraBddCas.c.

{
    int i;
    DdNode * bResult;
    DdNode * bCube, * bTemp, * bProd;

    assert( nVars >= Abc_Base2Log(nFuncs) );

    bResult = b0;   Cudd_Ref( bResult );
    for ( i = 0; i < nFuncs; i++ )
    {
        bCube   = Extra_bddBitsToCube( dd, i, nVars, pbVars, 1 );   Cudd_Ref( bCube );
        bProd   = Cudd_bddAnd( dd, bCube, pbFuncs[i] );         Cudd_Ref( bProd );
        Cudd_RecursiveDeref( dd, bCube );

        bResult = Cudd_bddOr( dd, bProd, bTemp = bResult );     Cudd_Ref( bResult );
        Cudd_RecursiveDeref( dd, bTemp );
        Cudd_RecursiveDeref( dd, bProd );
    }

    Cudd_Deref( bResult );
    return bResult;
} /* end of Extra_bddEncodingBinary */

DdNode* Extra_bddEncodingNonStrict	(	DdManager *	dd,
		DdNode **	pbColumns,
		int	nColumns,
		DdNode *	bVarsCol,
		DdNode **	pCVars,
		int	nMulti,
		int *	pSimple
	)

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

Synopsis [Solves the column encoding problem using a sophisticated method.]

Description [The encoding is based on the idea of deriving functions which depend on only one variable, which corresponds to the case of non-disjoint decompostion. It is assumed that the variables pCVars are ordered below the variables representing the solumns, and the first variable pCVars[0] is the topmost one.]

SideEffects []

SeeAlso [Extra_bddEncodingBinary]

Definition at line 184 of file extraBddCas.c.

{
    DdNode * bEncoded, * bResult;
    int nVarsCol = Cudd_SupportSize(dd,bVarsCol);
    abctime clk;

    // cannot work with more that 32-bit codes
    assert( nMulti < 32 );

    // perform the preliminary encoding using the straight binary code
    bEncoded = Extra_bddEncodingBinary( dd, pbColumns, nColumns, pCVars, nMulti );   Cudd_Ref( bEncoded );
    //printf( "Node count = %d", Cudd_DagSize(bEncoded) );

    // set the backgroup value for counting minterms
    s_Terminal = b0;
    // set the level of the encoding variables
    s_EncodingVarsLevel = dd->invperm[pCVars[0]->index];

    // the current number of backtracks
    s_BackTracks = 0;
    // the variables that are cofactored on the topmost level where everything starts (no vars)
    s_Field[0][0] = b1;   
    // the size of the best set of "simple" encoding variables found so far
    s_nVarsBest   = 0;

    // set the relation to be accessible to traversal procedures
    s_Encoded = bEncoded;
    // the set of all vars to be accessible to traversal procedures
    s_VarAll  = bVarsCol;
    // the column multiplicity
    s_MultiStart  = nMulti;


    clk = Abc_Clock();
    // find the simplest encoding
    if ( nColumns > 2 )
    EvaluateEncodings_rec( dd, bVarsCol, nVarsCol, nMulti, 1 );
//  printf( "The number of backtracks = %d\n", s_BackTracks );
//  s_EncSearchTime += Abc_Clock() - clk;

    // allocate the temporary storage for the columns
    s_pbTemp = (DdNode **)ABC_ALLOC( char, nColumns * sizeof(DdNode *) );

//  clk = Abc_Clock();
    bResult = CreateTheCodes_rec( dd, bEncoded, 0, pCVars );   Cudd_Ref( bResult );
//  s_EncComputeTime += Abc_Clock() - clk;
    
    // delocate the preliminarily encoded set
    Cudd_RecursiveDeref( dd, bEncoded );
//  Cudd_RecursiveDeref( dd, aEncoded );

    ABC_FREE( s_pbTemp );

    *pSimple = s_nVarsBest;
    Cudd_Deref( bResult );
    return bResult;
}

st__table* Extra_bddNodePathsUnderCut	(	DdManager *	dd,
		DdNode *	bFunc,
		int	CutLevel
	)

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

Synopsis [Collects the nodes under the cut and, for each node, computes the sum of paths leading to it from the root.]

Description [The table returned contains the set of BDD nodes pointed to under the cut and, for each node, the BDD of the sum of paths leading to this node from the root The sums of paths in the table are referenced. CutLevel is the first DD level considered to be under the cut.]

SideEffects []

SeeAlso [Extra_bddNodePaths]

Definition at line 263 of file extraBddCas.c.

{
    st__table * Visited;  // temporary table to remember the visited nodes
    st__table * CutNodes; // the result goes here
    st__table * Result; // the result goes here
    DdNode * aFunc;

    s_CutLevel = CutLevel;

    Result  = st__init_table( st__ptrcmp, st__ptrhash);;
    // the terminal cases
    if ( Cudd_IsConstant( bFunc ) )
    {
        if ( bFunc == b1 )
        {
            st__insert( Result, (char*)b1, (char*)b1 );
            Cudd_Ref( b1 );
            Cudd_Ref( b1 );
        }
        else
        {
            st__insert( Result, (char*)b0, (char*)b0 );
            Cudd_Ref( b0 );
            Cudd_Ref( b0 );
        }
        return Result;
    }

    // create the ADD to simplify processing (no complemented edges)
    aFunc = Cudd_BddToAdd( dd, bFunc );   Cudd_Ref( aFunc );

    // Step 1: Start the tables and collect information about the nodes above the cut 
    // this information tells how many edges point to each node
    Visited  = st__init_table( st__ptrcmp, st__ptrhash);;
    CutNodes = st__init_table( st__ptrcmp, st__ptrhash);;

    CountNodeVisits_rec( dd, aFunc, Visited );

    // Step 2: Traverse the BDD using the visited table and compute the sum of paths
    CollectNodesAndComputePaths_rec( dd, aFunc, b1, Visited, CutNodes );

    // at this point the table of cut nodes is ready and the table of visited is useless
    {
        st__generator * gen;
        DdNode * aNode;
        traventry * p;
        st__foreach_item( Visited, gen, (const char**)&aNode, (char**)&p )
        {
            Cudd_RecursiveDeref( dd, p->bSum );
            ABC_FREE( p );
        }
        st__free_table( Visited );
    }

    // go through the table CutNodes and create the BDD and the path to be returned
    {
        st__generator * gen;
        DdNode * aNode, * bNode, * bSum;
        st__foreach_item( CutNodes, gen, (const char**)&aNode, (char**)&bSum)
        {
            // aNode is not referenced, because aFunc is holding it
            bNode = Cudd_addBddPattern( dd, aNode );  Cudd_Ref( bNode ); 
            st__insert( Result, (char*)bNode, (char*)bSum );
            // the new table takes both refs
        }
        st__free_table( CutNodes );
    }

    // dereference the ADD
    Cudd_RecursiveDeref( dd, aFunc );

    // return the table
    return Result;

} /* end of Extra_bddNodePathsUnderCut */

int Extra_bddNodePathsUnderCutArray	(	DdManager *	dd,
		DdNode **	paNodes,
		DdNode **	pbCubes,
		int	nNodes,
		DdNode **	paNodesRes,
		DdNode **	pbCubesRes,
		int	CutLevel
	)

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

Synopsis [Collects the nodes under the cut in the ADD starting from the given set of ADD nodes.]

Description [Takes the array, paNodes, of ADD nodes to start the traversal, the array, pbCubes, of BDD cubes to start the traversal with in each node, and the number, nNodes, of ADD nodes and BDD cubes in paNodes and pbCubes. Returns the number of columns found. Fills in paNodesRes (pbCubesRes) with the set of ADD columns (BDD paths). These arrays should be allocated by the user.]

SideEffects []

SeeAlso [Extra_bddNodePaths]

Definition at line 355 of file extraBddCas.c.

{
    st__table * Visited;  // temporary table to remember the visited nodes
    st__table * CutNodes; // the nodes under the cut go here
    int i, Counter;

    s_CutLevel = CutLevel;

    // there should be some nodes
    assert( nNodes > 0 );
    if ( nNodes == 1 && Cudd_IsConstant( paNodes[0] ) )
    {
        if ( paNodes[0] == a1 )
        {
            paNodesRes[0] = a1;          Cudd_Ref( a1 );
            pbCubesRes[0] = pbCubes[0];  Cudd_Ref( pbCubes[0] );
        }
        else
        {
            paNodesRes[0] = a0;          Cudd_Ref( a0 );
            pbCubesRes[0] = pbCubes[0];  Cudd_Ref( pbCubes[0] );
        }
        return 1;
    }

    // Step 1: Start the table and collect information about the nodes above the cut 
    // this information tells how many edges point to each node
    CutNodes = st__init_table( st__ptrcmp, st__ptrhash);;
    Visited  = st__init_table( st__ptrcmp, st__ptrhash);;

    for ( i = 0; i < nNodes; i++ )
        CountNodeVisits_rec( dd, paNodes[i], Visited );

    // Step 2: Traverse the BDD using the visited table and compute the sum of paths
    for ( i = 0; i < nNodes; i++ )
        CollectNodesAndComputePaths_rec( dd, paNodes[i], pbCubes[i], Visited, CutNodes );

    // at this point, the table of cut nodes is ready and the table of visited is useless
    {
        st__generator * gen;
        DdNode * aNode;
        traventry * p;
        st__foreach_item( Visited, gen, (const char**)&aNode, (char**)&p )
        {
            Cudd_RecursiveDeref( dd, p->bSum );
            ABC_FREE( p );
        }
        st__free_table( Visited );
    }

    // go through the table CutNodes and create the BDD and the path to be returned
    {
        st__generator * gen;
        DdNode * aNode, * bSum;
        Counter = 0;
        st__foreach_item( CutNodes, gen, (const char**)&aNode, (char**)&bSum)
        {
            paNodesRes[Counter] = aNode;   Cudd_Ref( aNode ); 
            pbCubesRes[Counter] = bSum;
            Counter++;
        }
        st__free_table( CutNodes );
    }

    // return the number of cofactors found
    return Counter;

} /* end of Extra_bddNodePathsUnderCutArray */

st__table* Extra_CollectNodes

(

DdNode *

Func

)

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

Synopsis [Collects all the nodes of one DD into the table.]

Description []

SideEffects []

SeeAlso []

Definition at line 458 of file extraBddCas.c.

{
    st__table * tNodes;
    tNodes = st__init_table( st__ptrcmp, st__ptrhash );
    extraCollectNodes( Func, tNodes );
    return tNodes;
}

unsigned Extra_CountCofactorMinterms	(	DdManager *	dd,
		DdNode *	bFunc,
		DdNode *	bVarsCof,
		DdNode *	bVarsAll
	)

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

Synopsis [Counts the number of encoding minterms pointed to by the cofactor of the function.]

Description []

SideEffects [None]

Definition at line 910 of file extraBddCas.c.

{
    unsigned HKey;
    DdNode * bFuncR;

    // if the function is zero, there are no minterms
//  if ( bFunc == b0 )
//      return 0;

//  if ( st__lookup(Visited, (char*)bFunc, NULL) )
//      return 0;

//  HKey = hashKey2c( s_Signature, bFuncR );
//  if ( HHTable1[HKey].Sign == s_Signature && HHTable1[HKey].Arg1 == bFuncR ) // this node is visited
//      return 0;


    // check the hash-table 
    bFuncR = Cudd_Regular(bFunc);
//  HKey = hashKey2( s_Signature, bFuncR, _TABLESIZE_COF );
    HKey = hashKey2( s_Signature, bFunc, _TABLESIZE_COF );
    for ( ;  HHTable1[HKey].Sign == s_Signature; HKey = (HKey+1) % _TABLESIZE_COF )
//      if ( HHTable1[HKey].Arg1 == bFuncR ) // this node is visited
        if ( HHTable1[HKey].Arg1 == bFunc ) // this node is visited
            return 0;


    // if the function is already the code
    if ( dd->perm[bFuncR->index] >= s_EncodingVarsLevel )
    {
//      st__insert(Visited, (char*)bFunc, NULL);

//      HHTable1[HKey].Sign = s_Signature;
//      HHTable1[HKey].Arg1 = bFuncR;

        assert( HHTable1[HKey].Sign != s_Signature );
        HHTable1[HKey].Sign = s_Signature;
//      HHTable1[HKey].Arg1 = bFuncR;
        HHTable1[HKey].Arg1 = bFunc;

        return Extra_CountMintermsSimple( bFunc, (1<<s_MultiStart) );
    }
    else
    {
        DdNode * bFunc0,    * bFunc1;
        DdNode * bVarsCof0, * bVarsCof1;
        DdNode * bVarsCofR = Cudd_Regular(bVarsCof);
        unsigned Res;

        // get the levels
        int LevelF = dd->perm[bFuncR->index];
        int LevelC = cuddI(dd,bVarsCofR->index);
        int LevelA = dd->perm[bVarsAll->index];

        int LevelTop = LevelF;

        if ( LevelTop > LevelC )
             LevelTop = LevelC;

        if ( LevelTop > LevelA )
             LevelTop = LevelA;

        // the top var in the function or in cofactoring vars always belongs to the set of all vars
        assert( !( LevelTop == LevelF || LevelTop == LevelC ) || LevelTop == LevelA );

        // cofactor the function
        if ( LevelTop == LevelF )
        {
            if ( bFuncR != bFunc ) // bFunc is complemented 
            {
                bFunc0 = Cudd_Not( cuddE(bFuncR) );
                bFunc1 = Cudd_Not( cuddT(bFuncR) );
            }
            else
            {
                bFunc0 = cuddE(bFuncR);
                bFunc1 = cuddT(bFuncR);
            }
        }
        else // bVars is higher in the variable order 
            bFunc0 = bFunc1 = bFunc;

        // cofactor the cube
        if ( LevelTop == LevelC )
        {
            if ( bVarsCofR != bVarsCof ) // bFunc is complemented 
            {
                bVarsCof0 = Cudd_Not( cuddE(bVarsCofR) );
                bVarsCof1 = Cudd_Not( cuddT(bVarsCofR) );
            }
            else
            {
                bVarsCof0 = cuddE(bVarsCofR);
                bVarsCof1 = cuddT(bVarsCofR);
            }
        }
        else // bVars is higher in the variable order 
            bVarsCof0 = bVarsCof1 = bVarsCof;

        // there are two cases: 
        // (1) the top variable belongs to the cofactoring variables
        // (2) the top variable does not belong to the cofactoring variables

        // (1) the top variable belongs to the cofactoring variables
        Res = 0;
        if ( LevelTop == LevelC )
        {
            if ( bVarsCof1 == b0 ) // this is a negative cofactor
            {
                if ( bFunc0 != b0 )
                Res = Extra_CountCofactorMinterms( dd, bFunc0, bVarsCof0, cuddT(bVarsAll) );
            }
            else                        // this is a positive cofactor
            {
                if ( bFunc1 != b0 )
                Res = Extra_CountCofactorMinterms( dd, bFunc1, bVarsCof1, cuddT(bVarsAll) );
            }
        }
        else
        {
            if ( bFunc0 != b0 )
            Res += Extra_CountCofactorMinterms( dd, bFunc0, bVarsCof0, cuddT(bVarsAll) );
            
            if ( bFunc1 != b0 )
            Res += Extra_CountCofactorMinterms( dd, bFunc1, bVarsCof1, cuddT(bVarsAll) );
        }

//      st__insert(Visited, (char*)bFunc, NULL);

//      HHTable1[HKey].Sign = s_Signature;
//      HHTable1[HKey].Arg1 = bFuncR;

        // skip through the entries with the same signatures 
        // (these might have been created at the time of recursive calls)
        for ( ; HHTable1[HKey].Sign == s_Signature; HKey = (HKey+1) % _TABLESIZE_COF );
        assert( HHTable1[HKey].Sign != s_Signature );
        HHTable1[HKey].Sign = s_Signature;
//      HHTable1[HKey].Arg1 = bFuncR;
        HHTable1[HKey].Arg1 = bFunc;

        return Res;
    }
}

unsigned Extra_CountMintermsSimple ( DdNode *  bFunc, unsigned  max  )

static

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

Synopsis [Counts the number of minterms.]

Description [This function counts minterms for functions up to 32 variables using a local cache. The terminal value (s_Termina) should be adjusted for BDDs and ADDs.]

SideEffects [None]

Definition at line 1069 of file extraBddCas.c.

{
    unsigned HKey;

    // normalize
    if ( Cudd_IsComplement(bFunc) )
        return max - Extra_CountMintermsSimple( Cudd_Not(bFunc), max );

    // now it is known that the function is not complemented
    if ( cuddIsConstant(bFunc) )
        return ((bFunc==s_Terminal)? 0: max);

    // check cache
    HKey = hashKey2( bFunc, max, _TABLESIZE_MINT );
    if ( HHTable2[HKey].Arg1 == bFunc && HHTable2[HKey].Arg2 == max )
        return HHTable2[HKey].Res;
    else
    {
        // min = min0/2 + min1/2;
        unsigned min = (Extra_CountMintermsSimple( cuddE(bFunc), max ) >> 1) +
                       (Extra_CountMintermsSimple( cuddT(bFunc), max ) >> 1);

        HHTable2[HKey].Arg1 = bFunc;
        HHTable2[HKey].Arg2 = max;
        HHTable2[HKey].Res  = min;

        return min;
    }
}   /* end of Extra_CountMintermsSimple */

int Extra_ProfileWidth	(	DdManager *	dd,
		DdNode *	Func,
		int *	pProfile,
		int	CutLevel
	)

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

Synopsis [Fast computation of the BDD profile.]

Description [The array to store the profile is given by the user and should contain at least as many entries as there is the maximum of the BDD/ZDD size of the manager PLUS ONE. When we say that the widths of the DD on level L is W, we mean the following. Let us create the cut between the level L-1 and the level L and count the number of different DD nodes pointed to across the cut. This number is the width W. From this it follows the on level 0, the width is equal to the number of external pointers to the considered DDs. If there is only one DD, then the profile on level 0 is always 1. If this DD is rooted in the topmost variable, then the width on level 1 is always 2, etc. The width at the level equal to dd->size is the number of terminal nodes in the DD. (Because we consider the first level #0 and the last level #dd->size, the profile array should contain dd->size+1 entries.) ]

SideEffects [This procedure will not work for BDDs w/ complement edges, only for ADDs and ZDDs]

SeeAlso []

Definition at line 519 of file extraBddCas.c.

{
    st__generator * gen;
    st__table * tNodeTopRef; // this table stores the top level from which this node is pointed to
    st__table * tNodes;
    DdNode * node;
    DdNode * nodeR;
    int LevelStart, Limit;
    int i, size;
    int WidthMax;
  
    // start the mapping table
    tNodeTopRef = st__init_table( st__ptrcmp, st__ptrhash);;
    // add the topmost node to the profile
    extraProfileUpdateTopLevel( tNodeTopRef, 0, Func );

    // collect all nodes
    tNodes = Extra_CollectNodes( Func );
    // go though all the nodes and set the top level the cofactors are pointed from
//  Cudd_ForeachNode( dd, Func, genDD, node )
    st__foreach_item( tNodes, gen, (const char**)&node, NULL )
    {
//      assert( Cudd_Regular(node) );  // this procedure works only with ADD/ZDD (not BDD w/ compl.edges)
        nodeR = Cudd_Regular(node);
        if ( cuddIsConstant(nodeR) )
            continue;
        // this node is not a constant - consider its cofactors
        extraProfileUpdateTopLevel( tNodeTopRef, dd->perm[node->index]+1, cuddE(nodeR) );
        extraProfileUpdateTopLevel( tNodeTopRef, dd->perm[node->index]+1, cuddT(nodeR) );
    }
    st__free_table( tNodes );

    // clean the profile
    size = ddMax(dd->size, dd->sizeZ) + 1;
    for ( i = 0; i < size; i++ ) 
        pProfile[i] = 0;

    // create the profile
    st__foreach_item( tNodeTopRef, gen, (const char**)&node, (char**)&LevelStart )
    {
        nodeR = Cudd_Regular(node);
        Limit = (cuddIsConstant(nodeR))? dd->size: dd->perm[nodeR->index];
        for ( i = LevelStart; i <= Limit; i++ )
            pProfile[i]++;
    }

    if ( CutLevel != -1 && CutLevel != 0  )
        size = CutLevel;

    // get the max width
    WidthMax = 0;
    for ( i = 0; i < size; i++ ) 
        if ( WidthMax < pProfile[i] )
            WidthMax = pProfile[i];

    // deref the table
    st__free_table( tNodeTopRef );

    return WidthMax;
} /* end of Extra_ProfileWidth */

void extraCollectNodes	(	DdNode *	Func,
		st__table *	tNodes
	)

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

Synopsis [Collects all the BDD nodes into the table.]

Description []

SideEffects []

SeeAlso []

Definition at line 435 of file extraBddCas.c.

{
    DdNode * FuncR;
    FuncR = Cudd_Regular(Func);
    if ( st__find_or_add( tNodes, (char*)FuncR, NULL ) )
        return;
    if ( cuddIsConstant(FuncR) )
        return;
    extraCollectNodes( cuddE(FuncR), tNodes );
    extraCollectNodes( cuddT(FuncR), tNodes );
}

void extraProfileUpdateTopLevel	(	st__table *	tNodeTopRef,
		int	TopLevelNew,
		DdNode *	node
	)

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

Synopsis [Updates the topmost level from which the given node is referenced.]

Description [Takes the table which maps each BDD nodes (including the constants) into the topmost level on which this node counts as a cofactor. Takes the topmost level, on which this node counts as a cofactor (see Extra_ProfileWidthFast(). Takes the node, for which the table entry should be updated.]

SideEffects []

SeeAlso []

Definition at line 480 of file extraBddCas.c.

{
    int * pTopLevel;

    if ( st__find_or_add( tNodeTopRef, (char*)node, (char***)&pTopLevel ) )
    { // the node is already referenced
        // the current top level should be updated if it is larger than the new level
        if ( *pTopLevel > TopLevelNew ) 
             *pTopLevel = TopLevelNew;
    }
    else
    { // the node is not referenced
        // its level should be set to the current new level
        *pTopLevel = TopLevelNew;
    }
}

Variable Documentation

_HashEntry_cof HHTable1[_TABLESIZE_COF]

Definition at line 43 of file extraBddCas.c.

_HashEntry_mint HHTable2[_TABLESIZE_MINT]

Definition at line 53 of file extraBddCas.c.

int s_BackTrackLimit = 100

static

Definition at line 88 of file extraBddCas.c.

int s_BackTracks

static

Definition at line 87 of file extraBddCas.c.

int s_CutLevel = 0

static

Definition at line 64 of file extraBddCas.c.

DdNode* s_Encoded

static

Definition at line 80 of file extraBddCas.c.

int s_EncodingVarsLevel

static

Definition at line 93 of file extraBddCas.c.

DdNode* s_Field[8][256]

static

Definition at line 79 of file extraBddCas.c.

int s_MaxDepth = 5

static

Definition at line 72 of file extraBddCas.c.

int s_MultiStart

static

Definition at line 82 of file extraBddCas.c.

int s_nVarsBest

static

Definition at line 74 of file extraBddCas.c.

DdNode** s_pbTemp

static

Definition at line 85 of file extraBddCas.c.

unsigned s_Signature = 1

static

Definition at line 62 of file extraBddCas.c.

DdNode* s_Terminal

static

Definition at line 90 of file extraBddCas.c.

DdNode* s_VarAll

static

Definition at line 81 of file extraBddCas.c.

int s_VarOrderBest[32]

static

Definition at line 75 of file extraBddCas.c.

int s_VarOrderCur[32]

static

Definition at line 76 of file extraBddCas.c.