source: vis_dev/vis-2.3/src/ntm/ntm.c @ 104

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

  FileName    [ntm.c]

  PackageName [ntm]

  Synopsis    [Routines to build MDDs from a network.]

  Author      [Adnan Aziz and Tom Shiple]

  Copyright   [Copyright (c) 1994-1996 The Regents of the Univ. of California.
  All rights reserved.

  Permission is hereby granted, without written agreement and without license
  or royalty fees, to use, copy, modify, and distribute this software and its
  documentation for any purpose, provided that the above copyright notice and
  the following two paragraphs appear in all copies of this software.

  DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT
  OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF THE UNIVERSITY OF
  CALIFORNIA HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

  THE UNIVERSITY OF CALIFORNIA SPECIFICALLY DISCLAIMS ANY WARRANTIES,
  INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
  FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS ON AN
  "AS IS" BASIS, AND THE UNIVERSITY OF CALIFORNIA HAS NO OBLIGATION TO PROVIDE
  MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.]

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

#include "ntmInt.h"

static char rcsid[] UNUSED = "$Id: ntm.c,v 1.11 2009/04/11 01:45:44 fabio Exp $";

/**AutomaticStart*************************************************************/

/*---------------------------------------------------------------------------*/
/* Static function prototypes                                                */
/*---------------------------------------------------------------------------*/

static Mvf_Function_t * NodeBuildMvfRecursively(Ntk_Node_t * node, st_table * leaves, st_table * nodeToMvfTable, mdd_manager *mddMgr, mdd_t *careSet);
static Mvf_Function_t * NodeBuildInputMvf(Ntk_Node_t * node, mdd_manager *mddMgr);
#if 0
static Mvf_Function_t * NodeBuildPseudoInputMvf(Ntk_Node_t * node, mdd_manager * mddMgr);
#endif
static Mvf_Function_t * NodeBuildPseudoInputMvfNew(Ntk_Node_t * node, mdd_manager * mddMgr);
static Mvf_Function_t * NodeBuildConstantMvf(Ntk_Node_t * node, int constantValue, mdd_manager *mddMgr);
static Mvf_Function_t * NodeBuildInternalMvf(Ntk_Node_t * node, st_table * leaves, st_table * nodeToMvfTable, mdd_manager *mddMgr, mdd_t *careSet);
static Mvf_Function_t * NodeReadMvf(Ntk_Node_t * node, st_table * nodeToMvfTable);
static void NodeSetMvf(Ntk_Node_t * node, st_table * nodeToMvfTable, Mvf_Function_t * mvf);
static int CommandNtmTest(Hrc_Manager_t ** hmgr, int argc, char ** argv);
static void MvfSanityCheck(array_t *roots, array_t *mvfs);
static void RegionInitializeReferenceCounts(array_t *roots, st_table *leaves);
static void NodeDecrementRefCount(Ntk_Node_t *node, st_table *nodeToMvfTable);
static boolean TableTestIsContainedInArray(st_table *table1, array_t *nodeArrary);

/**AutomaticEnd***************************************************************/


/*---------------------------------------------------------------------------*/
/* Definition of exported functions                                          */
/*---------------------------------------------------------------------------*/

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

  Synopsis    [Initializes the network to MDD package.]

  SideEffects []

  SeeAlso     [Ntm_End]

******************************************************************************/
void
Ntm_Init(void)
{
  Cmd_CommandAdd("_ntm_test", CommandNtmTest, /* doesn't changes_network */ 0);
}


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

  Synopsis    [Ends the network to MDD package.]

  SideEffects []

  SeeAlso     [Ntm_Init]

******************************************************************************/
void
Ntm_End(void)
{
}


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

  Synopsis    [Builds multi-valued functions for roots, in terms of leaves.]

  Description [Takes an array of root nodes and a table of leaf nodes, and
  builds the multi-valued functions (MVFs) for the roots in terms of the
  leaves. This function returns an array of Mvf_Function_t*, in one-to-one
  correspondence with the roots array.  It is assumed that every path, from a
  root backwards to a combinational input, passes through a node in the leaves
  table, and that there are no combinational cycles within the region defined
  by the roots and leaves. Also, it is assumed that every node in the leaves
  table already has an MDD id.<p>

  A leaf that is a primary input, latch, or combinational node, is treated as
  a "free" input (i.e. can assume any value in its domain). A leaf that is a
  pseudo input can assume only those values for which it was specified.<p>

  The leaves table maps nodes (Ntk_Node_t*) to integers.  If the value
  corresponding to a leaf is NTM_UNUSED, then the MVF for the leaf is built
  as described above.  However, the value can be specified as the index of
  some value in the domain of the variable of the leaf.  For example, if leaf
  node x can take values (RED, GREEN, BLUE), then the value 1 refers to GREEN.
  In this case, the MVF built for x is simply the constant MVF representing
  GREEN. This feature can be used to evaluate the MVFs of the roots on a
  minterm, or partial minterm, over the leaves.<p>

  This function also takes the MDD careSet as an input.  If this argument is
  NULL, then it is ignored.  However, if it is not NULL, then all intermediate
  and final MDDs constructed are minimized with respect to the careSet.  Thus,
  the MVFs returned by the function may take an arbitrary value outside of the
  careSet.  This can be useful to keep the MDDs small.]

  Comment [We create a table mapping nodes to Mvf_Function_t's (for nodes for
  which Mvf_Function's have already been built); Call NodeBuildMvfRecursively
  on the roots. Free MVF's at internal nodes ASAP, so no excessive storage.]

  SideEffects []

******************************************************************************/
array_t *
Ntm_NetworkBuildMvfs(
  Ntk_Network_t * network,
  array_t * roots,
  st_table * leaves,
  mdd_t *careSet)
{
  int             i;
  st_generator   *stGen;
  Mvf_Function_t *mvf;
  Ntk_Node_t     *node;
  st_table       *nodeToMvfTable;
  Mvf_Function_t *tmpMvf;
  int             numRoots = array_n(roots);
  array_t        *result   = array_alloc(Mvf_Function_t *, numRoots);
  mdd_manager    *mddMgr   = Ntk_NetworkReadMddManager(network);

  /*
   * Before initializing the reference counts, verify that the leaves form a
   * support set for the roots.
   */
  if (!Ntk_NetworkTestLeavesCoverSupportOfRoots(network, roots, leaves)) {
    (void)fprintf(vis_stderr,"%s",error_string());
    fflush(vis_stderr);
    fail("Leaves do not cover support of roots");
  }

  /*
   * Each node in the region defined by the roots and leaves is assigned a
   * reference count equaling the number of fanouts within the region.  As a
   * special case, the roots are initialized to MAX_INT.
   */
  RegionInitializeReferenceCounts(roots, leaves);

  /*
   * For each root, compute its MVF and store a duplicate copy of it in the
   * result array. The nodeToMvfTable is used to keep track of intermediate
   * computations. Intermediate MVFs are freed as soon as possible by using
   * the reference count mechanism.
   */
  nodeToMvfTable = st_init_table(st_ptrcmp, st_ptrhash);
  for (i = 0; i < numRoots; i++) {
    Ntk_Node_t     *root   = array_fetch(Ntk_Node_t *, roots, i);

    tmpMvf = NodeBuildMvfRecursively(root, leaves,
                                                     nodeToMvfTable, mddMgr,
                                                     careSet);

    mvf = Mvf_FunctionDuplicate(tmpMvf);
    array_insert(Mvf_Function_t *, result, i, mvf);
  }

  /*
   * Because of the use of reference counting, the only nodes left in
   * nodeToMvfTable should be the roots.
   */
  assert(TableTestIsContainedInArray(nodeToMvfTable, roots));

  /*
   * Free the remaining MVFs (corresponding to the roots) from the
   * nodeToMvfTable.
   */
  st_foreach_item(nodeToMvfTable, stGen, &node, &mvf) {
    Mvf_FunctionFree(mvf);
  }
  st_free_table(nodeToMvfTable);

  return result;
}

/*---------------------------------------------------------------------------*/
/* Definition of internal functions                                          */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Definition of static functions                                            */
/*---------------------------------------------------------------------------*/


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

  Synopsis    [Builds MVF for a node, recursively in terms of fanins.]

  Description [Recursively builds Mvf_Functions_t's. Base cases - input nodes,
  latch nodes, constant nodes, pseudo inputs, and leaf nodes. Fail if a
  combinational input is reached that is not in leaves.  In the case that the
  node is combinational, and in the leaves, we treat it as an input.  When
  it's a pseudo input, we treat it as taking only values designated in table.]

  SideEffects []

  SeeAlso     [NodeBuildInputMvf,NodeBuildPseudoInputMvf,NodeBuildInternalMvf]

******************************************************************************/
static Mvf_Function_t *
NodeBuildMvfRecursively(
  Ntk_Node_t * node,
  st_table * leaves,
  st_table * nodeToMvfTable,
  mdd_manager *mddMgr,
  mdd_t *careSet)
{
  Mvf_Function_t *mvf = NodeReadMvf(node, nodeToMvfTable);


  /* If the MVF for this node has already been computed, then just return it. */
  if (mvf != NIL(Mvf_Function_t)) {
    return mvf;
  }


  if (Ntk_NodeTestIsConstant(node)) {
    /* Doesn't matter if constant is a leaf or not. */
    mvf = NodeBuildConstantMvf(node, NTM_UNUSED, mddMgr);
  }

  else {
    int constValue;
    if (st_lookup_int(leaves, (char *) node, &constValue)) {

      if (constValue == NTM_UNUSED) {

        /* Node is a leaf. */
        if ((Ntk_NodeTestIsPrimaryInput(node)) ||
            (Ntk_NodeTestIsLatch(node)) ||
            (Ntk_NodeTestIsCombinational(node))) {
          /* Node can assume any value. */
          mvf = NodeBuildInputMvf(node, mddMgr);
        }
        else if (Ntk_NodeTestIsPseudoInput(node)) {
          /* Node may assume only a subset of possible values. */
          mvf = NodeBuildPseudoInputMvfNew(node, mddMgr);
        }
        else {
          fail("Encountered unknown type in MVF recursion\n");
        }
      }
      else {
        /* treat the leaf node as being a constant taking the value constValue */
        mvf = NodeBuildConstantMvf(node, constValue, mddMgr);
      }
    }
    else {

      /* Node is not a leaf.  If it is a combinational input, then fail. */
      if (Ntk_NodeTestIsCombInput(node)) {
        fail("Encountered combinational input not in leaves table\n");
      }
      else {
        mvf = NodeBuildInternalMvf(node, leaves, nodeToMvfTable, mddMgr,
                                   careSet);
      }
    }
  }

  /* Minimize mvf wrt careSet, if careSet is not NULL. */
  if (careSet != NIL(mdd_t)) {
    Mvf_Function_t *tempMvf = mvf;

    mvf = Mvf_FunctionMinimize(tempMvf, careSet);
    Mvf_FunctionFree(tempMvf);
  }
  NodeSetMvf(node, nodeToMvfTable, mvf);
  return mvf;

}


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

  Synopsis  [Builds MVF for a node that is treated as a free input.]

  SideEffects []

******************************************************************************/
static Mvf_Function_t *
NodeBuildInputMvf(
  Ntk_Node_t * node,
  mdd_manager *mddMgr)
{
  int mddId = Ntk_NodeReadMddId(node);

  assert(mddId != NTK_UNASSIGNED_MDD_ID);
  return Mvf_FunctionCreateFromVariable(mddMgr, mddId);
}


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

  Synopsis    [Builds MVF for a node that is a pseudo input.]

  Description [Builds MVF for a node that is a pseudo input.  This node has a
  single output and no inputs. Its table has several row entries.  We build an
  MVF whose components correspond exactly to possible table outputs.]

  SideEffects []

  Comment [Although pseudo inputs, constants, and internal nodes all have
  tables, a single procedure cannot be used to build their MVF.  A pseudo
  input MVF is built in terms of its mddId, whereas a constant or internal is
  not.  A constant or pseudo input doesn't have any inputs, whereas an
  internal does.]

  SeeAlso     [Tbl_TableBuildMvfForNonDetConstant]

******************************************************************************/
static Mvf_Function_t *
NodeBuildPseudoInputMvfNew(
  Ntk_Node_t * node,
  mdd_manager * mddMgr)
{
  mdd_t *vMdd, *tMdd, *rMdd;
  int lIndex, needProcess, i;
  Mvf_Function_t *mvf;
  int             columnIndex = Ntk_NodeReadOutputIndex(node);
  Tbl_Table_t    *table       = Ntk_NodeReadTable(node);
  int             mddId       = Ntk_NodeReadMddId(node);

  assert(mddId != NTK_UNASSIGNED_MDD_ID);
  mvf = Tbl_TableBuildNonDetConstantMvf(table, columnIndex, mddId, mddMgr);

  rMdd = mdd_zero(mddMgr);
  needProcess = 0;
  lIndex = 0;
  for(i=0; i<mvf->num; i++) {
    vMdd = array_fetch(mdd_t *, mvf, i);
    if(mdd_equal(vMdd, rMdd)) {
      needProcess = 1;
    }
    else {
      lIndex = i;
    }
  }
  if(needProcess) {
    for(i=0; i<lIndex; i++) {
      vMdd = array_fetch(mdd_t *, mvf, i);
      tMdd = mdd_or(vMdd, rMdd, 1, 1);
      mdd_free(rMdd);
      rMdd = tMdd;
    }
    vMdd = array_fetch(mdd_t *, mvf, lIndex);
    mdd_free(vMdd);
    tMdd = mdd_not(rMdd);
    mdd_free(rMdd);
    array_insert(mdd_t *, mvf, lIndex, tMdd);
  }
  else {
    mdd_free(rMdd);
  }
  return mvf;
}

#if 0
static Mvf_Function_t *
NodeBuildPseudoInputMvf(
  Ntk_Node_t * node,
  mdd_manager * mddMgr)
{
  Mvf_Function_t *mvf;
  int             columnIndex = Ntk_NodeReadOutputIndex(node);
  Tbl_Table_t    *table       = Ntk_NodeReadTable(node);
  int             mddId       = Ntk_NodeReadMddId(node);

  assert(mddId != NTK_UNASSIGNED_MDD_ID);
  mvf = Tbl_TableBuildNonDetConstantMvf(table, columnIndex, mddId, mddMgr);

  return mvf;
}
#endif


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

  Synopsis [Builds MVF for a node with no inputs, and only one row in its
  table.]

  Description [Builds MVF for a constant.  If constantValue is NTM_UNUSED,
  then constantValue should be a legal index in the domain of the variable of
  node. In this case, regardless of the type of the node, an MVF is built
  where the component indexed by constantValue is one (i.e. the tautology) and
  all other components are zero.<p>

  If constantValue is not NTM_UNUSED, then node should be a constant,
  combinational node.  In this case, an MVF is built with a single component
  (indexed by the value of node) is one, and all other components are zero.]

  SideEffects []

******************************************************************************/
static Mvf_Function_t *
NodeBuildConstantMvf(
  Ntk_Node_t * node,
  int constantValue,
  mdd_manager *mddMgr)
{
  int             value        = 0; /* initialized to stop lint complaining */
  mdd_t          *oneMdd       = mdd_one(mddMgr);
  Var_Variable_t *variable     = Ntk_NodeReadVariable(node);
  int             numVarValues = Var_VariableReadNumValues(variable);
  Mvf_Function_t *mvf          = Mvf_FunctionAlloc(mddMgr, numVarValues);


  if (constantValue != NTM_UNUSED) {
    /* Use the given value. */
    assert((constantValue >= 0) && (constantValue < numVarValues));
    value = constantValue;
  }
  else {
    int          outputIndex = Ntk_NodeReadOutputIndex(node);
    Tbl_Table_t *table       = Ntk_NodeReadTable(node);

    assert(Ntk_NodeTestIsConstant(node));
    value = Tbl_TableReadConstValue(table, outputIndex);
    assert(value != -1);
  }

  Mvf_FunctionAddMintermsToComponent(mvf, value, oneMdd);
  mdd_free(oneMdd);
  return mvf;
}


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

  Synopsis [Builds MVF for an internal node in terms of its fanin's MVFs.]

  Description [Builds MVF for an internal node in terms of its fanin's
  MVFs. An internal node is a node that is in the transitive fanin of a root,
  but is not a leaf.]

  SideEffects []

******************************************************************************/
static Mvf_Function_t *
NodeBuildInternalMvf(
  Ntk_Node_t * node,
  st_table * leaves,
  st_table * nodeToMvfTable,
  mdd_manager *mddMgr,
  mdd_t *careSet)
{
  int             i;
  Mvf_Function_t *resultMvf;
  Ntk_Node_t     *faninNode;
  array_t        *faninMvfs   = array_alloc(Mvf_Function_t *, Ntk_NodeReadNumFanins(node));
  int             outputIndex = Ntk_NodeReadOutputIndex(node);
  Tbl_Table_t    *table       = Ntk_NodeReadTable(node);


  Ntk_NodeForEachFanin(node, i, faninNode) {
    Mvf_Function_t *tmpMvf = NodeBuildMvfRecursively(faninNode, leaves,
                                                     nodeToMvfTable, mddMgr,
                                                     careSet);
    array_insert(Mvf_Function_t *, faninMvfs, i, tmpMvf);
  }
  resultMvf = Tbl_TableBuildMvfFromFanins(table, outputIndex, faninMvfs, mddMgr);

  /* Mc_CheckValdityOfMvf(Ntk_NodeReadNetwork(node), mddMgr, node, resultMvf); */

  Ntk_NodeForEachFanin(node, i, faninNode) {
    NodeDecrementRefCount(faninNode, nodeToMvfTable);
  }

  /* Don't free the MVFs themselves, but just free the array. */
  array_free(faninMvfs);

  return resultMvf;
}


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

  Synopsis [Returns MVF corresponding to a node; returns NIL if node not in
  table.]

  SideEffects []

******************************************************************************/
static Mvf_Function_t *
NodeReadMvf(
  Ntk_Node_t * node,
  st_table * nodeToMvfTable)
{
  Mvf_Function_t *result = NIL(Mvf_Function_t);
  st_lookup(nodeToMvfTable, node, &result);

  return result;
}


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

  Synopsis    [Inserts node and corresponding MVF into table.]

  SideEffects []

******************************************************************************/
static void
NodeSetMvf(
  Ntk_Node_t * node,
  st_table * nodeToMvfTable,
  Mvf_Function_t * mvf)
{
  st_insert(nodeToMvfTable, (char *) node, (char *) mvf);
}


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

  Synopsis    [Hacked test for the ntm package.]

  CommandName [_ntm_test]

  CommandSynopsis [test the ntm package]

  CommandArguments [\[-h\] \[-v\]]

  CommandDescription [Test the ntm package.  This package is responsible for
  building the multi-valued functions (represented as MDDs) of the flattened
  network.  This command builds the multi-valued functions of the
  combinational outputs in terms of the combinational inputs.  The
  multi-valued functions are then deleted. <p>

  Command options:<p>

  <dl>

  <dt> -h
  <dd> Print the command usage.

  <dt> -v
  <dd> Print the sizes of the MDDs built.

  </dl>
  ]

  SideEffects []

******************************************************************************/
static int
CommandNtmTest(
  Hrc_Manager_t ** hmgr,
  int  argc,
  char ** argv)
{
  int            c;
  Ntk_Node_t    *node;
  lsGen          gen;
  array_t       *result; /* array of Mvf_Function_t* */
  array_t       *roots;
  st_table      *leaves;
  boolean        verbose = FALSE;              /* default */
  Ntk_Network_t *network = Ntk_HrcManagerReadCurrentNetwork(*hmgr);

  /*
   * Parse the command line.
   */
  util_getopt_reset();
  while ((c = util_getopt(argc, argv, "vh")) != EOF) {
    switch (c) {
      case 'v':
        verbose = 1;
        break;
      case 'h':
        goto usage;
      default:
        goto usage;
    }
  }

  if (network == NIL(Ntk_Network_t)) {
    return 1;
  }

  if (Ord_NetworkTestAreVariablesOrdered(network, Ord_InputAndLatch_c) == FALSE) {
    (void) fprintf(vis_stderr, "The MDD variables have not been ordered. ");
    (void) fprintf(vis_stderr, "Use static_order.\n");
    return 1;
  }

  roots = array_alloc(Ntk_Node_t *, 0);
  Ntk_NetworkForEachCombOutput(network, gen, node) {
    array_insert_last(Ntk_Node_t *, roots, node);
  }

  leaves = st_init_table(st_ptrcmp, st_ptrhash);
  Ntk_NetworkForEachCombInput(network, gen, node) {
    st_insert(leaves, (char *) node, (char *) NTM_UNUSED);
  }

  result = Ntm_NetworkBuildMvfs(network, roots, leaves, NIL(mdd_t));

  if (verbose) {
    MvfSanityCheck(roots, result);
  }

  array_free(roots);
  st_free_table(leaves);

  /*
   * Free the array of MVFs.
   */
  Mvf_FunctionArrayFree(result);

  return 0;

usage:
  (void) fprintf(vis_stderr, "usage: _ntm_test [-h] [-v]\n");
  (void) fprintf(vis_stderr, "   -h print the command usage\n");
  (void) fprintf(vis_stderr, "   -v verbose\n");
  return 1;             /* error exit */
}


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

  Synopsis    [Checks that MDD sizes are meaningful.]

  SideEffects []

******************************************************************************/
static void
MvfSanityCheck(
  array_t *roots /* of Ntk_Node_t* */,
  array_t *mvfs  /* of Mvf_Function_t* */)
{
  int i;

  assert(array_n(roots) == array_n(mvfs));

  for (i = 0; i < array_n(roots); i ++) {
    int             value;
    mdd_t          *valueMdd;
    Ntk_Node_t     *root = array_fetch(Ntk_Node_t *, roots, i);
    Mvf_Function_t *mvf  = array_fetch(Mvf_Function_t *, mvfs, i);

    (void) fprintf(vis_stdout, "\nMDD stats for node %s:\n", Ntk_NodeReadName(root));

    Mvf_FunctionForEachComponent(mvf, value, valueMdd) {
      (void) fprintf(vis_stdout, "\tSize of MDD for value %d is %d\n", i,
                     mdd_size(valueMdd));
    }
  }
}


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

  Synopsis    [Initializes the reference counts in a region.]

  Description [Initializes the reference counts in the region defined by the
  roots and leaves.  This region includes the roots, and all nodes in the
  transitive fanin of the roots up to and including the leaves.  The reference
  count for a node in the region is set to be the number of fanouts of that
  node in the region (fanouts to leaf nodes and constant nodes are excluded).
  Root nodes are set to MAXINT, so that even after some decrements, their ref
  count won't fall to zero.]

  SideEffects [Uses the undef field of node.]

******************************************************************************/
static void
RegionInitializeReferenceCounts(
  array_t *roots,
  st_table *leaves)
{
  int           i;
  Ntk_Node_t   *node;
  st_generator *stGen;
  st_table     *regionNodes = Ntk_RegionFindNodes(roots, leaves);

  st_foreach_item(regionNodes, stGen, &node, NULL) {
    Ntk_Node_t *fanoutNode;
    long        refCount = 0;

    Ntk_NodeForEachFanout(node, i, fanoutNode) {
      if (st_is_member(regionNodes, (char *) fanoutNode)
          && !st_is_member(leaves, (char *) fanoutNode)
          && !Ntk_NodeTestIsConstant(fanoutNode)) {
        refCount++;
      }
    }
    Ntk_NodeSetUndef(node, (void *) refCount);
  }

  for(i = 0; i < array_n(roots); i++) {
    node = array_fetch(Ntk_Node_t *, roots, i);
    Ntk_NodeSetUndef(node, (void *) MAXINT);
  }

  st_free_table(regionNodes);
}

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

  Synopsis    [Decrements the ref count of a node.]

  Description [Decrements the ref count of a node.  If the ref count becomes
  zero, then remove node from nodeToMvfTable and free the MVF corresponding to
  node.]

  SideEffects []

******************************************************************************/
static void
NodeDecrementRefCount(
  Ntk_Node_t *node,
  st_table *nodeToMvfTable)
{
  Mvf_Function_t *mvf;
  long            refCount = (long) Ntk_NodeReadUndef(node);

  assert(refCount != 0);

  refCount--;

  if (refCount == 0) {
    st_delete(nodeToMvfTable, &node, &mvf);
    Mvf_FunctionFree(mvf);
  }

  Ntk_NodeSetUndef(node, (void *) refCount);
}

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

  Synopsis    [Returns TRUE if table1 is contained in nodeArray; else FALSE.]

  Description [Table1 is a hash table where the keys are nodes. NodeArray is
  an array of nodes.  This function returns TRUE if the set of key nodes in
  table1 is contained in the set of nodes in nodeArray.  It returns FALSE upon
  finding the first key node in table1 that is not in nodeArray.]

  SideEffects []

******************************************************************************/
static boolean
TableTestIsContainedInArray(
  st_table *table1,
  array_t *nodeArrary)
{
  int             i;
  st_generator   *stGen;
  Ntk_Node_t     *node;
  Mvf_Function_t *mvf;
  st_table       *table2 = st_init_table(st_ptrcmp, st_ptrhash);

  /* Create a hash table from the array. */
  arrayForEachItem(Ntk_Node_t *, nodeArrary, i, node) {
    st_insert(table2, (char *) node, NIL(char));
  }

  st_foreach_item(table1, stGen, &node, &mvf) {
    if (!st_is_member(table2, node)) {
      st_free_table(table2);
      return FALSE;
    }
  }

  st_free_table(table2);
  return TRUE;
}