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diff --git a/src/bdd/dsd/dsdCheck.c b/src/bdd/dsd/dsdCheck.c
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+/**CFile****************************************************************
+
+  FileName    [dsdCheck.c]
+
+  PackageName [DSD: Disjoint-support decomposition package.]
+
+  Synopsis    [Procedures to check the identity of root functions.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 8.0. Started - September 22, 2003.]
+
+  Revision    [$Id: dsdCheck.c,v 1.0 2002/22/09 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "dsdInt.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+typedef struct Dsd_Cache_t_  Dds_Cache_t;
+typedef struct Dsd_Entry_t_  Dsd_Entry_t;
+
+struct Dsd_Cache_t_
+{
+    Dsd_Entry_t *     pTable;
+    int               nTableSize;
+    int               nSuccess;
+    int               nFailure;
+};
+
+struct Dsd_Entry_t_
+{
+    DdNode * bX[5];
+};
+
+static Dds_Cache_t * pCache;
+
+static int Dsd_CheckRootFunctionIdentity_rec( DdManager * dd, DdNode * bF1, DdNode * bF2, DdNode * bC1, DdNode * bC2 );
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function********************************************************************
+
+  Synopsis    [(Re)allocates the local cache.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+void Dsd_CheckCacheAllocate( int nEntries )
+{
+    int nRequested;
+
+    pCache = ALLOC( Dds_Cache_t, 1 );
+    memset( pCache, 0, sizeof(Dds_Cache_t) );
+
+    // check what is the size of the current cache
+    nRequested = Cudd_Prime( nEntries );
+    if ( pCache->nTableSize != nRequested )
+    { // the current size is different
+        // deallocate the old, allocate the new
+        if ( pCache->nTableSize )
+            Dsd_CheckCacheDeallocate();
+        // allocate memory for the hash table
+        pCache->nTableSize = nRequested;
+        pCache->pTable = ALLOC( Dsd_Entry_t, nRequested );
+    }
+    // otherwise, there is no need to allocate, just clean
+    Dsd_CheckCacheClear();
+//    printf( "\nThe number of allocated cache entries = %d.\n\n", pCache->nTableSize );
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Deallocates the local cache.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+void Dsd_CheckCacheDeallocate()
+{
+    free( pCache->pTable );
+    free( pCache );
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Clears the local cache.]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+void Dsd_CheckCacheClear()
+{
+    int i;
+    for ( i = 0; i < pCache->nTableSize; i++ )
+        pCache->pTable[0].bX[0] = NULL;
+}
+
+
+/**Function********************************************************************
+
+  Synopsis    [Checks whether it is true that bF1(bC1=0) == bF2(bC2=0).]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Dsd_CheckRootFunctionIdentity( DdManager * dd, DdNode * bF1, DdNode * bF2, DdNode * bC1, DdNode * bC2 )
+{
+    int RetValue;
+//    pCache->nSuccess = 0;
+//    pCache->nFailure = 0;
+    RetValue = Dsd_CheckRootFunctionIdentity_rec(dd, bF1, bF2, bC1, bC2);
+//    printf( "Cache success = %d. Cache failure = %d.\n", pCache->nSuccess, pCache->nFailure );
+    return RetValue;
+}
+
+/**Function********************************************************************
+
+  Synopsis    [Performs the recursive step of Dsd_CheckRootFunctionIdentity().]
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+******************************************************************************/
+int Dsd_CheckRootFunctionIdentity_rec( DdManager * dd, DdNode * bF1, DdNode * bF2, DdNode * bC1, DdNode * bC2 )
+{
+    unsigned HKey;
+
+    // if either bC1 or bC2 is zero, the test is true
+//    if ( bC1 == b0 || bC2 == b0 )  return 1;
+    assert( bC1 != b0 );
+    assert( bC2 != b0 );
+
+    // if both bC1 and bC2 are one - perform comparison
+    if ( bC1 == b1 && bC2 == b1 )  return (int)( bF1 == bF2 );
+
+    if ( bF1 == b0 )
+        return Cudd_bddLeq( dd, bC2, Cudd_Not(bF2) );
+
+    if ( bF1 == b1 )
+        return Cudd_bddLeq( dd, bC2, bF2 );
+
+    if ( bF2 == b0 )
+        return Cudd_bddLeq( dd, bC1, Cudd_Not(bF1) );
+
+    if ( bF2 == b1 )
+        return Cudd_bddLeq( dd, bC1, bF1 );
+
+    // otherwise, keep expanding
+
+    // check cache
+//    HKey = _Hash( ((unsigned)bF1), ((unsigned)bF2), ((unsigned)bC1), ((unsigned)bC2) );
+    HKey = hashKey4( bF1, bF2, bC1, bC2, pCache->nTableSize );
+    if ( pCache->pTable[HKey].bX[0] == bF1 && 
+         pCache->pTable[HKey].bX[1] == bF2 && 
+         pCache->pTable[HKey].bX[2] == bC1 && 
+         pCache->pTable[HKey].bX[3] == bC2 )
+    {
+        pCache->nSuccess++;
+        return (int)pCache->pTable[HKey].bX[4]; // the last bit records the result (yes/no)
+    }
+    else
+    {
+
+        // determine the top variables
+        int RetValue;
+        DdNode * bA[4]  = { bF1, bF2, bC1, bC2 }; // arguments
+        DdNode * bAR[4] = { Cudd_Regular(bF1), Cudd_Regular(bF2), Cudd_Regular(bC1), Cudd_Regular(bC2) }; // regular arguments
+        int CurLevel[4] = { cuddI(dd,bAR[0]->index), cuddI(dd,bAR[1]->index), cuddI(dd,bAR[2]->index), cuddI(dd,bAR[3]->index) };
+        int TopLevel = CUDD_CONST_INDEX;
+        int i;
+        DdNode * bE[4], * bT[4];
+        DdNode * bF1next, * bF2next, * bC1next, * bC2next;
+
+        pCache->nFailure++;
+
+        // determine the top level
+        for ( i = 0; i < 4; i++ )
+            if ( TopLevel > CurLevel[i] )
+                 TopLevel = CurLevel[i];
+
+        // compute the cofactors
+        for ( i = 0; i < 4; i++ )
+        if ( TopLevel == CurLevel[i] )
+        {
+            if ( bA[i] != bAR[i] ) // complemented
+            {
+                bE[i] = Cudd_Not(cuddE(bAR[i]));
+                bT[i] = Cudd_Not(cuddT(bAR[i]));
+            }
+            else
+            {
+                bE[i] = cuddE(bAR[i]);
+                bT[i] = cuddT(bAR[i]);
+            }
+        }
+        else
+            bE[i] = bT[i] = bA[i];
+
+        // solve subproblems
+        // three cases are possible
+
+        // (1) the top var belongs to both C1 and C2
+        //     in this case, any cofactor of F1 and F2 will do, 
+        //     as long as the corresponding cofactor of C1 and C2 is not equal to 0
+        if ( TopLevel == CurLevel[2] && TopLevel == CurLevel[3] ) 
+        {
+            if ( bE[2] != b0 ) // C1
+            {
+                bF1next = bE[0];
+                bC1next = bE[2];
+            }
+            else
+            {
+                bF1next = bT[0];
+                bC1next = bT[2];
+            }
+            if ( bE[3] != b0 ) // C2
+            {
+                bF2next = bE[1];
+                bC2next = bE[3];
+            }
+            else
+            {
+                bF2next = bT[1];
+                bC2next = bT[3];
+            }
+            RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bF1next, bF2next, bC1next, bC2next );
+        }
+        // (2) the top var belongs to either C1 or C2
+        //     in this case normal splitting of cofactors
+        else if ( TopLevel == CurLevel[2] && TopLevel != CurLevel[3] ) 
+        {
+            if ( bE[2] != b0 ) // C1
+            {
+                bF1next = bE[0];
+                bC1next = bE[2];
+            }
+            else
+            {
+                bF1next = bT[0];
+                bC1next = bT[2];
+            }
+            // split around this variable
+            RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bF1next, bE[1], bC1next, bE[3] );
+            if ( RetValue == 1 ) // test another branch; otherwise, there is no need to test
+                RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bF1next, bT[1], bC1next, bT[3] );
+        }
+        else if ( TopLevel != CurLevel[2] && TopLevel == CurLevel[3] ) 
+        {
+            if ( bE[3] != b0 ) // C2
+            {
+                bF2next = bE[1];
+                bC2next = bE[3];
+            }
+            else
+            {
+                bF2next = bT[1];
+                bC2next = bT[3];
+            }
+            // split around this variable
+            RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bE[0], bF2next, bE[2], bC2next );
+            if ( RetValue == 1 ) // test another branch; otherwise, there is no need to test
+                RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bT[0], bF2next, bT[2], bC2next );
+        }
+        // (3) the top var does not belong to C1 and C2
+        //     in this case normal splitting of cofactors
+        else // if ( TopLevel != CurLevel[2] && TopLevel != CurLevel[3] )
+        {
+            // split around this variable
+            RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bE[0], bE[1], bE[2], bE[3] );
+            if ( RetValue == 1 ) // test another branch; otherwise, there is no need to test
+                RetValue = Dsd_CheckRootFunctionIdentity_rec( dd, bT[0], bT[1], bT[2], bT[3] );
+        }
+
+        // set cache
+        for ( i = 0; i < 4; i++ )
+            pCache->pTable[HKey].bX[i] = bA[i];
+        pCache->pTable[HKey].bX[4] = (DdNode*)RetValue;
+
+        return RetValue;
+    }
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+