Experiments with CEC for arithmetic circuits.

1 files changed, 1183 insertions, 0 deletions

diff --git a/src/proof/acec/acecFadds.c b/src/proof/acec/acecFadds.c
new file mode 100644
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--- /dev/null
+++ b/src/proof/acec/acecFadds.c
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+/**CFile****************************************************************
+
+  FileName    [acecFadds.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [CEC for arithmetic circuits.]
+
+  Synopsis    [Detecting half-adders and full-adders.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - June 20, 2005.]
+
+  Revision    [$Id: acecFadds.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "acecInt.h"
+#include "misc/vec/vecWec.h"
+#include "misc/tim/tim.h"
+
+ABC_NAMESPACE_IMPL_START
+
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+#define Dtc_ForEachCut( pList, pCut, i ) for ( i = 0, pCut = pList + 1; i < pList[0]; i++, pCut += pCut[0] + 1 )
+#define Dtc_ForEachFadd( vFadds, i )     for ( i = 0; i < Vec_IntSize(vFadds)/5; i++ )
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Detecting HADDs in the AIG.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Int_t * Gia_ManDetectHalfAdders( Gia_Man_t * p, int fVerbose )
+{
+    Vec_Int_t * vHadds = Vec_IntAlloc( 1000 );
+    Gia_Obj_t * pObj, * pFan0, * pFan1; 
+    int i, iLit, iFan0, iFan1, fComplDiff, Count, Counts[5] = {0};
+    ABC_FREE( p->pRefs );
+    Gia_ManCreateRefs( p );
+    Gia_ManHashStart( p );
+    Gia_ManForEachAnd( p, pObj, i )
+    {
+        if ( !Gia_ObjRecognizeExor(pObj, &pFan0, &pFan1) )
+            continue;
+        Count = 0;
+        if ( Gia_ObjRefNumId(p, Gia_ObjFaninId0(pObj, i)) > 1 )
+            Vec_IntPushTwo( vHadds, i, Gia_ObjFaninId0(pObj, i) ), Count++;
+        if ( Gia_ObjRefNumId(p, Gia_ObjFaninId1(pObj, i)) > 1 )
+            Vec_IntPushTwo( vHadds, i, Gia_ObjFaninId1(pObj, i) ), Count++;
+        iFan0 = Gia_ObjId( p, pFan0 );
+        iFan1 = Gia_ObjId( p, pFan1 );
+        fComplDiff =          (Gia_ObjFaninC0(Gia_ObjFanin0(pObj)) ^ Gia_ObjFaninC1(Gia_ObjFanin0(pObj)));
+        assert( fComplDiff == (Gia_ObjFaninC0(Gia_ObjFanin1(pObj)) ^ Gia_ObjFaninC1(Gia_ObjFanin1(pObj))) );
+        if ( fComplDiff )
+        {
+            if ( (iLit = Gia_ManHashLookupInt(p, Abc_Var2Lit(iFan0, 0), Abc_Var2Lit(iFan1, 0))) )
+                Vec_IntPushTwo( vHadds, i, Abc_Lit2Var(iLit) ), Count++;
+            if ( (iLit = Gia_ManHashLookupInt(p, Abc_Var2Lit(iFan0, 1), Abc_Var2Lit(iFan1, 1))) )
+                Vec_IntPushTwo( vHadds, i, Abc_Lit2Var(iLit) ), Count++;
+        }
+        else
+        {
+            if ( (iLit = Gia_ManHashLookupInt(p, Abc_Var2Lit(iFan0, 0), Abc_Var2Lit(iFan1, 1))) )
+                Vec_IntPushTwo( vHadds, i, Abc_Lit2Var(iLit) ), Count++;
+            if ( (iLit = Gia_ManHashLookupInt(p, Abc_Var2Lit(iFan0, 1), Abc_Var2Lit(iFan1, 0))) )
+                Vec_IntPushTwo( vHadds, i, Abc_Lit2Var(iLit) ), Count++;
+        }
+        Counts[Count]++;
+    }
+    Gia_ManHashStop( p );
+    ABC_FREE( p->pRefs );
+    if ( fVerbose )
+    {
+        int iXor, iAnd;
+        printf( "Found %d half-adders with XOR gates: ", Vec_IntSize(vHadds)/2 );
+        for ( i = 0; i <= 4; i++ )
+            printf( "%d=%d ", i, Counts[i] );
+        printf( "\n" );
+
+        Vec_IntForEachEntryDouble( vHadds, iXor, iAnd, i )
+            printf( "%3d : %5d %5d\n", i, iXor, iAnd );
+    }
+    return vHadds;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Derive GIA with boxes containing adder-chains.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Gia_ManIllustrateBoxes( Gia_Man_t * p )
+{
+    Tim_Man_t * pManTime = (Tim_Man_t *)p->pManTime;
+    int nBoxes = Tim_ManBoxNum( pManTime );
+    int i, k, curCi, curCo, nBoxIns, nBoxOuts;
+    Gia_Obj_t * pObj;
+    // walk through the boxes
+    curCi = Tim_ManPiNum(pManTime);
+    curCo = 0;
+    for ( i = 0; i < nBoxes; i++ )
+    {
+        nBoxIns = Tim_ManBoxInputNum(pManTime, i);
+        nBoxOuts = Tim_ManBoxOutputNum(pManTime, i);
+        printf( "Box %4d  [%d x %d] :   ", i, nBoxIns, nBoxOuts );
+        printf( "Input obj IDs = " );
+        for ( k = 0; k < nBoxIns; k++ )
+        {
+            pObj = Gia_ManCo( p, curCo + k );
+            printf( "%d ", Gia_ObjId(p, pObj) );
+        }
+        printf( "  Output obj IDs = " );
+        for ( k = 0; k < nBoxOuts; k++ )
+        {
+            pObj = Gia_ManCi( p, curCi + k );
+            printf( "%d ", Gia_ObjId(p, pObj) );
+        }
+        curCo += nBoxIns;
+        curCi += nBoxOuts;
+        printf( "\n" );
+    }
+    curCo += Tim_ManPoNum(pManTime);
+    // verify counts
+    assert( curCi == Gia_ManCiNum(p) );
+    assert( curCo == Gia_ManCoNum(p) );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Detecting FADDs in the AIG.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Dtc_ManCutMergeOne( int * pCut0, int * pCut1, int * pCut )
+{
+    int i, k;
+    for ( k = 0; k <= pCut1[0]; k++ )
+        pCut[k] = pCut1[k];
+    for ( i = 1; i <= pCut0[0]; i++ )
+    {
+        for ( k = 1; k <= pCut1[0]; k++ )
+            if ( pCut0[i] == pCut1[k] )
+                break;
+        if ( k <= pCut1[0] )
+            continue;
+        if ( pCut[0] == 3 )
+            return 0;
+        pCut[1+pCut[0]++] = pCut0[i];
+    }
+    assert( pCut[0] == 2 || pCut[0] == 3 );
+    if ( pCut[1] > pCut[2] )
+        ABC_SWAP( int, pCut[1], pCut[2] );
+    assert( pCut[1] < pCut[2] );
+    if ( pCut[0] == 2 )
+        return 1;
+    if ( pCut[2] > pCut[3] )
+        ABC_SWAP( int, pCut[2], pCut[3] );
+    if ( pCut[1] > pCut[2] )
+        ABC_SWAP( int, pCut[1], pCut[2] );
+    assert( pCut[1] < pCut[2] );
+    assert( pCut[2] < pCut[3] );
+    return 1;
+}
+int Dtc_ManCutCheckEqual( Vec_Int_t * vCuts, int * pCutNew )
+{
+    int * pList = Vec_IntArray( vCuts );
+    int i, k, * pCut;
+    Dtc_ForEachCut( pList, pCut, i )
+    {
+        for ( k = 0; k <= pCut[0]; k++ )
+            if ( pCut[k] != pCutNew[k] )
+                break;
+        if ( k > pCut[0] )
+            return 1;
+    }
+    return 0;
+}
+int Dtc_ObjComputeTruth_rec( Gia_Obj_t * pObj )
+{
+    int Truth0, Truth1;
+    if ( pObj->Value )
+        return pObj->Value;
+    assert( Gia_ObjIsAnd(pObj) );
+    Truth0 = Dtc_ObjComputeTruth_rec( Gia_ObjFanin0(pObj) );
+    Truth1 = Dtc_ObjComputeTruth_rec( Gia_ObjFanin1(pObj) );
+    return (pObj->Value = (Gia_ObjFaninC0(pObj) ? ~Truth0 : Truth0) & (Gia_ObjFaninC1(pObj) ? ~Truth1 : Truth1));
+}
+void Dtc_ObjCleanTruth_rec( Gia_Obj_t * pObj )
+{
+    if ( !pObj->Value )
+        return;
+    pObj->Value = 0;
+    if ( !Gia_ObjIsAnd(pObj) )
+        return;
+    Dtc_ObjCleanTruth_rec( Gia_ObjFanin0(pObj) );
+    Dtc_ObjCleanTruth_rec( Gia_ObjFanin1(pObj) );
+}
+int Dtc_ObjComputeTruth( Gia_Man_t * p, int iObj, int * pCut, int * pTruth )
+{
+    unsigned Truth, Truths[3] = { 0xAA, 0xCC, 0xF0 }; int i;
+    for ( i = 1; i <= pCut[0]; i++ )
+        Gia_ManObj(p, pCut[i])->Value = Truths[i-1];
+    Truth = 0xFF & Dtc_ObjComputeTruth_rec( Gia_ManObj(p, iObj) );
+    Dtc_ObjCleanTruth_rec( Gia_ManObj(p, iObj) );
+    if ( pTruth ) 
+        *pTruth = Truth;
+    if ( Truth == 0x96 || Truth == 0x69 )
+        return 1;
+    if ( Truth == 0xE8 || Truth == 0xD4 || Truth == 0xB2 || Truth == 0x71 ||
+         Truth == 0x17 || Truth == 0x2B || Truth == 0x4D || Truth == 0x8E )
+        return 2;
+    return 0;
+}
+void Dtc_ManCutMerge( Gia_Man_t * p, int iObj, int * pList0, int * pList1, Vec_Int_t * vCuts, Vec_Int_t * vCutsXor, Vec_Int_t * vCutsMaj )
+{
+    int fVerbose = 0;
+    Vec_Int_t * vTemp;
+    int i, k, c, Type, * pCut0, * pCut1, pCut[4];
+    Vec_IntFill( vCuts, 2, 1 );
+    Vec_IntPush( vCuts, iObj );
+    Dtc_ForEachCut( pList0, pCut0, i )
+    Dtc_ForEachCut( pList1, pCut1, k )
+    {
+        if ( !Dtc_ManCutMergeOne(pCut0, pCut1, pCut) )
+            continue;
+        if ( Dtc_ManCutCheckEqual(vCuts, pCut) )
+            continue;
+        Vec_IntAddToEntry( vCuts, 0, 1 );  
+        for ( c = 0; c <= pCut[0]; c++ )
+            Vec_IntPush( vCuts, pCut[c] );
+        if ( pCut[0] != 3 )
+            continue;
+        Type = Dtc_ObjComputeTruth( p, iObj, pCut, NULL );
+        if ( Type == 0 )
+            continue;
+        vTemp = Type == 1 ? vCutsXor : vCutsMaj;
+        if ( fVerbose )
+            printf( "%d = %s(", iObj, Type == 1 ? "XOR" : "MAJ" );
+        for ( c = 1; c <= pCut[0]; c++ )
+        {
+            if ( fVerbose )
+                printf( " %d", pCut[c] );
+            Vec_IntPush( vTemp, pCut[c] );
+        }
+        if ( fVerbose )
+            printf( " )\n" );
+        Vec_IntPush( vTemp, iObj );
+    }
+}
+void Dtc_ManComputeCuts( Gia_Man_t * p, Vec_Int_t ** pvCutsXor, Vec_Int_t ** pvCutsMaj, int fVerbose )
+{
+    Gia_Obj_t * pObj; 
+    int * pList0, * pList1, i, nCuts = 0;
+    Vec_Int_t * vTemp = Vec_IntAlloc( 1000 );
+    Vec_Int_t * vCutsXor = Vec_IntAlloc( Gia_ManAndNum(p) );
+    Vec_Int_t * vCutsMaj = Vec_IntAlloc( Gia_ManAndNum(p) );
+    Vec_Int_t * vCuts = Vec_IntAlloc( 30 * Gia_ManAndNum(p) );
+    Vec_IntFill( vCuts, Gia_ManObjNum(p), 0 );
+    Gia_ManCleanValue( p );
+    Gia_ManForEachCi( p, pObj, i )
+    {
+        Vec_IntWriteEntry( vCuts, Gia_ObjId(p, pObj), Vec_IntSize(vCuts) );
+        Vec_IntPush( vCuts, 1 );
+        Vec_IntPush( vCuts, 1 );
+        Vec_IntPush( vCuts, Gia_ObjId(p, pObj) );
+    }
+    Gia_ManForEachAnd( p, pObj, i )
+    {
+        pList0 = Vec_IntEntryP( vCuts, Vec_IntEntry(vCuts, Gia_ObjFaninId0(pObj, i)) );
+        pList1 = Vec_IntEntryP( vCuts, Vec_IntEntry(vCuts, Gia_ObjFaninId1(pObj, i)) );
+        Dtc_ManCutMerge( p, i, pList0, pList1, vTemp, vCutsXor, vCutsMaj );
+        Vec_IntWriteEntry( vCuts, i, Vec_IntSize(vCuts) );
+        Vec_IntAppend( vCuts, vTemp );
+        nCuts += Vec_IntEntry( vTemp, 0 );
+    }
+    if ( fVerbose )
+        printf( "Nodes = %d.  Cuts = %d.  Cuts/Node = %.2f.  Ints/Node = %.2f.\n", 
+            Gia_ManAndNum(p), nCuts, 1.0*nCuts/Gia_ManAndNum(p), 1.0*Vec_IntSize(vCuts)/Gia_ManAndNum(p) );
+    Vec_IntFree( vTemp );
+    Vec_IntFree( vCuts );
+    *pvCutsXor = vCutsXor;
+    *pvCutsMaj = vCutsMaj;
+}
+Vec_Int_t * Dtc_ManFindCommonCuts( Gia_Man_t * p, Vec_Int_t * vCutsXor, Vec_Int_t * vCutsMaj )
+{
+    int * pCuts0 = Vec_IntArray(vCutsXor);
+    int * pCuts1 = Vec_IntArray(vCutsMaj);
+    int * pLimit0 = Vec_IntLimit(vCutsXor);
+    int * pLimit1 = Vec_IntLimit(vCutsMaj);   int i;
+    Vec_Int_t * vFadds = Vec_IntAlloc( 1000 );
+    assert( Vec_IntSize(vCutsXor) % 4 == 0 );
+    assert( Vec_IntSize(vCutsMaj) % 4 == 0 );
+    while ( pCuts0 < pLimit0 && pCuts1 < pLimit1 )
+    {
+        for ( i = 0; i < 3; i++ )
+            if ( pCuts0[i] != pCuts1[i] )
+                break;
+        if ( i == 3 )
+        {
+            for ( i = 0; i < 4; i++ )
+                Vec_IntPush( vFadds, pCuts0[i] );
+            Vec_IntPush( vFadds, pCuts1[3] );
+            pCuts0 += 4;
+            pCuts1 += 4;
+        }
+        else if ( pCuts0[i] < pCuts1[i] )
+            pCuts0 += 4;
+        else if ( pCuts0[i] > pCuts1[i] )
+            pCuts1 += 4;
+    }
+    assert( Vec_IntSize(vFadds) % 5 == 0 );
+    return vFadds;
+}
+void Dtc_ManPrintFadds( Vec_Int_t * vFadds )
+{
+    int i;
+    Dtc_ForEachFadd( vFadds, i )
+    {
+        printf( "%6d : ", i );
+        printf( "%6d ", Vec_IntEntry(vFadds, 5*i+0) );
+        printf( "%6d ", Vec_IntEntry(vFadds, 5*i+1) );
+        printf( "%6d ", Vec_IntEntry(vFadds, 5*i+2) );
+        printf( " ->  " );
+        printf( "%6d ", Vec_IntEntry(vFadds, 5*i+3) );
+        printf( "%6d ", Vec_IntEntry(vFadds, 5*i+4) );
+        printf( "\n" );
+    }
+}
+int Dtc_ManCompare( int * pCut0, int * pCut1 )
+{
+    if ( pCut0[0] < pCut1[0] ) return -1;
+    if ( pCut0[0] > pCut1[0] ) return  1;
+    if ( pCut0[1] < pCut1[1] ) return -1;
+    if ( pCut0[1] > pCut1[1] ) return  1;
+    if ( pCut0[2] < pCut1[2] ) return -1;
+    if ( pCut0[2] > pCut1[2] ) return  1;
+    return 0;
+}
+int Dtc_ManCompare2( int * pCut0, int * pCut1 )
+{
+    if ( pCut0[4] < pCut1[4] ) return -1;
+    if ( pCut0[4] > pCut1[4] ) return  1;
+    return 0;
+}
+// returns array of 5-tuples containing inputs/sum/cout of each full adder
+Vec_Int_t * Gia_ManDetectFullAdders( Gia_Man_t * p, int fVerbose )
+{
+    Vec_Int_t * vCutsXor, * vCutsMaj, * vFadds;
+    Dtc_ManComputeCuts( p, &vCutsXor, &vCutsMaj, fVerbose );
+    qsort( Vec_IntArray(vCutsXor), Vec_IntSize(vCutsXor)/4, 16, (int (*)(const void *, const void *))Dtc_ManCompare );
+    qsort( Vec_IntArray(vCutsMaj), Vec_IntSize(vCutsMaj)/4, 16, (int (*)(const void *, const void *))Dtc_ManCompare );
+    vFadds = Dtc_ManFindCommonCuts( p, vCutsXor, vCutsMaj );
+    qsort( Vec_IntArray(vFadds), Vec_IntSize(vFadds)/5, 20, (int (*)(const void *, const void *))Dtc_ManCompare2 );
+    if ( fVerbose )
+        printf( "XOR3 cuts = %d.  MAJ cuts = %d.  Full-adders = %d.\n", Vec_IntSize(vCutsXor)/4, Vec_IntSize(vCutsMaj)/4, Vec_IntSize(vFadds)/5 );
+    if ( fVerbose )
+        Dtc_ManPrintFadds( vFadds );
+    Vec_IntFree( vCutsXor );
+    Vec_IntFree( vCutsMaj );
+    return vFadds;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Map each MAJ into the topmost MAJ of its chain.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+// maps MAJ nodes into FADD indexes
+Vec_Int_t * Gia_ManCreateMap( Gia_Man_t * p, Vec_Int_t * vFadds )
+{
+    Vec_Int_t * vMap = Vec_IntStartFull( Gia_ManObjNum(p) );  int i;
+    Dtc_ForEachFadd( vFadds, i )
+        Vec_IntWriteEntry( vMap, Vec_IntEntry(vFadds, 5*i+4), i );
+    return vMap;
+}
+// find chain length (for each MAJ, how many FADDs are rooted in its first input)
+int Gia_ManFindChains_rec( Gia_Man_t * p, int iMaj, Vec_Int_t * vFadds, Vec_Int_t * vMap, Vec_Int_t * vLength )
+{
+    assert( Vec_IntEntry(vMap, iMaj) >= 0 ); // MAJ
+    if ( Vec_IntEntry(vLength, iMaj) >= 0 )
+        return Vec_IntEntry(vLength, iMaj);
+    assert( Gia_ObjIsAnd(Gia_ManObj(p, iMaj)) );
+    {
+        int iFadd = Vec_IntEntry( vMap, iMaj );
+        int iXor0 = Vec_IntEntry( vFadds, 5*iFadd+0 );
+        int iXor1 = Vec_IntEntry( vFadds, 5*iFadd+1 );
+        int iXor2 = Vec_IntEntry( vFadds, 5*iFadd+2 );
+        int iLen0 = Vec_IntEntry( vMap, iXor0 ) == -1 ? 0 : Gia_ManFindChains_rec( p, iXor0, vFadds, vMap, vLength );
+        int iLen1 = Vec_IntEntry( vMap, iXor1 ) == -1 ? 0 : Gia_ManFindChains_rec( p, iXor1, vFadds, vMap, vLength );
+        int iLen2 = Vec_IntEntry( vMap, iXor2 ) == -1 ? 0 : Gia_ManFindChains_rec( p, iXor2, vFadds, vMap, vLength );
+        int iLen = Abc_MaxInt( iLen0, Abc_MaxInt(iLen1, iLen2) );
+        if ( iLen0 < iLen )
+        {
+            if ( iLen == iLen1 )
+            {
+                ABC_SWAP( int, Vec_IntArray(vFadds)[5*iFadd+0], Vec_IntArray(vFadds)[5*iFadd+1] );
+            }
+            else if ( iLen == iLen2 )
+            {
+                ABC_SWAP( int, Vec_IntArray(vFadds)[5*iFadd+0], Vec_IntArray(vFadds)[5*iFadd+2] );
+            }
+        }
+        Vec_IntWriteEntry( vLength, iMaj, iLen + 1 );
+        return iLen + 1;
+    }
+}
+// for each FADD find the longest chain and reorder its inputs
+void Gia_ManFindChains( Gia_Man_t * p, Vec_Int_t * vFadds, Vec_Int_t * vMap )
+{
+    int i;
+    // for each FADD find the longest chain rooted in it
+    Vec_Int_t * vLength = Vec_IntStartFull( Gia_ManObjNum(p) );
+    Dtc_ForEachFadd( vFadds, i )
+        Gia_ManFindChains_rec( p, Vec_IntEntry(vFadds, 5*i+4), vFadds, vMap, vLength );
+    Vec_IntFree( vLength );
+}
+// collect one carry-chain
+void Gia_ManCollectOneChain( Gia_Man_t * p, Vec_Int_t * vFadds, int iFaddTop, Vec_Int_t * vMap, Vec_Int_t * vChain )
+{
+    int iFadd;
+    Vec_IntClear( vChain );
+    for ( iFadd = iFaddTop; iFadd >= 0 && 
+          !Gia_ObjIsTravIdCurrentId(p, Vec_IntEntry(vFadds, 5*iFadd+3)) && 
+          !Gia_ObjIsTravIdCurrentId(p, Vec_IntEntry(vFadds, 5*iFadd+4)); 
+          iFadd = Vec_IntEntry(vMap, Vec_IntEntry(vFadds, 5*iFadd+0)) )
+          {
+                Vec_IntPush( vChain, iFadd );
+          }
+    Vec_IntReverseOrder( vChain );
+}
+void Gia_ManMarkWithTravId_rec( Gia_Man_t * p, int Id )
+{
+    Gia_Obj_t * pObj;
+    if ( Gia_ObjIsTravIdCurrentId(p, Id) )
+        return;
+    Gia_ObjSetTravIdCurrentId(p, Id);
+    pObj = Gia_ManObj( p, Id );
+    if ( Gia_ObjIsAnd(pObj) )
+        Gia_ManMarkWithTravId_rec( p, Gia_ObjFaninId0(pObj, Id) );
+    if ( Gia_ObjIsAnd(pObj) )
+        Gia_ManMarkWithTravId_rec( p, Gia_ObjFaninId1(pObj, Id) );
+}
+// returns mapping of each MAJ into the topmost elements of its chain
+Vec_Wec_t * Gia_ManCollectTopmost( Gia_Man_t * p, Vec_Int_t * vFadds, Vec_Int_t * vMap, int nFaddMin )
+{
+    int i, j, iFadd;
+    Vec_Int_t * vChain  = Vec_IntAlloc( 100 );
+    Vec_Wec_t * vChains = Vec_WecAlloc( Vec_IntSize(vFadds)/5 );
+    // erase elements appearing as FADD inputs
+    Vec_Bit_t * vMarksTop = Vec_BitStart( Vec_IntSize(vFadds)/5 );
+    Dtc_ForEachFadd( vFadds, i )
+        if ( (iFadd = Vec_IntEntry(vMap, Vec_IntEntry(vFadds, 5*i+0))) >= 0 )
+            Vec_BitWriteEntry( vMarksTop, iFadd, 1 );
+    // compress the remaining ones
+    Gia_ManIncrementTravId( p );
+    Dtc_ForEachFadd( vFadds, i )
+    {
+        if ( Vec_BitEntry(vMarksTop, i) )
+            continue;
+        Gia_ManCollectOneChain( p, vFadds, i, vMap, vChain );
+        if ( Vec_IntSize(vChain) < nFaddMin )
+            continue;
+        Vec_IntAppend( Vec_WecPushLevel(vChains), vChain );
+        Vec_IntForEachEntry( vChain, iFadd, j )
+        {
+            assert( !Gia_ObjIsTravIdCurrentId(p, Vec_IntEntry(vFadds, 5*iFadd+3)) );
+            assert( !Gia_ObjIsTravIdCurrentId(p, Vec_IntEntry(vFadds, 5*iFadd+4)) );
+            Gia_ManMarkWithTravId_rec( p, Vec_IntEntry(vFadds, 5*iFadd+3) );
+            Gia_ManMarkWithTravId_rec( p, Vec_IntEntry(vFadds, 5*iFadd+4) );
+        }
+    }
+    // cleanup
+    Vec_BitFree( vMarksTop );
+    Vec_IntFree( vChain );
+    return vChains;
+}
+// prints chains beginning in majority nodes contained in vTops
+void Gia_ManPrintChains( Gia_Man_t * p, Vec_Int_t * vFadds, Vec_Int_t * vMap, Vec_Wec_t * vChains )
+{
+    Vec_Int_t * vChain;
+    int i, k, iFadd, Count = 0;
+    Vec_WecForEachLevel( vChains, vChain, i )
+    {
+        Count += Vec_IntSize(vChain);
+        if ( i < 10 )
+        {
+            printf( "Chain %4d : %4d    ", i, Vec_IntSize(vChain) );
+            Vec_IntForEachEntry( vChain, iFadd, k )
+            {
+                printf( "%d(%d) ", iFadd, Vec_IntEntry(vFadds, 5*iFadd+4) );
+                if ( k != Vec_IntSize(vChain) - 1 )
+                    printf( "-> " );
+                if ( k > 6 )
+                {
+                    printf( "..." );
+                    break;
+                }
+            }
+            printf( "\n" );
+        }
+        else if ( i == 10 )
+            printf( "...\n" );
+
+    }
+    printf( "Total chains = %d. Total full-adders = %d.\n", Vec_WecSize(vChains), Count );
+}
+// map SUM bits and topmost MAJ into topmost FADD number
+Vec_Int_t * Gia_ManFindMapping( Gia_Man_t * p, Vec_Int_t * vFadds, Vec_Int_t * vMap, Vec_Wec_t * vChains )
+{
+    Vec_Int_t * vChain;
+    int i, k, iFadd = -1;
+    Vec_Int_t * vMap2Chain = Vec_IntStartFull( Gia_ManObjNum(p) );
+    Vec_WecForEachLevel( vChains, vChain, i )
+    {
+        assert( Vec_IntSize(vChain) > 0 );
+        Vec_IntForEachEntry( vChain, iFadd, k )
+        {
+            //printf( "Chain %d: setting SUM %d (obj %d)\n", i, k, Vec_IntEntry(vFadds, 5*iFadd+3) );
+            assert( Vec_IntEntry(vMap2Chain, Vec_IntEntry(vFadds, 5*iFadd+3)) == -1 );
+            Vec_IntWriteEntry( vMap2Chain, Vec_IntEntry(vFadds, 5*iFadd+3), i );
+        }
+        //printf( "Chain %d: setting CARRY (obj %d)\n", i, Vec_IntEntry(vFadds, 5*iFadd+4) );
+        assert( Vec_IntEntry(vMap2Chain, Vec_IntEntry(vFadds, 5*iFadd+4)) == -1 );
+        Vec_IntWriteEntry( vMap2Chain, Vec_IntEntry(vFadds, 5*iFadd+4), i );
+    }
+    return vMap2Chain;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Derive GIA with boxes containing adder-chains.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Int_t * Gia_ManCollectTruthTables( Gia_Man_t * p, Vec_Int_t * vFadds )
+{
+    int i, k, Type, Truth, pCut[4] = {3};
+    Vec_Int_t * vTruths = Vec_IntAlloc( 2*Vec_IntSize(vFadds)/5 );
+    Gia_ManCleanValue( p );
+    Dtc_ForEachFadd( vFadds, i )
+    {
+        for ( k = 0; k < 3; k++ )
+            pCut[k+1] = Vec_IntEntry( vFadds, 5*i+k );
+        Type = Dtc_ObjComputeTruth( p, Vec_IntEntry(vFadds, 5*i+3), pCut, &Truth );
+        assert( Type == 1 );
+        Vec_IntPush( vTruths, Truth );
+        Type = Dtc_ObjComputeTruth( p, Vec_IntEntry(vFadds, 5*i+4), pCut, &Truth );
+        assert( Type == 2 );
+        Vec_IntPush( vTruths, Truth );
+    }
+    return vTruths;
+}
+float * Gia_ManGenerateDelayTableFloat( int nIns, int nOuts )
+{
+    int i, Total = nIns * nOuts;
+    float * pDelayTable = ABC_ALLOC( float, Total + 3 );
+    pDelayTable[0] = 0;
+    pDelayTable[1] = nIns;
+    pDelayTable[2] = nOuts;
+    for ( i = 0; i < Total; i++ )
+        pDelayTable[i+3] = 1;
+    pDelayTable[i+3 - nIns] = -ABC_INFINITY;
+    return pDelayTable;
+}
+Tim_Man_t * Gia_ManGenerateTim( int nPis, int nPos, int nBoxes, int nIns, int nOuts )
+{
+    Tim_Man_t * pMan;
+    int i, curPi, curPo;
+    Vec_Ptr_t * vDelayTables = Vec_PtrAlloc( 1 );
+    Vec_PtrPush( vDelayTables, Gia_ManGenerateDelayTableFloat(nIns, nOuts) );
+    pMan = Tim_ManStart( nPis + nOuts * nBoxes, nPos + nIns * nBoxes );
+    Tim_ManSetDelayTables( pMan, vDelayTables );
+    curPi = nPis;
+    curPo = 0;
+    for ( i = 0; i < nBoxes; i++ )
+    {
+        Tim_ManCreateBox( pMan, curPo, nIns, curPi, nOuts, 0, 0 );
+        curPi += nOuts;
+        curPo += nIns;
+    }
+    curPo += nPos;
+    assert( curPi == Tim_ManCiNum(pMan) );
+    assert( curPo == Tim_ManCoNum(pMan) );
+    //Tim_ManPrint( pMan );
+    return pMan;
+}
+Gia_Man_t * Gia_ManGenerateExtraAig( int nBoxes, int nIns, int nOuts )
+{
+    Gia_Man_t * pNew = Gia_ManStart( nBoxes * 20 );
+    int i, k, pInLits[16], pOutLits[16];
+    assert( nIns < 16 && nOuts < 16 );
+    for ( i = 0; i < nIns; i++ )
+        pInLits[i] = Gia_ManAppendCi( pNew );
+    pOutLits[0] = Gia_ManAppendXor( pNew, Gia_ManAppendXor(pNew, pInLits[0], pInLits[1]), pInLits[2] );
+    pOutLits[1] = Gia_ManAppendMaj( pNew, pInLits[0], pInLits[1], pInLits[2] );
+    for ( i = 0; i < nBoxes; i++ )
+        for ( k = 0; k < nOuts; k++ )
+            Gia_ManAppendCo( pNew, pOutLits[k] );
+    return pNew;
+}
+void Gia_ManDupFadd( Gia_Man_t * pNew, Gia_Man_t * p, Vec_Int_t * vChain, Vec_Int_t * vFadds, Vec_Int_t * vMap, Vec_Wec_t * vChains, Vec_Int_t * vMap2Chain, Vec_Int_t * vTruths )
+{
+    extern void Gia_ManDupWithFaddBoxes_rec( Gia_Man_t * pNew, Gia_Man_t * p, Gia_Obj_t * pObj, Vec_Int_t * vFadds, Vec_Int_t * vMap, Vec_Wec_t * vChains, Vec_Int_t * vMap2Chain, Vec_Int_t * vTruths );
+    int i, k, iFadd = -1, iCiLit, pLits[3];
+    Gia_Obj_t * pObj;
+    // construct FADD inputs
+    Vec_IntForEachEntry( vChain, iFadd, i )
+        for ( k = 0; k < 3; k++ )
+        {
+            if ( i && !k ) continue;
+            pObj = Gia_ManObj( p, Vec_IntEntry(vFadds, 5*iFadd+k) );
+            Gia_ManDupWithFaddBoxes_rec( pNew, p, pObj, vFadds, vMap, vChains, vMap2Chain, vTruths );
+        }
+    // construct boxes
+    iCiLit = 0;
+    Vec_IntForEachEntry( vChain, iFadd, i )
+    {
+        int iXorTruth = Vec_IntEntry( vTruths, 2*iFadd+0 );
+        int iMajTruth = Vec_IntEntry( vTruths, 2*iFadd+1 );
+        for ( k = 0; k < 3; k++ )
+        {
+            pObj = Gia_ManObj( p, Vec_IntEntry(vFadds, 5*iFadd+k) );
+            pLits[k] = (!k && iCiLit) ? iCiLit : pObj->Value;
+            assert( pLits[k] >= 0 );
+        }
+        // normalize truth table
+        //    if ( Truth == 0xE8 || Truth == 0xD4 || Truth == 0xB2 || Truth == 0x71 ||
+        //         Truth == 0x17 || Truth == 0x2B || Truth == 0x4D || Truth == 0x8E )
+        if ( iMajTruth == 0x4D )
+            pLits[0] = Abc_LitNot(pLits[0]), iMajTruth = 0x8E, iXorTruth = 0xFF & ~iXorTruth;
+        else if ( iMajTruth == 0xD4 )
+            pLits[0] = Abc_LitNot(pLits[0]), iMajTruth = 0xE8, iXorTruth = 0xFF & ~iXorTruth;
+        else if ( iMajTruth == 0x2B )
+            pLits[1] = Abc_LitNot(pLits[1]), iMajTruth = 0x8E, iXorTruth = 0xFF & ~iXorTruth;
+        else if ( iMajTruth == 0xB2 )
+            pLits[1] = Abc_LitNot(pLits[1]), iMajTruth = 0xE8, iXorTruth = 0xFF & ~iXorTruth;
+        if ( iMajTruth == 0x8E )
+            pLits[2] = Abc_LitNot(pLits[2]), iMajTruth = 0xE8, iXorTruth = 0xFF & ~iXorTruth;
+        else if ( iMajTruth == 0x71 )
+            pLits[2] = Abc_LitNot(pLits[2]), iMajTruth = 0x17, iXorTruth = 0xFF & ~iXorTruth;
+        else assert( iMajTruth == 0xE8 || iMajTruth == 0x17 );
+        // normalize carry-in
+        if ( Abc_LitIsCompl(pLits[0]) )
+        {
+            for ( k = 0; k < 3; k++ )
+                pLits[k] = Abc_LitNot(pLits[k]);
+            iXorTruth = 0xFF & ~iXorTruth;
+            iMajTruth = 0xFF & ~iMajTruth;
+        }
+        // add COs
+        assert( !Abc_LitIsCompl(pLits[0]) );
+        for ( k = 0; k < 3; k++ )
+            Gia_ManAppendCo( pNew, pLits[k] );
+        // create CI
+        assert( iXorTruth == 0x96 || iXorTruth == 0x69 );
+        pObj = Gia_ManObj( p, Vec_IntEntry(vFadds, 5*iFadd+3) );
+        pObj->Value = Abc_LitNotCond( Gia_ManAppendCi(pNew), (int)(iXorTruth == 0x69) );
+        // create CI
+        assert( iMajTruth == 0xE8 || iMajTruth == 0x17 );
+        iCiLit = Abc_LitNotCond( Gia_ManAppendCi(pNew), (int)(iMajTruth == 0x17) );
+    }   
+    // assign carry out
+    assert( iFadd == Vec_IntEntryLast(vChain) );
+    pObj = Gia_ManObj( p, Vec_IntEntry(vFadds, 5*iFadd+4) );
+    pObj->Value = iCiLit;
+}
+void Gia_ManDupWithFaddBoxes_rec( Gia_Man_t * pNew, Gia_Man_t * p, Gia_Obj_t * pObj, Vec_Int_t * vFadds, Vec_Int_t * vMap, Vec_Wec_t * vChains, Vec_Int_t * vMap2Chain, Vec_Int_t * vTruths )
+{
+    int iChain;
+    if ( ~pObj->Value )
+        return;
+    assert( Gia_ObjIsAnd(pObj) );
+    iChain = Vec_IntEntry( vMap2Chain, Gia_ObjId(p, pObj) );
+/*
+    assert( iChain == -1 );
+    if ( iChain >= 0 )
+    {
+        Gia_ManDupFadd( pNew, p, Vec_WecEntry(vChains, iChain), vFadds, vMap, vChains, vMap2Chain, vTruths );
+        assert( ~pObj->Value );
+        return;
+    }
+*/
+    Gia_ManDupWithFaddBoxes_rec( pNew, p, Gia_ObjFanin0(pObj), vFadds, vMap, vChains, vMap2Chain, vTruths );
+    Gia_ManDupWithFaddBoxes_rec( pNew, p, Gia_ObjFanin1(pObj), vFadds, vMap, vChains, vMap2Chain, vTruths );
+    pObj->Value = Gia_ManAppendAnd( pNew, Gia_ObjFanin0Copy(pObj), Gia_ObjFanin1Copy(pObj) );
+}
+Gia_Man_t * Gia_ManDupWithNaturalBoxes( Gia_Man_t * p, int nFaddMin, int fVerbose )
+{
+    abctime clk = Abc_Clock();
+    Gia_Man_t * pNew;//, * pTemp;
+    Vec_Int_t * vFadds, * vMap, * vMap2Chain, * vTruths, * vChain;
+    Vec_Wec_t * vChains;
+    Gia_Obj_t * pObj;  
+    int i, nBoxes;
+    if ( Gia_ManBoxNum(p) > 0 )
+    {
+        printf( "Currently natural carry-chains cannot be detected when boxes are present.\n" );
+        return NULL;
+    }
+    assert( Gia_ManBoxNum(p) == 0 );
+
+    // detect FADDs
+    vFadds = Gia_ManDetectFullAdders( p, fVerbose );
+    assert( Vec_IntSize(vFadds) % 5 == 0 );
+    // map MAJ into its FADD
+    vMap = Gia_ManCreateMap( p, vFadds );
+    // for each FADD, find the longest chain and reorder its inputs
+    Gia_ManFindChains( p, vFadds, vMap );
+    // returns the set of topmost MAJ nodes
+    vChains = Gia_ManCollectTopmost( p, vFadds, vMap, nFaddMin );
+    if ( fVerbose )
+        Gia_ManPrintChains( p, vFadds, vMap, vChains );
+    if ( Vec_WecSize(vChains) == 0 )
+    {
+        Vec_IntFree( vFadds );
+        Vec_IntFree( vMap );
+        Vec_WecFree( vChains );
+        return Gia_ManDup( p );
+    }
+    // returns mapping of each MAJ into the topmost elements of its chain
+    vMap2Chain = Gia_ManFindMapping( p, vFadds, vMap, vChains );
+    // compute truth tables for FADDs
+    vTruths = Gia_ManCollectTruthTables( p, vFadds );
+    if ( fVerbose )
+        Abc_PrintTime( 1, "Carry-chain detection time", Abc_Clock() - clk );
+
+    // duplicate
+    clk = Abc_Clock();
+    Gia_ManFillValue( p );
+    pNew = Gia_ManStart( Gia_ManObjNum(p) );
+    pNew->pName = Abc_UtilStrsav( p->pName );
+    pNew->pSpec = Abc_UtilStrsav( p->pSpec );
+    Gia_ManConst0(p)->Value = 0;
+    Gia_ManForEachCi( p, pObj, i )
+        pObj->Value = Gia_ManAppendCi( pNew );
+    Vec_WecForEachLevel( vChains, vChain, i )
+        Gia_ManDupFadd( pNew, p, vChain, vFadds, vMap, vChains, vMap2Chain, vTruths );
+    Gia_ManForEachCo( p, pObj, i )
+        Gia_ManDupWithFaddBoxes_rec( pNew, p, Gia_ObjFanin0(pObj), vFadds, vMap, vChains, vMap2Chain, vTruths );
+    Gia_ManForEachCo( p, pObj, i )
+        Gia_ManAppendCo( pNew, Gia_ObjFanin0Copy(pObj) );
+    Gia_ManSetRegNum( pNew, Gia_ManRegNum(p) );
+    if ( Gia_ManRegNum(p) )
+    {
+        if ( fVerbose )
+            printf( "Warning: Sequential design is coverted into combinational one by adding white boxes.\n" );
+        pNew->nRegs = 0;
+    }
+    assert( !Gia_ManHasDangling(pNew) );
+
+    // cleanup
+    Vec_IntFree( vFadds );
+    Vec_IntFree( vMap );
+    Vec_WecFree( vChains );
+    Vec_IntFree( vMap2Chain );
+    Vec_IntFree( vTruths );
+    
+    // other information
+    nBoxes = (Gia_ManCiNum(pNew) - Gia_ManCiNum(p)) / 2;
+    assert( nBoxes == (Gia_ManCoNum(pNew) - Gia_ManCoNum(p)) / 3 );
+    pNew->pManTime  = Gia_ManGenerateTim( Gia_ManCiNum(p), Gia_ManCoNum(p), nBoxes, 3, 2 );
+    pNew->pAigExtra = Gia_ManGenerateExtraAig( nBoxes, 3, 2 );
+/*
+    // normalize
+    pNew = Gia_ManDupNormalize( pTemp = pNew, 0 );
+    pNew->pManTime  = pTemp->pManTime;  pTemp->pManTime  = NULL;
+    pNew->pAigExtra = pTemp->pAigExtra; pTemp->pAigExtra = NULL;
+    Gia_ManStop( pTemp );
+*/
+    //pNew = Gia_ManDupCollapse( pTemp = pNew, pNew->pAigExtra, NULL );
+    //Gia_ManStop( pTemp );
+
+    //Gia_ManIllustrateBoxes( pNew );
+    if ( fVerbose )
+        Abc_PrintTime( 1, "AIG with boxes construction time", Abc_Clock() - clk );
+    return pNew;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Converting AIG with annotated carry-chains into AIG with boxes.]
+
+  Description [Assumes that annotations are pObj->fMark0 or pObj->fMark1.
+  Only one of these can be set to 1.  If fMark0 (fMark1) is set to 1, 
+  the first (second) input of an AND-gate is chained.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Gia_ObjFanin0CopyCarry( Vec_Int_t * vCarries, Gia_Obj_t * pObj, int Id )
+{
+    if ( vCarries == NULL || Vec_IntEntry(vCarries, Gia_ObjFaninId0(pObj, Id)) == -1 )
+        return Gia_ObjFanin0Copy(pObj);
+    return Abc_LitNotCond( Vec_IntEntry(vCarries, Gia_ObjFaninId0(pObj, Id)), Gia_ObjFaninC0(pObj) );
+}
+int Gia_ObjFanin1CopyCarry( Vec_Int_t * vCarries, Gia_Obj_t * pObj, int Id )
+{
+    if ( vCarries == NULL || Vec_IntEntry(vCarries, Gia_ObjFaninId1(pObj, Id)) == -1 )
+        return Gia_ObjFanin1Copy(pObj);
+    return Abc_LitNotCond( Vec_IntEntry(vCarries, Gia_ObjFaninId1(pObj, Id)), Gia_ObjFaninC1(pObj) );
+}
+Gia_Man_t * Gia_ManDupWithArtificalFaddBoxes( Gia_Man_t * p, int fUseFanout, int fXorTrick )
+{
+    Gia_Man_t * pNew;
+    Gia_Obj_t * pObj;  
+    int nBoxes = Gia_ManBoxNum(p);
+    int i, nRealPis, nRealPos;
+    Vec_Int_t * vCarries = NULL;
+    // make sure two chains do not overlap
+    Gia_ManCleanPhase( p );
+    Gia_ManForEachCi( p, pObj, i )
+        assert( !pObj->fMark0 && !pObj->fMark1 );
+    Gia_ManForEachCo( p, pObj, i )
+        assert( !pObj->fMark0 && !pObj->fMark1 );
+    Gia_ManForEachAnd( p, pObj, i )
+    {
+        assert( !pObj->fMark0 || !pObj->fMark1 );
+        if ( pObj->fMark0 )
+        {
+            assert( Gia_ObjFanin0(pObj)->fPhase == 0 );
+            Gia_ObjFanin0(pObj)->fPhase = 1;
+        }
+        if ( pObj->fMark1 )
+        {
+            assert( Gia_ObjFanin1(pObj)->fPhase == 0 );
+            Gia_ObjFanin1(pObj)->fPhase = 1;
+        }
+    }
+    // create mapping for carry-chains
+    if ( !fUseFanout )
+        vCarries = Vec_IntStartFull( Gia_ManObjNum(p) );
+    // create references and discount carries
+    if ( vCarries )
+    {
+        Gia_ManCreateRefs( p );
+        Gia_ManForEachAnd( p, pObj, i )
+            if ( pObj->fMark0 )
+                Gia_ObjRefFanin0Dec( p, pObj );
+            else if ( pObj->fMark1 )
+                Gia_ObjRefFanin1Dec( p, pObj );
+    }
+    // if AIG already has (natural) FADD boxes, it should not un-normalized
+    Gia_ManFillValue( p );
+    pNew = Gia_ManStart( Gia_ManObjNum(p) );
+    pNew->pName = Abc_UtilStrsav( p->pName );
+    pNew->pSpec = Abc_UtilStrsav( p->pSpec );
+    Gia_ManConst0(p)->Value = 0;
+    Gia_ManForEachObj1( p, pObj, i )
+    {
+        if ( Gia_ObjIsCi(pObj) )
+            pObj->Value = Gia_ManAppendCi( pNew );
+        else if ( Gia_ObjIsCo(pObj) )
+            pObj->Value = Gia_ManAppendCo( pNew, Gia_ObjFanin0Copy(pObj) );
+        else if ( !pObj->fMark0 && !pObj->fMark1 ) // AND-gate
+            pObj->Value = Gia_ManAppendAnd( pNew, Gia_ObjFanin0Copy(pObj), Gia_ObjFanin1Copy(pObj) );
+        else // AND-gate with chain
+        {
+            int iCiLit, iOtherLit, iLit0, iLit1, iLit2, iXorLit;
+            assert( pObj->fMark0 != pObj->fMark1 );
+            iCiLit    = pObj->fMark0 ? Gia_ObjFanin0CopyCarry(vCarries, pObj, i) : Gia_ObjFanin1CopyCarry(vCarries, pObj, i);
+            iOtherLit = pObj->fMark0 ? Gia_ObjFanin1Copy(pObj) : Gia_ObjFanin0Copy(pObj);
+            assert( iCiLit >= 0 && iOtherLit >= 0 );
+            iLit0 = Abc_LitNotCond( iCiLit,    Abc_LitIsCompl(iCiLit) );
+            iLit1 = Abc_LitNotCond( iOtherLit, Abc_LitIsCompl(iCiLit) );
+            iLit2 = Abc_LitNotCond( 0,         Abc_LitIsCompl(iCiLit) );
+            // add COs
+            assert( !Abc_LitIsCompl(iLit0) );
+            Gia_ManAppendCo( pNew, iLit0 );
+            Gia_ManAppendCo( pNew, iLit1 );
+            Gia_ManAppendCo( pNew, iLit2 );
+            // add CI (unused sum bit)
+            iXorLit = Gia_ManAppendCi(pNew);
+            // add CI (carry bit)
+            pObj->Value = Abc_LitNotCond( Gia_ManAppendCi(pNew), Abc_LitIsCompl(iCiLit) );
+            if ( vCarries && pObj->fPhase )
+            {
+                Vec_IntWriteEntry( vCarries, i, pObj->Value );
+                if ( Gia_ObjRefNum(p, pObj) > 0 )
+                {
+                    if ( fXorTrick )
+                        pObj->Value = Gia_ManAppendAnd( pNew, Abc_LitNotCond(iXorLit, !Abc_LitIsCompl(iCiLit)), iOtherLit );
+                    else
+                        pObj->Value = Gia_ManAppendAnd( pNew, Gia_ObjFanin0Copy(pObj), Gia_ObjFanin1Copy(pObj) );
+                }
+            }
+            nBoxes++;
+        }
+    }
+    Gia_ManCleanPhase( p );
+    Vec_IntFreeP( &vCarries );
+    ABC_FREE( p->pRefs );
+    assert( !Gia_ManHasDangling(pNew) );
+    // other information
+//    nBoxes += (Gia_ManCiNum(pNew) - Gia_ManCiNum(p)) / 2;
+//    assert( nBoxes == Gia_ManBoxNum(p) + (Gia_ManCoNum(pNew) - Gia_ManCoNum(p)) / 3 );
+    nRealPis = Gia_ManBoxNum(p) ? Tim_ManPiNum((Tim_Man_t *)p->pManTime) : Gia_ManCiNum(p);
+    nRealPos = Gia_ManBoxNum(p) ? Tim_ManPoNum((Tim_Man_t *)p->pManTime) : Gia_ManCoNum(p);
+    pNew->pManTime  = Gia_ManGenerateTim( nRealPis, nRealPos, nBoxes, 3, 2 );
+    pNew->pAigExtra = Gia_ManGenerateExtraAig( nBoxes, 3, 2 );
+    // optionally normalize the AIG
+    return pNew;
+}
+Gia_Man_t * Gia_ManDupWithArtificalFaddBoxesTest( Gia_Man_t * p )
+{
+    Gia_Man_t * pNew;
+    Gia_Obj_t * pObj;
+    int i;
+    // label some and-gates
+    Gia_ManCleanMark01( p );
+    Gia_ManForEachAnd( p, pObj, i )
+    {
+        pObj->fMark0 = i % 5;
+        pObj->fMark1 = i % 7;
+        if ( pObj->fMark0 && pObj->fMark1 )
+            pObj->fMark0 = pObj->fMark1 = 0;
+    }
+
+    // output new AIG
+    pNew = Gia_ManDupWithArtificalFaddBoxes( p, 0, 0 );
+    Gia_ManCleanMark01( p );
+    return pNew;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Adds artificial carry chains to the manager.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+// computes AIG delay information when boxes are used
+int Gia_ManFindAnnotatedDelay( Gia_Man_t * p, int DelayC, int * pnBoxes, int fIgnoreBoxDelays )
+{
+    Gia_Obj_t * pObj;
+    int nRealPis = Gia_ManBoxNum(p) ? Tim_ManPiNum((Tim_Man_t *)p->pManTime) : Gia_ManCiNum(p);
+    int * pDelays = Vec_IntArray(p->vLevels);
+    int i, k, iBox, iBoxOutId, Delay, Delay0, Delay1, DelayMax = 0, nBoxes = 0;
+    Vec_IntFill( p->vLevels, Gia_ManObjNum(p), 0 );
+    Gia_ManForEachObj1( p, pObj, i )
+    {
+        if ( Gia_ObjIsCi(pObj) )
+        {
+            if ( fIgnoreBoxDelays )
+                continue;
+            // check if it is real PI
+            iBoxOutId = Gia_ObjCioId(pObj) - nRealPis;
+            if ( iBoxOutId < 0 )
+                continue;
+            // if it is a box output, find box number
+            iBox = iBoxOutId / 2;
+            assert( iBox < Gia_ManBoxNum(p) );
+            // check find the maximum delay of the box inputs
+            Delay = 0;
+            for ( k = 0; k < 3; k++ )
+            {
+                int Id = Gia_ObjId( p, Gia_ManCo(p, iBox*3+k) );
+                assert( Id < i );
+                Delay = Abc_MaxInt( Delay, pDelays[Id] );
+            }
+            // consider outputs
+            if ( iBoxOutId & 1 ) // carry output
+                Delay += DelayC;
+            else // sum output
+                Delay += 100;
+            pDelays[i] = Delay;
+            continue;
+        }
+        if ( Gia_ObjIsCo(pObj) )
+        {
+            pDelays[i] = pDelays[Gia_ObjFaninId0(pObj, i)];
+            DelayMax = Abc_MaxInt( DelayMax, pDelays[i] );
+            continue;
+        }
+        assert( !pObj->fMark0 || !pObj->fMark1 );
+        Delay0 = pDelays[Gia_ObjFaninId0(pObj, i)];
+        Delay1 = pDelays[Gia_ObjFaninId1(pObj, i)];
+        if ( pObj->fMark0 )
+        {
+            Delay = Abc_MaxInt( Delay0 + DelayC, Delay1 + 100 );
+            nBoxes++;
+        }
+        else if ( pObj->fMark1 )
+        {
+            Delay = Abc_MaxInt( Delay1 + DelayC, Delay0 + 100 );
+            nBoxes++;
+        }
+        else
+            Delay = Abc_MaxInt( Delay0 + 100, Delay1 + 100 );
+        pDelays[i] = Delay;
+    }
+    if ( pnBoxes )
+        *pnBoxes = nBoxes;
+    return DelayMax;
+}
+// check if the object is already used in some chain
+static inline int Gia_ObjIsUsed( Gia_Obj_t * pObj )
+{
+    return pObj->fMark0 || pObj->fMark1 || pObj->fPhase;
+}
+// finds internal node that can begin a new chain
+int Gia_ManFindChainStart( Gia_Man_t * p )
+{
+    Gia_Obj_t * pObj;
+    int * pDelays = Vec_IntArray(p->vLevels);
+    int i, iMax = -1, DelayMax = 0;
+    Gia_ManForEachAnd( p, pObj, i )
+    {
+        if ( Gia_ObjIsUsed(pObj) )
+            continue;
+        if ( DelayMax > pDelays[i] )
+            continue;
+        DelayMax = pDelays[i];
+        iMax = i;
+    }
+    return iMax;
+}
+// finds a sequence of internal nodes that creates a new chain
+int Gia_ManFindPath( Gia_Man_t * p, int DelayC, int nPathMin, int nPathMax, Vec_Int_t * vPath )
+{
+    Gia_Obj_t * pObj, * pFanin0, * pFanin1;
+    int * pDelays = Vec_IntArray(p->vLevels);
+    int i, iLit, iMax = Gia_ManFindChainStart( p );
+    if ( iMax == -1 )
+        return -1;
+    Vec_IntClear( vPath );
+    pObj = Gia_ManObj(p, iMax);
+    assert( Gia_ObjIsAnd(pObj) );
+    while ( Gia_ObjIsAnd(pObj) )
+    {
+        assert( !Gia_ObjIsUsed(pObj) );
+        pFanin0 = Gia_ObjFanin0(pObj);
+        pFanin1 = Gia_ObjFanin1(pObj);
+        if ( Gia_ObjIsUsed(pFanin0) && Gia_ObjIsUsed(pFanin1) )
+            break;
+        if ( Gia_ObjIsUsed(pFanin0) )
+        {
+            Vec_IntPush( vPath, Abc_Var2Lit(Gia_ObjId(p, pObj), 1) );
+            pObj = pFanin1;
+        }
+        else if ( Gia_ObjIsUsed(pFanin1) )
+        {
+            Vec_IntPush( vPath, Abc_Var2Lit(Gia_ObjId(p, pObj), 0) );
+            pObj = pFanin0;
+        }
+        else
+        {
+            if ( pDelays[Gia_ObjId(p, pFanin1)] > pDelays[Gia_ObjId(p, pFanin0)] )
+            {
+                Vec_IntPush( vPath, Abc_Var2Lit(Gia_ObjId(p, pObj), 1) );
+                pObj = pFanin1;
+            }
+            else
+            {
+                Vec_IntPush( vPath, Abc_Var2Lit(Gia_ObjId(p, pObj), 0) );
+                pObj = pFanin0;
+            }
+        }
+    }
+    if ( Vec_IntSize(vPath) < nPathMin )
+    {
+        Gia_ManObj(p, iMax)->fPhase = 1;
+        return 0;
+    }
+    // label nodes
+    if ( Vec_IntSize(vPath) > nPathMax )
+        Vec_IntShrink( vPath, nPathMax );
+    Vec_IntForEachEntry( vPath, iLit, i )
+    {
+        pObj = Gia_ManObj( p, Abc_Lit2Var(iLit) );
+        if ( Abc_LitIsCompl(iLit) )
+        {
+            assert( pObj->fMark1 == 0 );
+            pObj->fMark1 = 1;
+            assert( Gia_ObjFanin1(pObj)->fPhase == 0 );
+            Gia_ObjFanin1(pObj)->fPhase = 1;
+        }
+        else
+        {
+            assert( pObj->fMark0 == 0 );
+            pObj->fMark0 = 1;
+            assert( Gia_ObjFanin0(pObj)->fPhase == 0 );
+            Gia_ObjFanin0(pObj)->fPhase = 1;
+        }
+    }
+    return Vec_IntSize(vPath);
+}
+// iteratively create the given number of chains
+int Gia_ManIteratePaths( Gia_Man_t * p, int DelayC, int nPathMin, int nPathMax, int nPathLimit, int fIgnoreBoxDelays, int fVerbose )
+{
+    Gia_Obj_t * pObj;
+    Vec_Int_t * vPath = Vec_IntAlloc( 100 );
+    int i, RetValue, nBoxes, MaxDelay, nPaths = 0;
+    assert( p->vLevels == NULL );
+    p->vLevels = Vec_IntStart( Gia_ManObjNum(p) );
+    Gia_ManCleanMark01( p );
+    Gia_ManCleanPhase( p );
+    Gia_ManForEachCi( p, pObj, i )
+        pObj->fPhase = 1;
+    if ( fVerbose )
+        printf( "Running path detection: BoxDelay = %d, PathMin = %d, PathMax = %d, PathLimit = %d.\n", DelayC, nPathMin, nPathMax, nPathLimit );
+    for ( i = 0; i < nPathLimit; i++ )
+    {
+        MaxDelay = Gia_ManFindAnnotatedDelay( p, DelayC, &nBoxes, fIgnoreBoxDelays );
+        RetValue = Gia_ManFindPath( p, DelayC, nPathMin, nPathMax, vPath );
+        if ( RetValue == -1 )
+            break;
+        nPaths += (RetValue > 0);
+        if ( fVerbose )
+            printf( "Iter %5d : Paths = %2d. Boxes = %2d. Total boxes = %6d.  Max delay = %5d.\n", i, nPaths, RetValue, nBoxes, MaxDelay );
+    }
+    Vec_IntFree( vPath );
+    Vec_IntFreeP( &p->vLevels );
+    Gia_ManCleanPhase( p );
+    return 1;
+}
+// annotate artificial chains and then put them into boxes
+Gia_Man_t * Gia_ManDupWithArtificialBoxes( Gia_Man_t * p, int DelayC, int nPathMin, int nPathMax, int nPathLimit, int fUseFanout, int fXorTrick, int fIgnoreBoxDelays, int fVerbose )
+{
+    Gia_Man_t * pNew;
+/*
+    if ( Gia_ManBoxNum(p) > 0 )
+    {
+        printf( "Currently artifical carry-chains cannot be detected when natural ones are present.\n" );
+        return NULL;
+    }
+*/
+    Gia_ManIteratePaths( p, DelayC, nPathMin, nPathMax, nPathLimit, fIgnoreBoxDelays, fVerbose );
+    pNew = Gia_ManDupWithArtificalFaddBoxes( p, fUseFanout, fXorTrick );
+    Gia_ManCleanMark01( p );
+    return pNew;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+