src/main/java/org/apache/datasketches/pig/hll/AlgebraicFinal.java [80:96]:
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      if (f0 instanceof DataBag) {
        final DataBag innerBag = (DataBag) f0; // inputTuple.bag0.dataTupleN.f0:bag
        if (innerBag.size() == 0) { continue; }
        // If field 0 of a dataTuple is a Bag, all innerTuples of this inner bag
        // will be passed into the union.
        // It is due to system bagged outputs from multiple mapper Initial functions.
        // The Intermediate stage was bypassed.
        updateUnion(innerBag, union);
      } else if (f0 instanceof DataByteArray) { // inputTuple.bag0.dataTupleN.f0:DBA
        // If field 0 of a dataTuple is a DataByteArray, we assume it is a sketch
        // due to system bagged outputs from multiple mapper Intermediate functions.
        // Each dataTuple.DBA:sketch will merged into the union.
        final DataByteArray dba = (DataByteArray) f0;
        union.update(HllSketch.wrap(Memory.wrap(dba.get())));
      } else { // we should never get here
        throw new IllegalArgumentException("dataTuple.Field0 is not a DataBag or DataByteArray: "
            + f0.getClass().getName());
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src/main/java/org/apache/datasketches/pig/hll/AlgebraicIntermediate.java [82:98]:
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      if (f0 instanceof DataBag) {
        final DataBag innerBag = (DataBag) f0; // inputTuple.bag0.dataTupleN.f0:bag
        if (innerBag.size() == 0) { continue; }
        // If field 0 of a dataTuple is a Bag, all innerTuples of this inner bag
        // will be passed into the union.
        // It is due to system bagged outputs from multiple mapper Initial functions.
        // The Intermediate stage was bypassed.
        updateUnion(innerBag, union);
      } else if (f0 instanceof DataByteArray) { // inputTuple.bag0.dataTupleN.f0:DBA
        // If field 0 of a dataTuple is a DataByteArray, we assume it is a sketch
        // due to system bagged outputs from multiple mapper Intermediate functions.
        // Each dataTuple.DBA:sketch will merged into the union.
        final DataByteArray dba = (DataByteArray) f0;
        union.update(HllSketch.wrap(Memory.wrap(dba.get())));
      } else { // we should never get here
        throw new IllegalArgumentException("dataTuple.Field0 is not a DataBag or DataByteArray: "
            + f0.getClass().getName());
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