README
��[�!�[�B�u�i�l�d� �S�t�a�t�u�s�]�(�h�t�t�p�s�:�/�/�t�r�a�v�i�s�-�c�i�.�o�r�g�/�s�a�m�g�w�i�s�e�/�p�6�-�N�u�m�e�r�i�c�-�P�a�c�k�.�s�v�g�?�b�r�a�n�c�h�=�m�a�s�t�e�r�)�]�(�h�t�t�p�s�:�/�/�t�r�a�v�i�s�-�c�i�.�o�r�g�/�s�a�m�g�w�i�s�e�/�p�6�-�N�u�m�e�r�i�c�-�P�a�c�k�)�
�
�
�
�N�A�M�E�
�
�=�=�=�=�
�
�
�
�N�u�m�e�r�i�c�:�:�P�a�c�k� �-� �C�o�n�v�e�r�t� �R�a�k�u� �N�u�m�e�r�i�c�s� �t�o� �B�u�f�s� �a�n�d� �b�a�c�k� �a�g�a�i�n�!�
�
�
�
�S�Y�N�O�P�S�I�S�
�
�=�=�=�=�=�=�=�=�
�
�
�
� � � � �u�s�e� �N�u�m�e�r�i�c�:�:�P�a�c�k� �:�A�L�L�;�
�
�
�
� � � � �#� �p�a�c�k� �a�n�d� �u�n�p�a�c�k� �f�l�o�a�t�s�
�
� � � � �m�y� �B�u�f� ��f�l�o�a�t�-�b�u�f�.�p�e�r�l� �}� �-�>� �{� �u�n�p�a�c�k�-�f�l�o�a�t� ��d�o�u�b�l�e�-�b�u�f� �=� �p�a�c�k�-�d�o�u�b�l�e� �2�.�5�;�
�
� � � � �s�a�y� �"�{� ��d�o�u�b�l�e�-�b�u�f� �}�"�;�
�
�
�
� � � � �#� �p�a�c�k� �a�n�d� �u�n�p�a�c�k� �I�n�t� �(�s�e�e� �a�l�s�o� �i�n�t�6�4� �v�a�r�i�a�n�t�s�)�
�
� � � � �m�y� �B�u�f� ��i�n�t�-�b�u�f�.�p�e�r�l� �}� �-�>� �{� �u�n�p�a�c�k�-�i�n�t�3�2� ��l�i�t�t�l�e�-�e�n�d�i�a�n�-�b�u�f� �=� �p�a�c�k�-�i�n�t�3�2� �1�1�,� �:�b�y�t�e�-�o�r�d�e�r�(�l�i�t�t�l�e�-�e�n�d�i�a�n�)�;�
�
� � � � �s�a�y� �"�{� ��l�i�t�t�l�e�-�e�n�d�i�a�n�-�b�u�f�,� �:�b�y�t�e�-�o�r�d�e�r�(�l�i�t�t�l�e�-�e�n�d�i�a�n�)�
�
� � � � �}�"�;�
�
�
�
�D�E�S�C�R�I�P�T�I�O�N�
�
�=�=�=�=�=�=�=�=�=�=�=�
�
�
�
�N�u�m�e�r�i�c�:�:�P�a�c�k� �i�s� �a� �R�a�k�u� �m�o�d�u�l�e� �f�o�r� �p�a�c�k�i�n�g� �v�a�l�u�e�s� �o�f� �t�h�e� �N�u�m�e�r�i�c� �r�o�l�e� �i�n�t�o� �B�u�f� �o�b�j�e�c�t�s� �(�W�i�t�h� �t�h�e� �e�x�c�e�p�t�i�o�n� �o�f� �C�o�m�p�l�e�x� �n�u�m�b�e�r�s�)�.� �T�h�i�s� �m�o�d�u�l�e� �p�r�o�v�i�d�e�s� �a� �R�a�k�u�d�o� �c�o�m�p�a�t�i�b�l�e�,� �n�o�n�-�e�x�p�e�r�i�m�e�n�t�a�l�,� �n�u�m�e�r�i�c� �p�a�c�k�i�n�g� �a�n�d� �u�n�p�a�c�k�i�n�g� �f�a�c�i�l�i�t�y�,� �b�u�i�l�t� �w�i�t�h� �u�t�i�l�i�t�i�e�s� �o�f� �N�a�t�i�v�e�C�a�l�l�.� �I�n�t�e�g�e�r� �r�a�n�g�e�s� �f�r�o�m� �8� �t�o� �6�4� �b�i�t�s� �a�r�e� �s�u�p�p�o�r�t�e�d� �a�n�d� �f�l�o�a�t�i�n�g� �p�o�i�n�t� �a�s� �w�e�l�l� �a�s� �d�o�u�b�l�e� �p�r�e�c�i�s�i�o�n� �f�l�o�a�t�i�n�g� �p�o�i�n�t� �n�u�m�b�e�r�s�.� �B�y�t�e� �o�r�d�e�r� �d�e�f�a�u�l�t�s� �t�o� �t�h�e� �n�a�t�i�v�e� �b�y�t�e� �o�r�d�e�r� �o�f� �t�h�e� �s�y�s�t�e�m� �a�n�d� �c�a�n� �b�e� �s�p�e�c�i�f�i�e�d� �w�i�t�h� �t�h�e� �B�y�t�e�O�r�d�e�r� �e�n�u�m�.�
�
�
�
�N�u�m�e�r�i�c�:�:�P�a�c�k� �e�x�p�o�r�t�s� �t�h�e� �e�n�u�m� �B�y�t�e�O�r�d�e�r� �b�y� �d�e�f�a�u�l�t� �(�B�y�t�e�O�r�d�e�r� �i�s� �e�x�p�o�r�t�e�d� �a�s� �:�M�A�N�D�A�T�O�R�Y�)�.�
�
�
�
�<�t�a�b�l�e� �c�l�a�s�s�=�"�p�o�d�-�t�a�b�l�e�"�>�
�
�<�t�h�e�a�d�>�<�t�r�>�
�
�<�t�h�>�B�y�t�e�O�r�d�e�r�<�/�t�h�>� �<�t�h�>�D�e�s�c�r�i�p�t�i�o�n�<�/�t�h�>�
�
�<�/�t�r�>�<�/�t�h�e�a�d�>�
�
�<�t�b�o�d�y�>�
�
�<�t�r�>� �<�t�d�>�n�a�t�i�v�e�-�e�n�d�i�a�n�<�/�t�d�>� �<�t�d�>�T�h�e� �n�a�t�i�v�e� �b�y�t�e� �o�r�d�e�r�i�n�g� �o�f� �t�h�e� �c�u�r�r�e�n�t� �s�y�s�t�e�m�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�l�i�t�t�l�e�-�e�n�d�i�a�n�<�/�t�d�>� �<�t�d�>�C�o�m�m�o�n� �b�y�t�e� �o�r�d�e�r�i�n�g� �o�f� �c�o�n�t�e�m�p�o�r�a�r�y� �C�P�U�s�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�b�i�g�-�e�n�d�i�a�n�<�/�t�d�>� �<�t�d�>�A�l�s�o� �k�n�o�w�n� �a�s� �n�e�t�w�o�r�k� �b�y�t�e� �o�r�d�e�r�<�/�t�d�>� �<�/�t�r�>�
�
�<�/�t�b�o�d�y�>�
�
�<�/�t�a�b�l�e�>�
�
�
�
�B�y� �d�e�f�a�u�l�t� �N�u�m�e�r�i�c�:�:�P�a�c�k�'�s� �p�a�c�k� �a�n�d� �u�n�p�a�c�k� �f�u�n�c�t�i�o�n�s� �r�e�t�u�r�n� �a�n�d� �a�c�c�e�p�t� �b�i�g�-�e�n�d�i�a�n� �B�u�f�s�.� �T�o� �o�v�e�r�r�i�d�e� �t�h�i�s� �p�r�o�v�i�d�e� �t�h�e� �:�b�y�t�e�-�o�r�d�e�r� �n�a�m�e�d� �p�a�r�a�m�e�t�e�r� �w�i�t�h� �t�h�e� �e�n�u�m� �v�a�l�u�e� �f�o�r� �y�o�u�r� �d�e�s�i�r�e�d� �b�e�h�a�v�i�o�u�r�.� �T�o� �d�i�s�a�b�l�e� �b�y�t�e� �o�r�d�e�r� �m�a�n�a�g�e�m�e�n�t� �p�a�s�s� �:�b�y�t�e�-�o�r�d�e�r�(�n�a�t�i�v�e�-�e�n�d�i�a�n�)�.�
�
�
�
�U�s�e� �N�u�m�e�r�i�c�:�:�P�a�c�k� �:�A�L�L� �t�o� �e�x�p�o�r�t� �a�l�l� �e�x�p�o�r�t�a�b�l�e� �f�u�n�c�t�i�o�n�a�l�i�t�y�.�
�
�
�
�U�s�e� �:�f�l�o�a�t�s� �o�r� �:�i�n�t�s� �f�l�a�g�s� �t�o� �e�x�p�o�r�t� �s�u�b�s�e�t�s� �o�f� �t�h�e� �m�o�d�u�l�e�'�s� �f�u�n�c�t�i�o�n�a�l�i�t�y�.�
�
�
�
�<�t�a�b�l�e� �c�l�a�s�s�=�"�p�o�d�-�t�a�b�l�e�"�>�
�
�<�t�h�e�a�d�>�<�t�r�>�
�
�<�t�h�>�E�x�p�o�r�t� �t�a�g�<�/�t�h�>� �<�t�h�>�F�u�n�c�t�i�o�n�s�<�/�t�h�>�
�
�<�/�t�r�>�<�/�t�h�e�a�d�>�
�
�<�t�b�o�d�y�>�
�
�<�t�r�>� �<�t�d�>�:�f�l�o�a�t�s�<�/�t�d�>� �<�t�d�>�p�a�c�k�-�f�l�o�a�t�,� �u�n�p�a�c�k�-�f�l�o�a�t�,� �p�a�c�k�-�d�o�u�b�l�e�,� �u�n�p�a�c�k�-�d�o�u�b�l�e�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�:�i�n�t�s�<�/�t�d�>� �<�t�d�>�p�a�c�k�-�u�i�n�t�3�2�,� �p�a�c�k�-�i�n�t�3�2�,� �u�n�p�a�c�k�-�i�n�t�3�2�,� �u�n�p�a�c�k�-�u�i�n�t�3�2�,� �p�a�c�k�-�i�n�t�6�4�,� �u�n�p�a�c�k�-�i�n�t�6�4�,� �p�a�c�k�-�u�i�n�t�6�4�,� �u�n�p�a�c�k�-�u�i�n�t�6�4�,� �p�a�c�k�-�i�n�t�1�6�,� �u�n�p�a�c�k�-�i�n�t�1�6�,� �p�a�c�k�-�u�i�n�t�1�6�,� �u�n�p�a�c�k�-�u�i�n�t�1�6�,� �p�a�c�k�-�i�n�t�8�,� �u�n�p�a�c�k�-�i�n�t�8�,� �p�a�c�k�-�u�i�n�t�8�,� �u�n�p�a�c�k�-�u�i�n�t�8�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�:�b�e�r�<�/�t�d�>� �<�t�d�>�p�a�c�k�-�b�e�r�,� �u�n�p�a�c�k�-�b�e�r�,� �c�o�l�l�e�c�t�-�b�e�r�<�/�t�d�>� �<�/�t�r�>�
�
�<�/�t�b�o�d�y�>�
�
�<�/�t�a�b�l�e�>�
�
�
�
�C�H�A�N�G�E�S�
�
�=�=�=�=�=�=�=�
�
�
�
�<�t�a�b�l�e� �c�l�a�s�s�=�"�p�o�d�-�t�a�b�l�e�"�>�
�
�<�t�b�o�d�y�>�
�
�<�t�r�>� �<�t�d�>�A�d�d�e�d� �b�e�r� �e�n�c�o�d�i�n�g� �a�n�d� �d�e�c�o�d�i�n�g� �a�l�a� �p�e�r�l� �p�a�c�k� �&�#�3�9�;�w�&�#�3�9�;�<�/�t�d�>� �<�t�d�>�E�x�p�a�n�d�e�d� �p�o�t�e�n�t�i�a�l� �u�s�e� �c�a�s�e�s�<�/�t�d�>� �<�t�d�>�2�0�2�0�-�0�4�-�2�8�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�A�d�d�e�d� �8� �a�n�d� �1�6� �b�i�t� �i�n�t�e�g�e�r� �t�y�p�e�s�<�/�t�d�>� �<�t�d�>�E�x�p�a�n�d�e�d� �p�o�t�e�n�t�i�a�l� �u�s�e� �c�a�s�e�s�<�/�t�d�>� �<�t�d�>�2�0�2�0�-�0�4�-�2�7�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�R�e�m�o�v�e�d� �b�u�n�d�l�e�d� �n�a�t�i�v�e� �l�i�b�r�a�r�y�,� �n�o�w� �p�u�r�e� �p�e�r�l�6�<�/�t�d�>� �<�t�d�>�I�m�p�r�o�v�e�d� �p�o�r�t�a�b�i�l�i�t�y� �a�n�d� �r�e�l�i�a�b�i�l�i�t�y�<�/�t�d�>� �<�t�d�>�2�0�1�8�-�0�6�-�2�0�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�A�d�d�e�d� �p�a�c�k�-�u�i�n�t�3�2�,� �p�a�c�k�-�u�i�n�t�3�2� �a�n�d� �u�n�p�a�c�k�-�u�i�n�t�3�2�<�/�t�d�>� �<�t�d�>�A�d�d�e�d� �s�u�p�p�o�r�t� �f�o�r� �u�n�s�i�g�n�e�d� �t�y�p�e�s�<�/�t�d�>� �<�t�d�>�2�0�1�7�-�0�4�-�2�0�<�/�t�d�>� �<�/�t�r�>� �<�t�r�>� �<�t�d�>�C�h�a�n�g�e�d� �n�a�m�e�d� �a�r�g�u�m�e�n�t� �:�e�n�d�i�a�n�n�e�s�s� �t�o� �:�b�y�t�e�-�o�r�d�e�r�<�/�t�d�>� �<�t�d�>�S�i�g�n�a�t�u�r�e�s� �n�o�w� �r�e�a�d� �m�o�r�e� �n�a�t�u�r�a�l�l�y�<�/�t�d�>� �<�t�d�>�2�0�1�6�-�0�8�-�3�0�<�/�t�d�>� �<�/�t�r�>�
�
�<�/�t�b�o�d�y�>�
�
�<�/�t�a�b�l�e�>�
�
�
�
�S�E�E� �A�L�S�O�
�
�=�=�=�=�=�=�=�=�
�
�
�
�R�a�k�u�d�o� �c�o�r�e� �f�r�o�m� �6�.�d� �2�0�1�8� �a�n�d� �l�a�t�e�r� �s�u�p�p�o�r�t�s� �r�e�a�d�i�n�g� �v�a�l�u�e�s� �f�r�o�m� �a� �b�l�o�b�8� �w�i�t�h� �a� �v�e�r�y� �s�i�m�i�l�a�r� �i�n�t�e�r�f�a�c�e� �t�o� �t�h�i�s� �m�o�d�u�l�e�,� �s�e�e� �t�h�e� �d�o�c�s� �h�e�r�e�:� �[�h�t�t�p�s�:�/�/�d�o�c�s�.�p�e�r�l�6�.�o�r�g�/�t�y�p�e�/�B�l�o�b�#�M�e�t�h�o�d�s�_�o�n�_�b�l�o�b�8�_�o�n�l�y�_�(�6�.�d�,�_�2�0�1�8�.�1�2�_�a�n�d�_�l�a�t�e�r�)�]�(�h�t�t�p�s�:�/�/�d�o�c�s�.�p�e�r�l�6�.�o�r�g�/�t�y�p�e�/�B�l�o�b�#�M�e�t�h�o�d�s��o�n��b�l�o�b�8��o�n�l�y��(�6�.�d�,��2�0�1�8�.�1�2��a�n�d�_�l�a�t�e�r�)�)�.�
�
�
�
�T�h�e� �[�N�a�t�i�v�e�:�:�P�a�c�k�i�n�g�]�(�h�t�t�p�s�:�/�/�g�i�t�h�u�b�.�c�o�m�/�p�d�f�-�r�a�k�u�/�N�a�t�i�v�e�-�P�a�c�k�i�n�g�-�r�a�k�u�)� �m�o�d�u�l�e� �p�r�o�v�i�d�e�s� �a� �r�o�l�e� �b�a�s�e�d� �p�a�c�k�i�n�g� �m�e�c�h�a�n�i�s�m� �f�o�r� �c�l�a�s�s�e�s�.�
�
�
�
�T�h�e� �[�B�i�n�a�r�y�:�:�S�t�r�u�c�t�u�r�e�d�]�(�h�t�t�p�s�:�/�/�g�i�t�h�u�b�.�c�o�m�/�a�v�u�s�e�r�o�w�/�p�e�r�l�6�-�b�i�n�a�r�y�-�s�t�r�u�c�t�u�r�e�d�)� �m�o�d�u�l�e� �a�p�p�e�a�r�s� �t�o� �b�e� �s�i�m�i�l�a�r� �t�o� �N�a�t�i�v�e�:�:�P�a�c�k�i�n�g� �b�u�t� �i�m�p�l�e�m�e�n�t�e�d� �v�i�a� �a� �c�l�a�s�s� �i�n�h�e�r�i�t�a�n�c�e� �i�n�t�e�r�f�a�c�e�.�
�
�
�
�T�h�e� �[�P�5�p�a�c�k�]�(�h�t�t�p�s�:�/�/�m�o�d�u�l�e�s�.�r�a�k�u�.�o�r�g�/�d�i�s�t�/�P�5�p�a�c�k�:�c�p�a�n�:�E�L�I�Z�A�B�E�T�H�)� �m�o�d�u�l�e� �i�s� �a� �r�e�-�i�m�p�l�e�m�e�n�t�a�t�i�o�n� �o�f� �p�e�r�l� �5�'�s� �p�a�c�k� �s�u�b�r�o�u�t�i�n�e� �(�R�a�k�u�'�s� �p�a�c�k� �s�u�b�r�o�u�t�i�n�e� �i�s� �c�u�r�r�e�n�t�l�y� �e�x�p�e�r�i�m�e�n�t�a�l� �i�n� �r�a�k�u�d�o�)�.�
�
�
�
�A�U�T�H�O�R�
�
�=�=�=�=�=�=�
�
�
�
�S�a�m� �G�i�l�l�e�s�p�i�e� �<�s�a�m�g�w�i�s�e�@�g�m�a�i�l�.�c�o�m�>�
�
�
�
�C�O�P�Y�R�I�G�H�T� �A�N�D� �L�I�C�E�N�S�E�
�
�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�=�
�
�
�
�C�o�p�y�r�i�g�h�t� �2�0�1�6� �S�a�m� �G�i�l�l�e�s�p�i�e�
�
�
�
�T�h�i�s� �l�i�b�r�a�r�y� �i�s� �f�r�e�e� �s�o�f�t�w�a�r�e�;� �y�o�u� �c�a�n� �r�e�d�i�s�t�r�i�b�u�t�e� �i�t� �a�n�d�/�o�r� �m�o�d�i�f�y� �i�t� �u�n�d�e�r� �t�h�e� �A�r�t�i�s�t�i�c� �L�i�c�e�n�s�e� �2�.�0�.�
�
�
�
�F�U�N�C�T�I�O�N�S�
�
�=�=�=�=�=�=�=�=�=�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�f�l�o�a�t�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�f�l�o�a�t�(� � � � � � �R�a�t�(�C�o�o�l�)� �$�r�a�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a� �R�a�t� �i�n�t�o� �a� �s�i�n�g�l�e�-�p�r�e�c�i�s�i�o�n� �f�l�o�a�t�i�n�g�-�p�o�i�n�t� �B�u�f� �(�e�.�g�.� �f�l�o�a�t�)�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�f�l�o�a�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �R�a�t�s� �a�n�d� �f�l�o�a�t�s� �a�r�e� �n�o�t� �d�i�r�e�c�t�l�y� �a�n�a�l�o�g�o�u�s� �a�n�d� �a�s� �s�u�c�h� �y�o�u� �s�h�o�u�l�d� �e�x�p�e�c�t� �s�o�m�e� �v�a�r�i�a�t�i�o�n� �i�n� �t�h�e� �v�a�l�u�e�s� �p�a�c�k�e�d� �v�i�a� �t�h�i�s� �m�e�t�h�o�d� �a�n�d� �t�h�e� �o�r�i�g�i�n�a�l� �v�a�l�u�e�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�f�l�o�a�t�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�f�l�o�a�t�(� � � � � � �B�u�f� �$�f�l�o�a�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �R�a�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a� �B�u�f� �c�o�n�t�a�i�n�i�n�g� �a� �s�i�n�g�l�e�-�p�r�e�c�i�s�i�o�n� �f�l�o�a�t�i�n�g�-�p�o�i�n�t� �n�u�m�b�e�r� �(�f�l�o�a�t�)� �i�n�t�o� �a� �N�u�m�e�r�i�c�.� �R�e�t�u�r�n�s� �a� �R�a�t� �o�b�j�e�c�t� �o�n� �a� �N�a�N� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�f�l�o�a�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�i�n�t�3�2�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�i�n�t�3�2�(� � � � � � �I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a� �4� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a� �s�i�g�n�e�d� �3�2� �b�i�t� �i�n�t�e�g�e�r� �[������2�,�1�4�7�,�4�8�3�,�6�4�8� �t�o� �2�,�1�4�7�,�4�8�3�,�6�4�7�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�i�n�t�3�2�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�i�n�t�3�2�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a� �s�i�g�n�e�d� �4� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�u�i�n�t�3�2�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�u�i�n�t�3�2�(� � � � � � �U�I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a� �4� �b�y�t�e� �u�n�s�i�g�n�e�d� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a�n� �u�n�s�i�g�n�e�d� �3�2� �b�i�t� �i�n�t�e�g�e�r� �[�0� �t�o� �4�,�2�9�4�,�9�6�7�,�2�9�5�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�3�2�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�3�2�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a�n� �u�n�s�i�g�n�e�d� �4� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�d�o�u�b�l�e�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�d�o�u�b�l�e�(� � � � � � �R�a�t�(�C�o�o�l�)� �$�r�a�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a� �R�a�t� �i�n�t�o� �a� �d�o�u�b�l�e�-�p�r�e�c�i�s�i�o�n� �f�l�o�a�t�i�n�g�-�p�o�i�n�t� �B�u�f� �(�e�.�g�.� �d�o�u�b�l�e�)�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�f�l�o�a�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �R�a�t�s� �a�n�d� �d�o�u�b�l�e�s� �a�r�e� �n�o�t� �d�i�r�e�c�t�l�y� �a�n�a�l�o�g�o�u�s� �a�n�d� �a�s� �s�u�c�h� �y�o�u� �s�h�o�u�l�d� �e�x�p�e�c�t� �s�o�m�e� �v�a�r�i�a�t�i�o�n� �i�n� �t�h�e� �v�a�l�u�e�s� �p�a�c�k�e�d� �v�i�a� �t�h�i�s� �m�e�t�h�o�d� �a�n�d� �t�h�e� �o�r�i�g�i�n�a�l� �v�a�l�u�e�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�d�o�u�b�l�e�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�d�o�u�b�l�e�(� � � � � � �B�u�f� �$�d�o�u�b�l�e�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �R�a�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a� �B�u�f� �c�o�n�t�a�i�n�i�n�g� �a� �d�o�u�b�l�e�-�p�r�e�c�i�s�i�o�n� �f�l�o�a�t�i�n�g�-�p�o�i�n�t� �n�u�m�b�e�r� �(�d�o�u�b�l�e�)� �i�n�t�o� �a� �N�u�m�e�r�i�c�.� �R�e�t�u�r�n�s� �a� �R�a�t� �o�n� �N�a�N� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�f�l�o�a�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�i�n�t�6�4�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�i�n�t�6�4�(� � � � � � �I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a�n� �8� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a� �s�i�g�n�e�d� �6�4� �b�i�t� �i�n�t�e�g�e�r� �[������9�,�2�2�3�,�3�7�2�,�0�3�6�,�8�5�4�,�7�7�5�,�8�0�8� �t�o� �9�,�2�2�3�,�3�7�2�,�0�3�6�,�8�5�4�,�7�7�5�,�8�0�7�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�i�n�t�6�4�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�i�n�t�6�4�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a� �s�i�g�n�e�d� �8� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�u�i�n�t�6�4�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�u�i�n�t�6�4�(� � � � � � �U�I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �U�I�n�t� �t�o� �a�n� �8� �b�y�t�e� �u�n�s�i�g�n�e�d� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a�n� �u�n�s�i�g�n�e�d� �6�4�b�i�t� �i�n�t�e�g�e�r� �[�0� �t�o� �1�8�,�4�4�6�,�7�4�4�,�0�7�3�,�7�0�9�,�5�5�1�,�6�1�5�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�6�4�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�6�4�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a�n� �u�n�s�i�g�n�e�d� �8� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�i�n�t�1�6�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�i�n�t�1�6�(� � � � � � �I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a� �2� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a� �s�i�g�n�e�d� �1�6�b�i�t� �i�n�t�e�g�e�r� �[������3�2�,�7�6�8� �t�o� �3�2�,�7�6�7�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�i�n�t�1�6�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�i�n�t�1�6�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a� �s�i�g�n�e�d� �2� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�u�i�n�t�1�6�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�u�i�n�t�1�6�(� � � � � � �U�I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a� �2� �b�y�t�e� �u�n�s�i�g�n�e�d� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a�n� �u�n�s�i�g�n�e�d� �1�6�b�i�t� �i�n�t�e�g�e�r� �[�0� �t�o� �6�5�,�5�3�5�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�1�6�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�1�6�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a�n� �u�n�s�i�g�n�e�d� �2� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�i�n�t�8�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�i�n�t�8�(� � � � � � �I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a� �1� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a� �s�i�g�n�e�d� �8� �b�i�t� �i�n�t�e�g�e�r� �[������1�2�8� �t�o� �1�2�7�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�i�n�t�8�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�i�n�t�8�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a� �s�i�g�n�e�d� �1� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�u�i�n�t�8�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�u�i�n�t�8�(� � � � � � �U�I�n�t�(�C�o�o�l�)� �$�i�n�t�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�P�a�c�k� �a�n� �I�n�t� �t�o� �a� �1� �b�y�t�e� �u�n�s�i�g�n�e�d� �i�n�t�e�g�e�r� �b�u�f�f�e�r� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.� �B�e� �a�w�a�r�e� �t�h�a�t� �t�h�e� �b�e�h�a�v�i�o�u�r� �o�f� �I�n�t� �v�a�l�u�e�s� �o�u�t�s�i�d�e� �t�h�e� �r�a�n�g�e� �o�f� �a�n� �u�n�s�i�g�n�e�d� �1�6�b�i�t� �i�n�t�e�g�e�r� �[�0� �t�o� �2�5�5�]� �i�s� �u�n�d�e�f�i�n�e�d�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�8�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�u�i�n�t�8�(� � � � � � �B�u�f� �$�i�n�t�-�b�u�f�,� � � � � � �B�y�t�e�O�r�d�e�r� �:�$�b�y�t�e�-�o�r�d�e�r� �=� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �I�n�t� � �
��
�
�
�
�
�U�n�p�a�c�k� �a�n� �u�n�s�i�g�n�e�d� �1� �b�y�t�e� �i�n�t�e�g�e�r� �b�u�f�f�e�r�.� �E�x�p�o�r�t�e�d� �v�i�a� �t�a�g� �:�i�n�t�s�.�
�
�
�
�#�#�#� �s�u�b� �p�a�c�k�-�b�e�r�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �p�a�c�k�-�b�e�r�(� � � � � � �I�n�t� �$�v�a�l� �w�h�e�r�e� �{� �.�.�.� �}� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�A�n�a�l�o�g�u�e� �t�o� �t�h�e� �p�e�r�l� �p�a�c�k� �'�w�'� �o�p�t�i�o�n�.� �W�h�i�c�h� �i�s� �s�t�a�t�e�d� �t�o� �b�e� �d�i�f�f�e�r�e�n�t� �t�o� �A�N�S�.�1� �B�E�R� �f�o�r�m�a�t�,� �s�e�e�:� �h�t�t�p�s�:�/�/�p�e�r�l�d�o�c�.�p�e�r�l�.�o�r�g�/�p�e�r�l�p�a�c�k�t�u�t�.�h�t�m�l�#�A�n�o�t�h�e�r�-�P�o�r�t�a�b�l�e�-�B�i�n�a�r�y�-�E�n�c�o�d�i�n�g� �T�h�i�s� �e�n�c�o�d�i�n�g� �h�a�n�d�l�e�s� �a�n� �u�n�s�i�g�n�e�d� �i�n�t�e�g�e�r� �v�a�l�u�e� �o�f� �a�n� �a�r�b�i�t�r�a�r�y� �s�i�z�e� �i�n� �t�h�e� �m�i�n�i�m�u�m� �n�u�m�b�e�r� �o�f� �b�y�t�e�s�.� �E�a�c�h� �b�y�t�e� �h�a�s� �7� �b�i�t�s� �a�v�a�i�l�a�b�l�e� �w�i�t�h� �t�h�e� �f�i�r�s�t� �b�i�t� �s�i�g�n�a�l�l�i�n�g� �c�o�n�t�i�n�u�a�t�i�o�n� �o�r� �c�o�n�c�l�u�s�i�o�n� �o�f� �t�h�e� �e�n�c�o�d�e�d� �v�a�l�u�e�.�
�
�
�
�#�#�#� �s�u�b� �u�n�p�a�c�k�-�b�e�r�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �u�n�p�a�c�k�-�b�e�r�(� � � � � � �B�u�f� �$�b�y�t�e�s� � �)� �r�e�t�u�r�n�s� �U�I�n�t� � �
��
�
�
�
�
�C�o�r�r�e�s�p�o�n�d�i�n�g� �u�n�p�a�c�k�e�r� �f�o�r� �p�a�c�k�-�b�e�r�,� �t�h�e� �r�e�s�u�l�t�i�n�g� �I�n�t� �w�i�l�l� �b�e� �0� �t�o� �a�n� �a�r�b�i�t�r�a�r�y� �l�i�m�i�t�.� �D�e�c�o�d�i�n�g� �w�i�l�l� �a�l�w�a�y�s� �r�e�s�u�l�t� �i�n� �a� �v�a�l�u�e� �b�u�t� �a�n� �e�r�r�o�r� �i�n� �t�h�e� �e�n�c�o�d�i�n�g� �w�i�l�l� �n�o�t� �b�e� �r�e�p�o�r�t�e�d�.� �Y�o�u� �c�a�n� �u�s�e� �c�o�l�l�e�c�t�-�b�e�r�(�)� �t�o� �o�b�t�a�i�n� �a� �s�u�b� �b�u�f�f�e�r� �f�o�r� �d�e�c�o�d�i�n�g� �f�r�o�m� �a�n�o�t�h�e�r� �b�u�f�f�e�r�.�
�
�
�
�#�#�#� �s�u�b� �c�o�l�l�e�c�t�-�b�e�r�
�
�
�
��
��p�e�r�l�6� � �s�u�b� �c�o�l�l�e�c�t�-�b�e�r�(� � � � � � �B�u�f� �$�b�y�t�e�s�,� � � � � � �I�n�t� �:�$�o�f�f�s�e�t� �w�h�e�r�e� �{� �.�.�.� �}� �=� �0� � �)� �r�e�t�u�r�n�s� �B�u�f� � �
��
�
�
�
�
�T�h�i�s� �u�t�i�l�i�t�y� �r�e�t�u�r�n�s� �a� �c�o�p�y� �o�f� �t�h�e� �s�u�b� �b�u�f�f�e�r� �c�o�n�t�a�i�n�i�n�g� �a� �b�e�r� �e�n�c�o�d�e�d� �i�n�t�e�g�e�r� �f�r�o�m� �t�h�e� �g�i�v�e�n� �o�f�f�s�e�t�.� �T�h�e� �s�u�b� �b�u�f�f�e�r� �c�a�n� �t�h�e�n� �b�e� �g�i�v�e�n� �t�o� �u�n�p�a�c�k� �b�e�r� �t�o� �d�e�c�o�d�e� �t�h�e� �b�u�f�f�e�r� �i�n�t�o� �a�n� �I�n�t�.�
�
�