An approach to the application of shift-and-add algorithms on engineering and industrial processes

Different kinds of algorithms can be chosen so as to compute elementary functions. Among all of them, it is worthwhile mentioning the shift-and-add algorithms due to the fact that they have been specifically designed to be very simple and to save computer resources. In fact, almost the only operations usually involved with these methods are additions and shifts, which can be easily and efficiently performed by a digital processor. Shift-and-add algorithms allow fairly good precision with low cost iterations. The most famous algorithm belonging to this type is CORDIC. CORDIC has the capability of approximating a wide variety of functions with only the help of a slight change in their iterations. In this paper, we will analyze the requirements of some engineering and industrial problems in terms of type of operands and functions to approximate. Then, we will propose the application of shift-and-add algorithms based on CORDIC to these problems. We will make a comparison between the different methods applied in terms of the precision of the results and the number of iterations required.

Concording EU trade and production data over time. National Bank of Belgium Working Paper No. 239, December 2012

This paper provides concordance procedures for product-level trade and production data in the EU and examines the implications of changing product classifications on measured product adding and dropping at Belgian firms. Using the algorithms developed by Pierce and Schott (2012a, 2012b), the paper develops concordance procedures that allow researchers to trace changes in coding systems over time and to translate product-level production and trade data into a common classification that is consistent both within a single year and over time. Separate procedures are created for the eightdigit Combined Nomenclature system used to classify international trade activities at the product level within the European Union as well as for the eight-digit Prodcom categories used to classify products in European domestic production data. The paper further highlights important differences in coverage between the Prodcom and Combined Nomenclature classifications which need to be taken into account when generating combined domestic production and international trade data at the product level. The use of consistent product codes over time results in less product adding and dropping at continuing firms in the Belgian export and production data.