Decimal Multiplication in FPGA with a Novel Decimal Adder/Subtractor

Financial and commercial data are mostly represented in decimal format. To avoid errors introduced when converting some decimal fractions to binary, these data are processed with decimal arithmetic. Most processors only have hardwired binary arithmetic units. So, decimal operations are executed with slow software-based decimal arithmetic functions. For the fast execution of decimal operations, dedicated hardware units have been proposed and designed in FPGA. Decimal multiplication is found in most decimal-based applications and so its optimized design is very important for fast execution. In this paper two new parallel decimal multipliers in FPGA are proposed. These are based on a new decimal adder/subtractor also proposed in this paper. The new decimal multipliers improve state-of-the-art parallel decimal multipliers. Compared to previous architectures, implementation results show that the proposed multipliers achieve 26% better area and 12% better performance. Also, the new decimal multipliers reduce the area and performance gap to binary multipliers and are smaller for 32 digit operands.

Enhanced Binary MQ Arithmetic Coder with Look-Up Table

Binary MQ arithmetic coding is widely used as a basic entropy coder in multimedia coding system. MQ coder esteems high in compression efficiency to be used in JBIG2 and JPEG2000. The importance of arithmetic coding is increasing after it is adopted as a unique entropy coder in HEVC standard. In the binary MQ coder, arithmetic approximation without multiplication is used in the process of recursive subdivision of range interval. Because of the MPS/LPS exchange activity that happens in the MQ coder, the output byte tends to increase. This paper proposes an enhanced binary MQ arithmetic coder to make use of look-up table (LUT) for (A × Qe) using quantization skill to improve the coding efficiency. Multi-level quantization using 2-level, 4-level and 8-level look-up tables is proposed in this paper. Experimental results applying to binary documents show about 3% improvement for basic context-free binary arithmetic coding. In the case of JBIG2 bi-level image compression standard, compression efficiency improved about 0.9%. In addition, in the case of lossless JPEG2000 compression, compressed byte decreases 1.5% using 8-level LUT. For the lossy JPEG2000 coding, this figure is a little lower, about 0.3% improvement of PSNR at the same rate.

The First Interpretations of the Yi-jing in the West and in Russia

The Yi-jing易經(Canon of Changes), or Zhou yi周易(All-Encompassing Cyclical Changes of the Zhou [era]), is “the book of books” of Chinese culture, which is also claimed to be the primary source of binary numeration, first described in the West by Leibniz. He was always interested in China, familiar with the binary code of tri and hexagrams (gua) of the Yi-jing and acknowledged its mythical creator, the ancestor emperor Fuxi, as the discoverer of binary arithmetic, and himself – as the one who found it again after four thousand years. At present, historical data do not allow us making an accurate conclusion about the dependence or independence of this outstanding discovery in Europe from the Chinese prototype. The time of the penetration of the initial information about the Yi-jing into Europe is still hidden by a veil of secrecy. The lack of a message about it in the book of Marco Polo is one of its mysteries. At the same time in the Mediterranean area traces of acquaintance with the Yi-jing studies are visible in such cultural phenomena as astrology and alchemy, Kabbalah and the teachings of Ramon Llull, sextine and hexachord. The beginning of the European study of the Yi-jing was laid by Jesuit missionaries who arrived in China at theend of the 16th century. Among them, by the end of the 17 th century, a whole trend of “Yi-jingists” or “figuralists” was formed. They saw Yi-jing as the Chinese Bible, embodying the original Divine Revelation in the form of the kabbalistic “figures” of the gua and being an expression of the common, sacred and antediluvian “hieroglyphic science” of the ancient world, that is, “Metaphysics of numbers, or general scientific method”, “containing all other knowledge”. Apparentlythe first information in Russia about the Yi-jing was published by the first Russiansinologist, German historian and philologist-polyglot G. (Th.) S. Bayer in the two-volume Museum Sinicum (Petersburg, 1730) in Latin. In Russian the primary in -formation about Yi-jing became available to the reader half a century later owing to the coryphaeus of Russian sinology of the 18th century Aleksei L. Leontiev. In 1782 he published an illustrated and commented translation of a fragment from Yi-jing (named Convenient Base) as an appendix to his translation of the Manchu text of the Statutes of the Great Qing (大清會典Dai-Qing hui-dian). Leontiev mentioned the French abbot who visited St. Petersburg in 1769 as the initiator of his appeal to the Yi-jing, but did not indicate his name. Petr E. Skachkov (1892–1964) agreed with Vsevolod S. Kolokolov (1896–1979) that this abbot was the famous French Jesuit missionary and versatile scientist Antoine Gaubil (1689–1759). However, he died ten years earlier. Most likely the interlocutor of Leontiev was a well-known theologian and economist-physiocrat, French abbot Nicolas Baudeau (1730–1792), who held confidential negotiations with Catherine IIin 1769 in St. Petersburg in connection with the situation in Poland. The secrecy of this mission on the eve of the first partition of Poland fully explains the concealment of his name in 1782 when he was still alive and preparing the second partition of Poland. Apparently, a look at the Yi-jing of the French enlighteners184 and physiocrats, expressed by F. Quesnay (1694–1774) and reported by Baudeauto Leontiev prompted him to link the ancient canon with Statutes of the Great Qing. Vasilii P. Vasiliev (1818–1900) expressed a number of original thoughts about the Yi-jing, which may have influenced the creation of his graphic system of Chinese characters and Mendeleev periodic table. Yulian K. Shchutsky (1897–1938), the first Russian researcher who specially studied the Yi-jing and wrote an extensive monograph about it, strangely ignored the statements of his domestic predecessors, but his innovative approach anticipated the neo-mystic Jungian tendency in Western interpretations of the Canon in the 20 th century. Due to the psychologization and aestheticization of the Yi-jing sanctified by world authorities in this field, after the Second World War this neo-mysticism penetrated the mass Western culture which repeated the initial success prepared by figuralists three centuries earlier on a new level and larger scale.

A nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter

In this paper, a nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter is presented, which refines 2D point-normal pairs. The construction of the scheme is built upon the stationary linear generalized subdivision scheme of arbitrary degree with a tension parameter, by replacing the weighted binary arithmetic average in the linear scheme with the circle average. For such a nonlinear scheme, we investigate its smoothness and get that it can reach $C^{1}$ C 1 with suitable choices of the tension parameter when degree $m\geq 3$ m ≥ 3 . Besides, the nonlinear scheme can reconstruct the circle and the selection of parameters and initial normal vectors can effectively control the shape of the limit curves.

“Discourse on the Natural Theology of the Chinese”

Leibniz wrote the “Discourse on the Natural Theology of the Chinese” during the last year of his life. Previously, he had praised the polity and societal peace of the Chinese empire, deeming it superior to that of Christian Europe. Various thinkers used such a claim to argue that a pagan society could be ethical and politically stable without the belief in God. Leibniz sought to demonstrate that the intellectual and spiritual foundations of ancient Confucianism were indeed monotheistic and that this was the basis of their well-ordered society. He attempted to show that the classical Chinese believed in the tenets of a natural theology (i.e. belief in the existence of a monotheistic God and an incorporeal and hence immortal soul). He even attributed the discovery of binary arithmetic, not to himself, but to the ancient founder of the Yi Jing, thus further legitimating ancient Chinese knowledge (“science”).

HEVC Video Encryption Algorithm Based on Integer Dynamic Coupling Tent Mapping

A selective encryption algorithm is proposed to improve the efficiency of high efficiency video coding (HEVC) video encryption and ensure the security of HEVC videos. The algorithm adopts the integer dynamic coupling tent mapping optimization model as the pseudo-random sequence generator, and multi-core parallelization is used as the sequence generation mechanism. The binstrings during the process of context adaptive binary arithmetic coding are selected for encryption, which conforms to the features of invariable binstream and compatible format in terms of video encryption. Performance tests for six types of standard videos with different resolutions were performed. The results indicated that the encryption algorithm has a large key space and benefits from a high encryption effect.