NON-TRADITIONAL CALCULATIONS OF ELEMENTARY MATHEMATICAL OPERATIONS: Part 1. MULTIPLICATION AND DIVISION

Igor Filippenko

Abstract


Different computational systems are a set of functional units and processors that can work together and exchange data with each other if required. In most cases, data transmission is organized in such a way that enables for the possibility of connecting each node of the system to the other node of the system. Thus, a computer system consists of components for performing arithmetic operations, and an integrated data communication system, which allows for information interaction between the nodes, and combines them into a single unit. When designing a given type of computer systems, problems might occur if:

– computing nodes of the system cannot simultaneously start and finish data processing over a certain time interval;

– procedures for processing data in the nodes of the system do not start and do not end at a certain time;

– the number of computational nodes of the inputs and outputs of the system is different.

This article proposes an unconventional approach to constructing a mathematical model of adaptive-quantum computation of arithmetic operations of multiplication and division using the principle of predetermined random self-organization proposed by Ashby in 1966, as well as the method of the dynamics of averages and of the adaptive system of integration of the system of logical-differential equations for the dynamics of number-average states of particles S1, S2 of sets. This would make it easier to solve some of the problems listed above.


Keywords


сalculus systems; computational systems; processor; functional nodes of the systems; interaction between functional nodes of systems; execution time of arithmetic operations; adaptive-quantum calculations of arithmetic operations

Full Text:

PDF

References


Akushskiy, I. Ya., Yudickiy, D. I. (1968). Mashinnaya arifmetika v ostatochnyh klassah. Moscow: "Sov. radio", 440.

Torgashev, V. A. (1973). Sistema ostatochnyh klassov i nadezhnost' CVM. Moscow: "Sov. radio ", 120.

Sin'kov, M. V., Gubareni, N. M. (1979). Nepozicionnye predstavleniya v mnogomernyh chislovyh sistemah. Kyiv, 140.

Diniz, P. C., Marques, E., Bertels, K., Fernandes, M. M., Cardoso, J. M. P. (Eds.) (2007). Reconfigurable Computing: Architectures, Tools and Applications. Lecture Notes in Computer Science. doi: https://doi.org/10.1007/978-3-540-71431-6

Korolev, L. N. (2005). Arhitektura elektronnyh vychislitel'nyh mashin. Moscow: "Nauchniy mir ", 272.

Shin, C., Lee, S.-W., Gaudiot, J.-L. (2003). Dynamic scheduling issues in SMT architectures. Proceedings International Parallel and Distributed Processing Symposium. doi: https://doi.org/10.1109/ipdps.2003.1213179

Shin, C., Lee, S.-W., Gaudiot, J.-L. (2006). Adaptive dynamic thread scheduling for simultaneous multithreaded architectures with a detector thread. Journal of Parallel and Distributed Computing, 66 (10), 1304–1321. doi: https://doi.org/10.1016/j.jpdc.2006.06.003

Evans, J. J., Hood, C. S., Gropp, W. D. (2003). Exploring the relationship between parallel application run-time variability and network performance in clusters. 28th Annual IEEE International Conference on Local Computer Networks, 2003. LCN’03. Proceedings. doi: https://doi.org/10.1109/lcn.2003.1243180

Eshbi, U. R., Kal'bertson, Dzh. T., Dzvis, M. D., Klini, S. K., de Leu, K., Makkey, D. M. et. al.; Lyapunov, A. A. (Ed.) (1956). Avtomaty. Sbornik statey. Moscow: Inostrannaya literatura, 404.

Aberer, K., Datta, A., Hauswirth, M. (2005). P-Grid: Dynamics of Self-Organizing Processes in Structured Peer-to-Peer Systems. Lecture Notes in Computer Science, 137–153. doi: https://doi.org/10.1007/11530657_10

Whisnant, K., Kalbarczyk, Z. T., Iyer, R. K. (2003). A system model for dynamically reconfigurable software. IBM Systems Journal, 42 (1), 45–59. doi: https://doi.org/10.1147/sj.421.0045

Prehofer, C., Bettstetter, C. (2005). Self-organization in communication networks: principles and design paradigms. IEEE Communications Magazine, 43 (7), 78–85. doi: https://doi.org/10.1109/mcom.2005.1470824

Shin, C., Lee, S.-W., Gaudiot, J.-L. (2006). Adaptive dynamic thread scheduling for simultaneous multithreaded architectures with a detector thread. Journal of Parallel and Distributed Computing, 66 (10), 1304–1321. doi: https://doi.org/10.1016/j.jpdc.2006.06.003

Tuck, N., Tullsen, D. M. (2005). Multithreaded Value Prediction. 11th International Symposium on High-Performance Computer Architecture. doi: https://doi.org/10.1109/hpca.2005.22

Stallings, W. (2003). Data and computer communications. Prentice Hall, 864.

Ventcel', E. S. (1972). Issledovanie operaciy. Moscow: Sovetskoe radio, 552.




DOI: http://dx.doi.org/10.21303/2461-4262.2018.00686

Refbacks

  • There are currently no refbacks.




Copyright (c) 2018 Igor Filippenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN 2461-4262 (Online), ISSN 2461-4254 (Print)