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Calculating the Sum of Multidigit Values in a Parallel Computational Model

  • NEW MEANS OF CYBERNETICS, INFORMATICS, COMPUTER ENGINEERING, AND SYSTEMS ANALYSIS
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Abstract

The authors propose a new method for finding the sum of two or more multidigit values in a parallel computational model. The method reduces finding the sum of a large number of multidigit values to the sum of two multidigit values by carry-save addition, which can be efficiently implemented in a parallel computational model based on carry-lookahead addition of groups of words. The algorithms for implementing the operation of finding the sum of values on one processor and on k processors are proposed. The complexity analysis is carried out for the proposed algorithms.

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References

  1. R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the ACM, Vol. 21, No. 2, 120–126 (1978). https://doi.org/10.1145/359340.359342.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. V. Anisimov, Algorithmic Theory of Large Numbers. Modular Arithmetic of Large Numbers [in Ukrainian], Akademperiodyka, Kyiv (2001).

  3. V. K. Zadiraka and O. S. Oleksiuk, Computer Arithmetic of Multi-Digit Numbers [in Ukrainian], Kyiv (2003).

  4. V. K. Zadiraka, Theory of Computing Fourier Transform [in Russian], Naukova Dumka, Kyiv (1983).

    MATH  Google Scholar 

  5. V. K. Zadiraka and A. M. Tereshchenko, Computer Arithmetic of Multi-Bit Numbers in Sequential and Parallel Computational Models [in Ukrainian], Naukova Dumka, Kyiv (2021).

    Google Scholar 

  6. Y. Nykolaychuk, M. Kasyanchuk, I. Yakymenko, and S. Ivasyev, “Effective method of modular multiplication in theoretic-numerical Rademacher–Krestenson’s basis,” Academic J. of Lviv Polytechnic, Ser. Computer Systems and Networks, No. 806, 195–199 (2014). URL: http://nbuv.gov.ua/UJRN/VNULPKSM_2014_806_31.

  7. O. M. Khimich and V. A. Sydoruk, “Using mixed precision in mathematical modeling,” Mathematical and Computer Modelling, Ser. Physical and Mathematical Sciences, Iss. 19, 180–187 (2019). 10.32626/2308-5878.2019-19.180-187.

  8. A. V. Anisimov, “Carryless addition,” Cybern. Syst. Analysis, Vol. 32, No. 2, 153–163 (1996). https://doi.org/10.1007/BF02366527.

    Article  MATH  Google Scholar 

  9. R. W. Floyd and D. E. Knuth, “Addition machines,” SIAM J. Comput., Vol. 19, No. 2, 329–340 (1990). https://doi.org/10.1137/0219022.

    Article  MathSciNet  MATH  Google Scholar 

  10. C. C. McGeoch, “Parallel addition,” The American Mathematical Monthly, Vol. 100, No. 9, 867–871 (1993). URL: http://www.jstor.org/stable/2324666.

    Article  MathSciNet  Google Scholar 

  11. A. N. Tereshchenko and V. K. Zadiraka, “Parallel addition based on vector operations,” Artificial Intelligence, No. 2, 122–137 (2018). URL: http://dspace.nbuv.gov.ua/handle/123456789/162381.

    Google Scholar 

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Correspondence to V. K. Zadiraka.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 3, May–June, 2022, pp. 174–182.

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Zadiraka, V.K., Tereshchenko, A.M. Calculating the Sum of Multidigit Values in a Parallel Computational Model. Cybern Syst Anal 58, 473–480 (2022). https://doi.org/10.1007/s10559-022-00478-7

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  • DOI: https://doi.org/10.1007/s10559-022-00478-7

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