Geodesic
Scalable algorithms for the integer arithmetics and rational calculations in heterogeneous computation environment
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 4 (2015) no. 2, pp. 71-88

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Algorithmic analysis of large-scale problems that are sensitive to rounding errors requires precise rational calculations in the distributed computing environment. Enhanced efficiency of thesoftware my be gained to heterogeneous computing systems that perform local basic arithmeticoperations simultaneously using large number of ultralight threads. This paper examines thescalability algorithms for basic arithmetic operations and methods of its improvement. Thepossibility of increasing of the software efficiency using massive parallelism in heterogeneouscomputing systems is described. The use of reduntant number system allows you to performthe operation of algebraic addition in constant time and to construct scalable algorithms for allbasic arithmetic operations. Scalability of the basic integer arithmetic algorithms can be easilytransferred to a rational arithmetic.
Keywords: integer arithmetics, rational arithmetics, sclable alrorithms, position number system, reduntant number system. 
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     author = {V. A. Golodov and A. V. Panyukov},
     title = {Scalable algorithms for the integer arithmetics and rational calculations in heterogeneous computation environment},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
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     volume = {4},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2015_4_2_a5/}
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V. A. Golodov; A. V. Panyukov. Scalable algorithms for the integer arithmetics and rational calculations in heterogeneous computation environment. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 4 (2015) no. 2, pp. 71-88. http://geodesic.mathdoc.fr/item/VYURV_2015_4_2_a5/