Geodesic
Parallel algorithms of integer arithmetic in radix notations for~heterogeneous computation systems with massive parallelism
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 117-126

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For the analysis of huge problems which are very sensitive to the rounding errors, the software providing rational calculations is developed. Software uses MPI interface for communication in the distributed computational environment. Improved efficiency of such software my be achieved by using heterogeneous computation systems. Local arithmetic operations with long numbers may be done in parallel mode with a lot of processes per one operation. This work introduces the research of increasing of the scalability of basic arithmetic operations. Abilities of the massive parallelism for the heterogeneous computation systems for the efficiency improving are shown. Redundant numerical system with a constant time of the addition operation is introduced. It allows to design well scaled algorithms for all basic arithmetic operations with integer numbers. Scalability of the basic integer arithmetic algorithms is easy applied to rational arithmetic.
Keywords: integer computer arithmetic; heterogeneous computer system; radix notation; massive parallelism. 
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     author = {A. V. Panyukov and V. A. Golodov},
     title = {Parallel algorithms of integer arithmetic in radix notations for~heterogeneous computation systems with massive parallelism},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {117--126},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a9/}
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A. V. Panyukov; V. A. Golodov. Parallel algorithms of integer arithmetic in radix notations for~heterogeneous computation systems with massive parallelism. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 117-126. http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a9/