Geodesic
A parallel-processing-oriented method for the representation of multi-digit floating-point numbers
Numerical methods and programming, Tome 15 (2014) no. 4, pp. 631-643

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The extended precision of calculations is required in solving many scientific and engineering problems. The solution time is a critical parameter to accomplish and, therefore, new methods should be developed for fast high-precision arithmetic. In this paper a new modular-positional format for the representation of floating-point multi-digit numbers is proposed. The main concept of this format is to represent and ensure the digit-parallel processing of floating-point mantissas in residue number systems. The method of interval-positional characteristics is used to increase the speed of complex non-modular operations. Several algorithms for performing arithmetic operations and rounding in the new modular-positional floating-point format are considered. The results of studies of their vectorization efficiency and performance compared to some analogs (MPFR - Multiple Precision Floating-Point Reliable library, NTL - Number Theory Library, and Wolfram Mathematica) are discussed.
Keywords: residue number system, high-precision computations, modular-position floating-point format, multi-digit numbers, arithmetic operations, high performance. 
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     author = {K. S. Isupov and A. N. Maltsev},
     title = {A parallel-processing-oriented method for the representation of multi-digit floating-point numbers},
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     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_4_a8/}
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K. S. Isupov; A. N. Maltsev. A parallel-processing-oriented method for the representation of multi-digit floating-point numbers. Numerical methods and programming, Tome 15 (2014) no. 4, pp. 631-643. http://geodesic.mathdoc.fr/item/VMP_2014_15_4_a8/