Parallel multiple-precision arithmetic based on residue number system

This paper deals with algorithms of multiple-precision arithmetic, based on the use of multi module residue number systems for representing of arbitrary length significands of floating-point numbers; the exponent is represented in the binary number system. Such number representation provides a large dynamic range and allows for effective parallelization of arithmetic operations on the digits of multiple-precision significands across RNS modules. This agrees well with the architectural features of modern parallel computing systems. Additionally, the attributive information which provides a fast estimation for the relative value of significand and allows you to increase the speed of executing complex non-modular operations in RNS, such as comparison, overflow control, rounding, etc., is included into the number format. Results of an experimental study on precision, performance and SIMD efficiency of multiple-precision algorithms are presented. (In Russian).