Parallel multiple-precision arithmetic based on residue number system

The paper considers algorithms of high-precision arithmetic based on the use of multimodular residual class systems (SOK) for the representation of mantissas of numbers with a floating point of arbitrary digit capacity; the order is stored in binary notation. Such a representation provides a large dynamic range and allows efficient parallelization of arithmetic operations over digits of multi-digit mantissas on SOK modules, which agrees well with the features of the architecture of modern parallel computing systems. Additionally, attribute information is included in the numerical format, which provides a quick estimate of the magnitude of the mantissa scaled with respect to the product of the modules, and facilitates the accelerated implementation of a number of non-modular procedures, such as comparison, overflow control, rounding, etc., which are problematic for SOK. and speed of algorithms, as well as the efficiency of using SIMD