Modular-positional data format and software package for digit-parallel high-precision floating point calculations

A new way of organization of high-precision floating point computations, which allows parallelizing arithmetic operations down to separate digits of multi-digit floating point mantissas through using a modular-positional data representation format, is considered. The main concept of this for mat is to represent the floating point mantissas in residue number system (RNS) and the exponent part in positional system. Floating point mantissas go with their positional characteristic that allows to successfully implement efficient algorithms for non-modular operations in RNS, such as division (special case), and rounding. Using this approach a software solution named High Precision Digit Parallel Solver (HPDP-Solver) is developed. HPDP-Solver can be flexibly configured for a specific PC configuration, resulting in a more efficient use of its resources. The results obtained during the experimental performance study of HPDP-Solver proved its advantages in solving high-precision numerical problems if compared to a world-famous GNU Multiple Precision Arithmetic Library. HPDP-Solver can be used to solve problems that have some special demands on computational precision.