Algorithm for Calculation the Carry and Borrow Signs in Multi-digit Operations in the Parallel Computational Model

Abstract

The fast algorithm to calculate carry signs and borrow signs for implementation of fast multi-digit operations in the parallel computational model is proposed. The proposed algorithm also makes it possible to predict carry signs in the case of an addition operation and predict borrow signs for a subtraction operation. It is shown how the sign prediction algorithm is implemented in operations in which each parallel processor proceeds the separate group of words into which multi-digit numbers are divided. The iterative calculations of carry signs of grouped words are described. The sign calculation algorithm as component of new modifications of multi-digit addition, subtraction, comparison, the sum of three or more numbers in the parallel computational model is presented. The sign calculation algorithm provides general approach to the implementation of multiplication, division, multiplication by modulo, exponentiation by modulo in the parallel computational model. In the form of a table, a general analysis of the complexity of algorithms and an analysis of the complexity by the number of single-word operations per processor are given.