Sequential & Parallel Algorithms for Big-Integer Numbers Subtraction

TL;DR

This paper introduces two new algorithms for big-integer subtraction, one sequential and one parallel, which divide large numbers into blocks for efficient processing, demonstrated using C#.NET on multi-processor systems.

Contribution

The paper presents novel sequential and parallel algorithms for big-integer subtraction that divide inputs into blocks, improving efficiency over traditional bitwise methods.

Findings

Both algorithms reduce input size by dividing into 60-bit blocks.

Parallel algorithm leverages multi-processor systems for faster computation.

Algorithms are implemented and tested in C#.NET 2005.

Abstract

Many emerging computer applications require the processing of large numbers, larger than what a CPU can handle. In fact, the top of the line PCs can only manipulate numbers not longer than 32 bits or 64 bits. This is due to the size of the registers and the data-path inside the CPU. As a result, performing arithmetic operations such as subtraction on big-integer numbers is to some extend limited. Different algorithms were designed in an attempt to solve this problem; they all operate on big-integer numbers by first converting them into a binary representation then performing bitwise operations on single bits. Such algorithms are of complexity O(n) where n is the total number of bits in each operand. This paper proposes two new algorithms for performing arithmetic subtraction on big-integer numbers. The two algorithms are different in that one is sequential while the other is parallel. The similarity between them is that both follow the same concept of dividing the big-integer inputs into several blocks or tokens of 60 bits (18 digits) each; thus reducing the input size n in O(n) by a factor of 60. Subtraction of corresponding tokens, one from each operand, is performed as humans perform subtraction, using a pencil and a paper in the decimal system. Both algorithms are to be implemented using MS C#.NET 2005 and tested over a multiple processor system. Further studies can be done on other arithmetic operations such as addition and multiplication.