Computing cube root of a positive number

Abstract

Proposed here is a new algorithm to compute the cube root of large positive integer. The algorithm is based on the implementation of long division method also known as manual method we usually use to find the square root of a number. To implement the long division method, the given number is first represented in a radix-10 representa and then Bino’s Model of Multiplication is used to systematically implement the long division method. A representa is a special array to represent a number in the form of an array so as to enable us to treat the representas in the same way as we treat numbers. This simplifies the difficulty of dealing large numbers in a computer. Also, at the same time it simplifies the implementation of long division method to find the cube root of positive number, ranging from single digit number to arbitrarily large positive number such as RSA challenge numbers. The algorithm can be used to compute cube root of a non-perfect cube number up to desired precision and each computed digit of cube root gives the best precision. Cube root of 2, 5, 10 up to 30 digits and integer parts of cube roots of first few and last few RSA challenge numbers are also provided in the experimental result to show that the algorithm works perfectly to compute the cube root of any positive integer, however small or large it may be.

Keywords:Bino‘s Model of Multiplication, Convolution, Cube of a large number, Large number manipulation, Long division method, RSA challenge numbers, Representa, Cube root computation