Integer Representation of Decimal Numbers for Exact Computations

TL;DR

This paper introduces a method to represent decimal numbers as integers for precise mathematical computations without rounding errors.

Contribution

A novel integer-based scheme for exact arithmetic operations on decimal numbers stored as floating points.

Findings

Decimal numbers can be converted to integers for exact multiplication, addition, and subtraction.

The method ensures precision by limiting the number of digits to the left and right of the decimal point.

The approach is constrained by a maximum of nine digits to the left and fourteen digits in total for each number.

Abstract

A scheme is presented and software is documented for representing as integers input decimal numbers that have been stored in a computer as double precision floating point numbers and for carrying out multiplications, additions and subtractions based on these numbers in an exact manner. The input decimal numbers must not have more than nine digits to the left of the decimal point. The decimal fractions of their floating point representations are all first rounded off at a prespecified location, a location no more than nine digits away from the decimal point. The number of digits to the left of the decimal point for each input number besides not being allowed to exceed nine must then be such that the total number of digits from the leftmost digit of the number to the location where round-off is to occur does not exceed fourteen.