Take a number, say 7290125. It is stored as an unsigned 64-bit integer. We want to represent this number as a byte-pair sequence.
The idea of this algorithm is to use a pair of bytes to calculate part of the digits.
In the byte-pair, (a, b), both a and b can have values from 0 to 255. The idea is to translate the byte-pair as an exponent expression. Basically part of the digits of the original number is the same as the digits in a ^ b
In the above number, 729 = 27 ^ 2 and 125 = 5 ^ 3. But what about the 0 in the middle? Well, if there are 0 values in the middle that have not been encoded yet, then we use the byte pair (0, n). Basically it means the digit 0 is repeaing n times.
So the result is 7290125 = (27, 2) (0, 1) (5, 3)
Remember that this is a byte-pair sequence, so the 64-bit unsigned integer has been represented as 3 pairs of bytes, so a 75% reduction in size in the case of 7290125.
This simple explanation is theoretical. Not all numbers can result in reduction like this. This program calculates the compression factor for a range of numbers. For numbers above a certain threshold, there is no compression at all, in fact there could be an increase in size.
