Infinite precision math

This is a thread that will be weaved together with n-body, GCF, and non imaginary solutions to roots considered imaginary.

This is a principle I developed a long time ago and never applied it because I never had an application until now. The idea of infinite precision is a misnomer and is really vastly improved with known error limits, would be better.

The basic concept is simple to a programmer. I suspect the Egyptians did math in this way. I can do this math and I can convert decimal math. The general principle is defining a number as composed of two parts which are the numerator and the denominator where each is a linked list that expands as products are applied. The final computation is fairly convolved and requires the factoring of elements and combination in ways that are not used in an FPU.

A very simple example might be 1/2 * 2/3 * 5/9 would be 1->2->5 /with/ 2->3->9 The process is actually more time consuming and may not be usable in this case, but I am going to make an attempt at programming that and measuring to see if there is gain.

The process involves dealing with a whole series of numbers, instead of performing a calculation and losing precision sequentially and multiplicatively. I never got it to work very well and it is the GCF issue and perhaps that will solve some limitations of this method. IDK

ADDED: The advantage of this is that the errors can be pushed in either direction to cancel in some cases.