I'm trying to think about how I would go about doing calculations on extremely large numbers (to infinitum - intergers no floats) if the language construct is incapable of handling numbers larger than a certain value.
I am sure I am not the first nor the last to ask this question but the search terms I am using aren't giving me an algorithm to handle those situations. Rather most suggestions offer a language change or variable change, or talk about things that seem irrelevant to my search. So I need a little guideance.
I would sketch out an algorithm like this:
Determine the max length of the integer variable for the language.
If a number is more than half the length of the max length of the variable split it in an array. (give a little play room)
Array order  = the numbers most to the right [n-max] = numbers most to the left
Ex. Num: 29392023 Array:23, Array: 20, array: 39, array:29
Since I established half the length of the variable as the mark off point I can then calculate the ones, tenths, hundredths, etc. Place via the halfway mark so that if a variable max length was 10 digits from 0 to 9999999999 then I know that by halfing that to five digits give me some play room.
So if I add or multiply I can have a variable checker function that see that the sixth digit (from the right) of array is the same place as the first digit (from the right) of array.
Dividing and subtracting have their own issues which I haven't thought about yet.
I would like to know about the best implementations of supporting larger numbers than the program can.