In computer science, large integer and large integer arithmetic refer to particular techniques for handling of integers, rather than the size of these integers.
Integers represent the simplest addressable unit (8-bits in an 8-bit machine, 16-bits in a 16-bit machine, etc). They can be extended with long integers, but typically only doubly so (double precision). Reals, can also be used, and while they can be extended by orders, reals inherently lose precision when compared with integers, (in most normal mathematics done on computers). This leads to large integers, where each radix is joined in a linked list. This requires the programmer to create custom half-addition and overflow. This slows processing down immensely, but creates a situation where integers, and by extension, reals, can have a completely arbitrary size, without any loss of precision.