I assume that you mean one that is bigger than a Long. Is the big integer an arbitrarily large number? Does it have to be an integer, or is it an arbitrarily large decimal value, as well?
Big Integer style classes are like Strings. They can be as large as needed; the bigger the number, the more bytes it takes up. I don't see why they couldn't make a Big Decimal as well and track significant digits. though I expect any classes like this to be horribly slow computationally.
The speed depends on whether they have based it on Strings (which I doubt), or have done it fully numerically.
Even if it is fully numerical, the speed will be worse than the normal numeric data types (due to the need to split the number into processor-sized chunks), but should be noticeably better than the vast majority of custom-made solutions.
For simple operations (such as +-=< etc) the time could well be around double the equivalent amount of normal data types (eg: if it is 10 times the size of an Integer, the time taken will be 20 times as much as doing the same operation with an Integer). Of course the more complex operations (/*^ etc) will be much slower by comparison.
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