There is an corresponding inaccuracy between the mathematical set of integers and the set of integers implemented on any given computer. The abstract math is infinite, the computers are not. Computers get overflows on integer ops (errors) which actually closely correspond to the underflow and rounding errors of floating point operations. It doesn't matter if you are talking about extended mutilple precision integers or not, they all still overflow somewhere if only when they run out of usable memory.
Andy Messier wrote: > The set of integers, on the other hand, are often exact in their > intended use. If they are used to count discrete objects, you can > add, subtract, multiply and divide (you can use the modulus to retain > the precise remainder of a division). If they are use as integers, > their operations are precisely what you want, without any error. > However, if you chose to use integers as a fixed point representation > of real numbers, I'd argue that this representation is inexact, just > like floating-point representation. > > _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
