Roundoff error is a form of noise that pervades all calculations performed on computers (other than those dealing strictly with integers). Roundoff error occurs because computers can only use finite strings of digits to represent any given number, while many numbers are often not representable by finite strings. Numbers as commonplace as or 1/3, for example, cannot be perfectly represented as finite strings: 1/3 = .3333333 . . . (the 3's repeat forever). If one represents 1/3 using, say, five digits of precision (1/3 = 3.3333 x 10^-1), a roundoff error has been introduced of 1/3 - (3.3333 x 10^-1) = 3.333. . . x 10^-6. Such errors may seem small, but they can and do accumulate in long chains of calculations. In some studies, including simulations of chaotic phenomena (physical processes extremely sensitive to small changes in their initial conditions), roundoff error may even lead to completely erroneous outcomes. What is more, since roundoff error may accumulate differently on different computers, completely...