point representations are inherently imprecise; how accurate do the operation results have to be?
Obviously, accurate enough. 😉 Unfortunately, it is very difficult to determine how much accuracy remains after a non-trivial computation is performed using a specific precision, yet precision (number of bits used to store a value) is all that one can directly control. An excellent overview is given in What Every Computer Scientist Should Know About Floating-Point Arithmetic; it isn’t exactly light reading, but at least it’s lighter than the IEEE 754/854 standards. The standards provide for different bases (e.g., 2, 10, 16), rounding modes, predictive infinities, NaN (Not-a-Number), denormalized arithmetic, etc. The result is that fully compliant implementations of floating point can have a very wide range of accuracy… and there also are many “slightly” non-compliant versions that omit some of the more complex features (which have very little impact, if any, on accuracy). Grossly inferior accuracy, such as the old Crays yielded, is essentially gone from modern machines except for ex
