Mike McCarty wrote: > David kerber wrote: > >> Mike McCarty wrote: >> >>> From the website... >>> >>> "Since floating point computations are inexact, after every iteration >>> the floating point values are rounded back to integers." >>> >>> Floating point operations are not inexact. There is exactly one >>> properly computed result for any given floating point operation. >>> >>> >> That is not what inexact means, though. Inexact means that the result >> is not (always) exactly correct. Your definition would be saying that >> they are precise (repeatable), but they are still not exact. >> > > No, floating point operations are exact, and are always > exactly correct (barring hardware or software failure). > > Looking in my largest dictionary (1929 pages) Funk & Wagnall's > New Comprehensive International Dictionary, I find... > > in-ex-act adj Not exact, accurate or true. > > That's the full definition. All floating point operations > are exact, accurate, and true. They just aren't the same > as the corresponding operations on (mathematical) real numbers. > In fact, floating point numbers are integers, just with > a different set of operations defined on them. As such, the > operations on them are exact, accurate, and true in precisely > the same way ordinary integer operations on them are exact, > accurate, and true. There is only one exact result which must > be the one produced. > > Each FP number may be used to represent precisely one real number. > The operations on the FP numbers correspond closely to other operations > performed on those representable real numbers. But the result is > constrained to be another integer, an exact machine number. This number > may or may not correspond to the real number which is the result > If it doesn't correspond to the real number, then it's inexact. Take the calculation 7 divided by 10. The correct answer is 0.7 (seven tenths). If you try this in a binary computer, you do not get the correct answer; you get the the closest number that floating-point numbers can come to 0.7, but it is not exactly 0.7, and therefore is inexact, or inaccurate if you prefer that term.
> of the corresponding real number operation. That's all. If the > result of the real number operation is not representable, then > the FP result cannot, even in principle, correspond to the > real number result. There is no inaccuracy or inexactness or > incorrectness involved. > I guess it's just a difference in our definitions of inexact. By standard scientific definitions (which I guess may not correspond to computer science's definitions), if it can't represent the correct answer exactly, then it's inexact. D _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
