On Tue, 2008-07-15 at 12:26 -0400, tedd wrote: > At 4:52 PM +0100 7/15/08, Ford, Mike wrote: > >On 15 July 2008 14:33, tedd advised: > > > Mike: > >> > >> No reason to be rude. > >> > >> I said: > >> > >> "Round-off errors normally don't enter into things unless your doing > >> multiplication and division operations." > >> > >> And that is not "Bull" -- it's true. You can add and subtract all the > >> floating point numbers (the one's we are talking about here) you want > >> without any rounding errors whatsoever. > > > >Sorry, I do apologise if I came over too strongly -- there was no > >intention to offend. > > > >However, you really can't dismiss the effects of round-off errors on > >addition and subtraction as lightly as that. It's simply not true that > >approximations only occur at the point of doing multiplication and > >division -- there *are* approximations involved in addition and > >subtraction, and it is necessary to be aware that this is the case -- as > >Jay proved, 0.1+0.2 is hardly ever exactly 0.3. In this sort of case, it > >may well be that an appropriate degree of suspicion is simply to round > >to 2 decimal places at every stage, or compare the absolute difference > >to .001, but nonetheless one has to *know* that this is necessary. > > > >Ummm -- sorry, better </rant>, now!!! > > No problem about the rudeness -- email is a terrible form of > communication. Sometimes we don't realize how we are being perceived. > > I know full well about what you speak and why there are problems > dealing with numbers. > > My only point here was that the OP was talking about his > balance-sheet not balancing at the end of the day. > > I said that if all he was doing was adding and subtracting, then he > wouldn't have any problems -- those operations are not subject to the > rounding errors that division and multiplication induce. And > experience has shown me that my claim is true. I can add and subtract > dollars and cents all day without an error whatsoever. > > Now, if you get into more complicated math, such as > multiplication/division then of course rounding errors come into play > much more noticeably. It is true that not every number can be > represented in binary because of the limits of the processor. Take > for example pi, no computer in the world has capabilities to > represent that number in it's totality (i.e., unlimited precision).
Umm... here it is to unlimited precision: π Cheers, Rob. -- http://www.interjinn.com Application and Templating Framework for PHP -- PHP General Mailing List (http://www.php.net/) To unsubscribe, visit: http://www.php.net/unsub.php
