RE: [PHP] Math Weirdness

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). However, if one defines the precision, then that's a different matter. As with the OP's problem, the precision he was dealing with was simply 0.00 and addition and subtraction operations don't come into play at the precision level (i.e., 0.10 + 0.20 will equal 0.30 no matter how many times you add it). In addition, the algorithm that used to round the number also comes into play. For example php always round down and that introduces bias, as proved here: http://webbytedd.com/bbb/rounding/ So, all in all, I agree with your statements, but I just don't think you fully appreciated what I was trying to communicate to the OP. Cheers, tedd -- ------- http://sperling.com http://ancientstones.com http://earthstones.com