RE: [PHP] Math Weirdness

On 15 July 2008 14:33, tedd advised: > At 11:24 AM +0100 7/15/08, Ford, Mike wrote: >> On 14 July 2008 20:47, tedd advised: >> >> > Round-off errors normally don't enter into things unless your doing >> > multiplication and division operations. At that point, > what you get >>> back from the operation is an approximation and not the actual >>> number. >> >> Bull! Nearly all computer floating point numbers are approximations >> because of being held in binary rather than decimal. Any number with a >> (decimal) fractional part that doesn't end with the digit 5 is >> necessarily an approximation, and that's only half the story. So as soon >> as you involve numbers like 0.1 or 0.2, you've already got minor >> inaccuracies which will propagate through any kind of arithmetic -- it's >> just worse with multiplication or division because these tend to result >> in inaccuracy in more significant digits! >> >> Bottom line: a floating point value should *always* be treated with an >> appropriate degree of suspicion. >> >> Cheers! >> >> Mike > > 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!!! Cheers! Mike -- Mike Ford, Electronic Information Developer, C507, Leeds Metropolitan University, Civic Quarter Campus, Woodhouse Lane, LEEDS, LS1 3HE, United Kingdom Email: m.ford@leedsmet.ac.uk Tel: +44 113 812 4730 To view the terms under which this email is distributed, please go to http://disclaimer.leedsmet.ac.uk/email.htm