> ps: I've never understood people who prefer fast answers to > correct ones.
7 - 100 * 7r100 0 7 - 100 * 0.07 _8.88178e_16 The first is slow but "correct". The second is fast but "not correct". But there are any number of situations where I would prefer the second approach. (The first uses exact rational arithmetic; the second uses 64-bit floating point.) ----- Original Message ----- From: Robert Bernecky <[EMAIL PROTECTED]> Date: Friday, October 5, 2007 9:43 Subject: Re: [Jgeneral] 9!:10 and linear display To: General forum <[email protected]> > This topic may have beaten to death by now, but a few comments: > > 1. Guy Steele and Jon White wrote > "How to print floating-point numbers accurately" > in 1990 (SIGPLAN PLDI 1990). This paper set the > stage for > proper formatting of floating-point numbers. > > 2. Doug Forkes analyzed their approach (which was available > by rumor quite a bit earlier, new of which had been > brought to > us at I.P. Sharp by LMB (Larry M. Breed)), and > rewrote the > floating-point > formatter for SHARP APL. Doug's approach was, if I > recall > correctly, quite a bit faster than the Steele/White > approach. I think he did something along the lines > of what Burger and > Dybvig, below, did, but would welcome word from > Doug on this. > > Doug's implementation had one notable effect: > The bug reports > that we'd get about once a month about bad > formatting of 0.07, > which would print as something like > 0.070000000000001 with the > old formatter, but which printed as 0.07 with the > new one, simply > stopped coming in. > > 3. Robert G. Burger and R. Kent Dybvig. Printing floating-point > numbersquickly and accurately. In Proceedings of the ACM SIGPLAN > '96 Conference > on Programming Language Design and Implementation, pages 108--116. > http://citeseer.ist.psu.edu/28233.html > This paper presents the same approach to numeric formatting, but their > algorithm is substantially faster than that of Steele and White. > > The change is NOT, in my opinion, cosmetic, as it also corrects > a number > of other evils, such as racheting, which can occur when you repeatedly > format and unformat a number, and it slowly increases or > decreases in > value. > Both papers are worthy of reading, as they make it quite evident that > correct formatting is (a) not costly and is (b) not merely cosmetic. > > 4. I have heard rumors that the new IEEE floating-point standard will > contain formatting rules that conform to the above > papers. That means that new FPU boxes will likely > include formatter and > unformatter instructions, at which point any > complaints about > "large price to pay" will certainly go away. > > Bob > > ps: I've never understood people who prefer fast answers to > correct ones. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
