Amoss

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Again, welcome! Chris Roy 04:57, 19 Apr 2004 (UTC)

Floating point

Greetings:

Just a quick note; I don't have a lot of time right now.

It wasn't my intention to do any "angry reverts" in my recent work on the page (though I've done a few in the more distant past.) If my recent changes struck you as wanton reversion, that was a coincidence. I've been trying to follow other people's suggestions, and steer the article toward the right thing. What I recall of my recent changes (no time to go through the history in detail) was that I made the "above the TOC" (table of contents) section list 4 ways of representing numbers: (1) integers (point implicitly at the right), (2) ordinary written mathematical notation (with a point), (3) written scientific notation (with "x10^-3), and (4) the real thing. I believed that understanding (4) required a context of (1), (2) and (3). It was in response to a comment by JakeVortex that I put those 4 below the TOC, listing only (4), without its context, above the TOC. I really believe that this organization, discussing only (4) above the TOC and listing the context shortly afterward, is the right thing, and that at least the first few paragraphs, both above and below the TOC, are starting to be really correct. I really believe that this description, as a sort of numeral representation, is the right way to describe it, and that my sentence "could be thought of as a computer realization of scientific notation" is a good one. Apparently you don't agree. Those changes may have been like a reversion to a much earlier version. If so, it was a coincidence. Or maybe it would be better described as my original proclivities coming back. Whatever. We can discuss this further on the talk page.

The bit about rationals: I consider the fact that all representable FP numbers are rational to be a coincidence, and not fundamental, which is why I've been downplaying that. (I don't remember at the moment whether I completely reverted your text along those lines, or just seemed to.) Aside from the fact that all FP numbers represent reals that happen to be rational, there is nothing special about the rationals here. People use FP to solve differential equations, invert matrices, etc. etc. These are generally thought of as operations over the field of reals. If FP arithmetic were to be suddenly magically endowed with the ability to represent all rationals exactly, all the usual accuracy problems would remain. Well, most of them. You could invert matrices exactly, but you couldn't solve diff. eq.s, or compute pi or exp or log or sin ....

The fact that FP doesn't represent all reals, and the accuracy problems that arise therefrom, are sort of a hot-button item for me. I've seen too much "floating point mysticism" (or maybe "superstition", but really it's ignorance), and I want to be sure this article dispels same. Therefore, it's important to me that the article say that FP numbers are intended to model the reals, and that they do this only approximately because they exactly represent only a subset of the reals and any result is rounded to the nearest representable number. It's perfectly appropriate to mention somewhere that those representable numbers are rational, but that's not what is fundamental, and it really shouldn't be in the first few paragraphs.

William Ackerman 00:47, 6 December 2006 (UTC)