Talk:Floating-point arithmetic/Archive 3

message: I have reverted much of the changes to the "misconceptions"
section.  This section should be about the "FP numbers are
approximations" misconception, and how one can replace it with
clear thinking.  It should not be about the many accuracy problems that can arise -- that
topic is treated extensively later.
I believe that the detailed bit-by-bit analysis of "0.1" and "0.01", while tedious,
is important for an understanding of what is actually going on.
William Ackerman 16:36, 31 July 2006 (UTC)
thread_title:  Misconceptions 

message: This article contains a tremendous amount of information!  It may be too much information, if there is such a thing.  To me, it reads rather like a textbook than an encyclopedia article.  I'm new here and I'm not quite sure what to do about it.  Any ideas?  Sns 04:49, 21 August 2006 (UTC)
replies: text: It is better to have too much, then not enough information. Michael.Pohoreski 17:00, 16 March 2007 (UTC)
thread_title:  Too much info? 

message: Clearly something needs to be done.  Here is an outline of what I propose.  I may do it over the weekend, if no one else reorganizes it or indicates here that they don't agree.
The main thing is that the "common misconceptions" section goes into way too much detail near the top of the article.  Now, talking about misconceptions early on is important, because some misconceptions are extremely widespread.  But the mention near the top should be very brief.  Just say that a FP number represents an actual real number exactly.  FP numbers are not "approximations to real numbers", and they do not "represent some small range of real numbers".  All the rest, including the details of 0.1 * 0.1, can wait until after people know how FP operations work.  That material is way too intimidating and confusing that early in the article.
Then the details of the representation, the operations, rounding, overflow, etc.
Then the "problems".  These problems are the consequences of the way the operations work (which will have been explained by that point) and the expectations of real arithmetic.  A lot more work is needed here.  First, the "peculiar properties" and the "problems" sections need to be combined.  Other than that, I think there are a lot of open questions about how to proceed.  Perhaps there should be a first part about "what can go wrong" and a second part about "what to do about it".
That is, the second part discusses the Kahan Summation Method and the example of Archimedes' calculation of pi.
Perhaps the material on how to code things to get better accuracy should be a completely separate article.  It's a very big topic in general, and this is an encyclopedia. William Ackerman 15:24, 23 August 2006 (UTC)
replies: text: Others have raised this complaint.  I really think the bit-by-bit explanation of the format belongs here.  This is the page of a central concept in computers.  There was a time when IEEE representation was just a proposal, but it's now the way nearly every computer operates.  It belongs here, even if it is duplicated on the IEEE page. William Ackerman 23:53, 30 August 2006 (UTC)
thread_title: Reorganization

message: A number of people have suggested, one way or the other, that this article duplicates material from the IEEE floating-point standard and shouldn't do so.  I strongly disagree, at least to the level of detail presently given on this page.  Of course, the IEEE page goes into enormous detail that doesn't belong on this page. However, I believe that a person should be able to figure out the bit representation of a floating-point number just from this page.  It should definitely go into that level of detail.  That means rounding, exponent bias, how the fields are packed, etc.
: I think it depends on what you mean. I disagree quite strongly on the question of being able to decode any floating point number form the information on this page. This is really best served (if at all, but I agree that somewhere in wikipedia would be appropriate) on the page for the particular format. This page will have enough detail. That said, it may be valuable to walk through one format in detail in the interest of being explicit. But even then, we might be better off just refering the reader to some particular FP format's page such as single precision that discusses the encoding in detail. Many people who write floating point algorithms don't really need to concern themselves with the encoding details, so I don't this this is essential to the topic of this page. --Jake 00:33, 12 October 2006 (UTC)
replies: text: I think I'm coming around a little more to your point of view.  The single precision and double precision pages seem to say, much more succinctly than IEEE, the gist of what needs to be said. William Ackerman 01:36, 13 October 2006 (UTC)

text: Talk:Floating point/Removed sections
I think the section on Exceptional values and exceptions under the IEEE standard should be mostly addressed in IEEE floating-point standard. In this article we should really be setting up the questions that need to be addressed, and leave the other page to answer them (for that particular case). If we wanted to have a page on VAX floating point or Cray floating point, they would address this situations differently. --Jake 00:33, 12 October 2006 (UTC)
thread_title:  Cutting back on IEEE info 

message: Following the suggestions of KSmrq, I have added some "survey of other approaches" material near the top.  I'm not happy with having so much material (a whole screenful) above the index.  Should this be moved to the end?  Is it appropriate?  Is it too technical?
Yes, I'm aware that rational arithmetic is a redlink.  I think such an article should exist. William Ackerman 01:25, 13 October 2006 (UTC)
thread_title:  Survey paragraph in intro 

message: Editors have been known to remove external links from this article if they are added with no history comment and with no discussion on the talk page.  Please discuss the value of your proposed link here if you want it not to be cleaned out regularly.  (You can help!)  EdJohnston 17:59, 24 October 2006 (UTC)
replies: text: The Floating point page is, as you see, mostly devoted to bit formats, hardware, and compiler issues. The paper by Izquierdo and Polhill that you cite is about making numerical calculations robust. That seems to fit with the traditional definition of Numerical analysis.    I suggest you consider adding it there, or at least propose it on their Talk page. EdJohnston 19:38, 2 November 2006 (UTC)
thread_title:  Discuss links here 

message: I've thought more about what we are really trying to say that floating-point is, and done another round of editing.  If I've stepped on anyone's toes, I really didn't mean to.  We are making progress.
The section headings "overview" and "basics" are just wrong.  Any ideas on restructuring that?  Things are pretty badly ordered at this point, and there's a lot of redundancy.
Amoss -- I like the concept of the "window" that the digits must lie in, and that the radix point can slide anywhere relative to.  But it's inconsistently applied at present.  Do you think you can work out a way to use that metaphor clearly and consistently throughout the introduction?  Or at least throughout parts of it? William Ackerman 01:13, 24 November 2006 (UTC)
replies: text: I like much of the content in the intro, but I think it is getting a little too details for the intro. It reads more like a section on "digit string representations" which would provide background and context for the article. I think the intro should boil down the essence of the whole article to serve either as an executive summary for someone who wants the short story, or as a way to wet the appetite for someone reading the article. So beyond digit strings I think the intro should touch on values, arithmetic, and introduce the notion of exceptions. There should be a reference to IEEE 754, and some reference to the troubles resulting from floating point numbers being different from real numbers that leads to the need for numerical analysis. To keep it introductory, each of these topics should get little more than a sentence each, and leave the section in the article to do the real work. --Jake 19:32, 27 November 2006 (UTC)
thread_title:  More restructuring of introductory material