Talk:IEEE 754

decimal exponent

I did a revert to a change on decimal exponent values. I believe it is right, because of the way they are defined, but I start this in case someone wants to discuss it, as I noted in the edit summary. Gah4 (talk) 17:20, 19 January 2024 (UTC)

The change was correct. The decimal exponent values got wrong in 1179557460 (but before that, there were already errors in some values for decimal64, which were introduced in the previous change 1179553657 by Nsmeds). I've corrected another value in 1197287634. — Vincent Lefèvre (talk) 22:17, 19 January 2024 (UTC)

OK, I am confused. What I see now isn't what I remember from the differences I saw before. There is always the question of the position of the decimal point, and I thought it was just that. In any case, we are discussing them, which is what I wanted. Gah4 (talk) 03:49, 20 January 2024 (UTC)

Concerning the position of the decimal point, this can make a difference of 15 or 16 in the exponent for decimal64, but here, this was a factor 2. — Vincent Lefèvre (talk) 13:53, 20 January 2024 (UTC)

Yes, I thought it was closer to 15, and now I see that it was a factor of 2. That is why I said I was confused about it. In any case, it is good to discuss here. Gah4 (talk) 23:22, 20 January 2024 (UTC)

I am sorry for not keeping in touch on this issue. There have been some other things keeping me occupied lately. Looking at the table as it stands today https://en.wikipedia.org/w/index.php?title=IEEE_754&oldid=1210204290 I am happy with the way it looks as regards the table on some useful properties of the IEEE-754 floating point formats. I went through my spreadsheet to compare FP formats and found a bug in the computations of estimated log10(MAXVAL) and have a public (LibreOffice) copy uploaded to my Google Drive share

I will update the table with adjusted values of the Decimal format log10(Maxval) estimates. I am not sure, but I think that is the issue you discussed in this thread? Nsmeds (talk) 17:13, 25 February 2024 (UTC)

This is what I think the best approx is to log10(MAXVAL)

${\alpha =1+maxexp},{\beta =maxexp-digits}$

$log_{10}(10^{\alpha }-10^{\beta })=\alpha +log_{10}(1-10^{\beta -\alpha })=\alpha +{{log_{10}(1-10^{\beta -\alpha })} \over {ln(10)}}=$

$=\lbrace {\alpha >\beta >0}\rbrace ={\alpha -{{10^{\beta -\alpha }} \over {ln(10)}}}+\Omega ({10^{2\cdot (\beta -\alpha )})}=$

$={\alpha -log_{10}(e)\cdot 10^{\beta -\alpha }}={\alpha -10\cdot log_{10}(e)\cdot 10^{\beta -\alpha -1}}\approx {\alpha -4.34\cdot 10^{\beta -\alpha -1}}$

$={(1+maxexp)-4.34\cdot 10^{-(1+digits)}}$ Nsmeds (talk) 18:44, 25 February 2024 (UTC)

Yes, if there are p digits, then the correction term is

$\ln(1-10^{-p})/\ln(10)\approx -10^{-p}/\ln(10)\approx -4.34\cdot 10^{-p-1}$

— Vincent Lefèvre (talk) 03:21, 26 February 2024 (UTC)

Thanks for confirming. If you want to (and if you have access to LibreOffice/OpenOffice and dare to enable my macros), have a look at the spreadsheet. Some of the formats there are not officially accepted and/or necessarily correctly described, but I find it illuminating to feed in various research formats and see what comes out. :-) Nsmeds (talk) 08:39, 26 February 2024 (UTC)

Introduction to History

@Nsmeds: Though I agree that an introduction in IEEE 754#History would be useful, there are several issues with what has been added in 1210457800, so that I'm going to revert this change (mainly because of the first point below):

• First, this should be an introduction to the history of the standardization of floating-point arithmetic, not a history on FP arithmetic (there is an article Floating-point arithmetic on this larger subject, with its own history). So, here, it should just be explained what was before IEEE 754 and why standardization was needed.
• In the added text, "non-enumerable" is pointless and misleading: The issue compared to integers is that the considered numbers cannot be represented exactly in general. This is the case even if you restrict to the computable real numbers (which form the subset of R that really matters in computing), which are enumerable (countable), but also just rational numbers.
• Binary representation is not always used.
• The last two sentences are not clear, but anyway, they are not related to the standardization (like the whole paragraph).
• The image is missing, but anyway, it is not related to the standardization either.
• Note that "mantissa" and "de-normal" are not the correct terms (there are also English and typographic mistakes).

BTW, in section History of Floating-point arithmetic, there is a paragraph on the standardization, which could serve as a basis:

Initially, computers used many different representations for floating-point numbers. The lack of standardization at the mainframe level was an ongoing problem by the early 1970s for those writing and maintaining higher-level source code; these manufacturer floating-point standards differed in the word sizes, the representations, and the rounding behavior and general accuracy of operations. Floating-point compatibility across multiple computing systems was in desperate need of standardization by the early 1980s, leading to the creation of the IEEE 754 standard once the 32-bit (or 64-bit) word had become commonplace. This standard was significantly based on a proposal from Intel, which was designing the i8087 numerical coprocessor; Motorola, which was designing the 68000 around the same time, gave significant input as well.

— Vincent Lefèvre (talk) 01:54, 27 February 2024 (UTC)

@Vincent Lefèvre I agree with your comments. Hopefully there is someone with us able to volunteer a more suitable introductory paragraph? Nsmeds (talk) 12:50, 27 February 2024 (UTC)

Definition or explanation for MAXVAL missing

The article presents a table with a column for the property MAXVAL. This term MAXVAL is neither defined nor explained nor referenced in the article or any of the articles binary16, binary32, ..., which are mentioned by the footnote [b]. —87.123.51.236 (talk) 10:32, 18 September 2025 (UTC)

Update body references to refer to IEEE 754-2019?

The article makes several references to the 2019 revision. However, references within the body of the article still refer to the 2008 revision. Shouldn't these references be updated to the (current) 2019 revision? MiguelDecimal128 (talk) 20:05, 15 June 2026 (UTC)

If you want you can update the references, though the previous ones likely do a fine job of verifying claims in the article. If you do, make sure you are careful about it, clicking through to make sure the section numbers haven't changed, quotations match word for word, etc. –jacobolus (t) 21:45, 15 June 2026 (UTC)

However, claims that are valid in a previous revision of the standard may no longer be valid for the current revision. For instance, the minNum and maxNum operations from IEEE 754-2008 have been removed (replaced) in the 2019 revision. That's why one needs to check the 2019 revision and update the references. Of course, the History section should still refer to the 2008 revision when needed.

There is the article IEEE 754-2008 revision for what this revision changed. A similar article for the IEEE 754-2019 revision would be useful too (though there are much fewer changes). — Vincent Lefèvre (talk) 10:27, 26 June 2026 (UTC)