Someone was adding a bit to IEEE 754-2008 about expression evaluation and a bit of the standard there struck me as worth querying.
My reading of the preferred width recommendations in IEEE 754-2008 is that if you have a statement
where x, y, z are all double but the block has preferred width extended then y and z should be added using extended precision and then assigned to x, so one would have double rounding. Is that correct do you think? Thanks Dmcq ( talk) 23:33, 6 April 2012 (UTC)
The Technical Barnstar | |
I am awarding you this Technical Barnstar for your work on IEEE floating point. Good Job! Guy Macon ( talk) 03:21, 13 November 2012 (UTC) |
Could you take a look at Quadruple-precision floating-point format#Double-double arithmetic an perhaps expand it a bit? In particular, many embedded processors have 32-bit floating point arithmetic, and there is a lot of interest in combining two, three or four 32-bit numbers to get extended precision. Yet double-single and quad-single don't seem to be covered anywhere on Wikipedia. Thanks! -- Guy Macon ( talk) 08:51, 15 November 2012 (UTC)
Why the formulas are incorrect? If you mean rounding half-integer always up (like MS Excel function EVEN() do), or always down - it is not bankers' rounding.
If the fraction of number is 0.5 (half-integer), then rounded number is the even integer nearest (maybe up, maybe down) to initial number.
0.5 rounded to 0; 1.5 to 2; 2.5 to 2; 3.5 to 4; 4.5 to 4 and so on.
-0.5 rounded to 0; -1.5 to -2; -2.5 to -2; -3.5 to -4; -4.5 to -4 and so on.
On the other hand each even number has two entries of half-integers: 0 has 0.5 and -0.5; 2 has 1.5 and 2.5; -2 has -1.5 and -2.5 an so on.
That is the point of banker's rounding - unbiased rounding.
It is almost the same arguments for rounding half to odd formula.
If you are confused with multiplier (factor) before floor brackets, or addend inside floor brackets, you should understand that the floor or ceiling brackets are not usual brackets (parentheses) - you can't carry out or in anything, except integer addend (subtrahend), as usual as you do with simple brackets. Floor and ceiling functions have some unique rules. Anyway, just try my formulas with few half-integer numbers and say where I have mistaken. :-)
P.S. Sorry for my English.
Borman05 ( talk) 16:49, 11 April 2014 (UTC)
You have removed my edit in that page qithout understanding what was posted. Please make sure to READ the relevant talk page for a deeper clarification. Only after you have debunked the claims in that page (if indeed they are wrong) is that you may remove my post. Talk:Pwd#PWD meaning. — Preceding unsigned comment added by JustToHelp ( talk • contribs) 05:38, 22 December 2014 (UTC)
Genepy Quantum (
talk) 01:57, 11 November 2015 (UTC)
Why are you reverting my correct changes?
You can calculate the range of data types in this way:
short int: 2 bytes i.e. 16 bits.
216 = 65536 possibilities.
Now let's consider number including zero: we have 65536 numbers from 0 to 65535 (including 0 and 65535).
If you split this range with the sign behaviour of the type you have: 32768 numbers from -32768 to -1 and 32768 numbers from 0 to 32767.
So for a 2 bytes signed data type the range is [-32768 ; 32767].
for a 4 bytes signed data type is [-2147483648 ; 2147483647]
etc...
If you still don't want to understand, compile and run this easy C source code, testing it with, for example, -32768 -32769 +32768.
you can also change the type of 'a' to test it more.
'#include <stdio.h>
int main()
{
short int a;
printf ("\nInsert a number: ");
scanf("%hi",&a);
printf ("\nYour number is: %hi \n\n", a);
return 0;
}
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Here's the way it is now:
unsigned char
the basic type used for arrays suitable to store arbitrary non-bit-field objects: its lack of padding bits and trap representations, the definition of object representation, and the possibility of aliasing.There are three clauses:
Number 1 is an something that is true of unsigned char arrays. They lack padding bits and trap representations. Number 3 is the opposite. There is no possible of aliasing in unsigned char arrays. You see how that's changing sides in the middle?
The first should be changed to "the possibility of padding bits and trap representations" exclusive-or the last should be changed to "the impossibility of aliasing". - Richfife ( talk) 02:07, 15 December 2015 (UTC)
unsigned char
arrays.
Vincent Lefèvre (
talk) 08:04, 15 December 2015 (UTC)restrict
(in C11, §6.7.3.1).
Vincent Lefèvre (
talk) 12:48, 3 May 2016 (UTC)High! You've just reverted an edit on page
C data types. I would like to discuss type ranges. Really, standard says that, for example, short should be from -32767 to 32767. But in fact any compiler (clang-3.6, gcc and microsoft according to msdn) allows you to set signed short
-32768 without any warnings ( -Wall, Wextra, -Wpedantic
, even with -std=iso9899:1990
). So I guess we should change range to from −(2N − 1) to +(2N − 1 − 1)
Yanpas (
talk) 20:23, 17 January 2016 (UTC)
short
and either sign-magnitude or ones' complement representation (both allowed by the C standard), the value −32768 is not possible and the range is [−32767,32767]. Such implementations existed in the past, and might still exist nowadays. There also exist implementations where a short
has more than 16 bits.
Vincent Lefèvre (
talk) 23:47, 17 January 2016 (UTC)FLT_RADIX
is still there. But now, decimal floating point tends to be implemented with _Decimal64
, etc. (not yet in the C standard). I'm not sure about the pocket calculators, though.
Vincent Lefèvre (
talk) 15:32, 26 April 2016 (UTC)Where does C standard tells about CHAR_BITS >= 8? — Preceding unsigned comment added by 86.57.146.226 ( talk) 09:47, 26 February 2016 (UTC)
CHAR_BIT
8", and the first paragraph of this section says: "Their implementation-defined values shall be equal or greater in magnitude (absolute value) to those shown, with the same sign." So, this means CHAR_BIT
≥ 8.
Vincent Lefèvre (
talk) 11:24, 26 February 2016 (UTC)
I'm ok with your . I even kind of like it (how "a bit more" is ambiguous). The sign bit is overhead that does not double.. [Mantissa is/could be larger, usually not double]. Note unums, that do actually have a sign bit in version 1, but he broke away with them in "Unums 2.0" (that is no separate + and - zero). This will make floating-point obsolete.. eventually (see his book, "End of error"). comp.arch ( talk) 14:31, 26 April 2016 (UTC)
u[0] = 2 u[1] = -4 u[n+1] = 111 - 1130 / u[n] + 3000 / (u[n] * u[n-1])
We can almost compare apples with apples by comparing traditional interval arithmetic, using 16-bit floats, with SORNs restricted to connected sets so that they can be stored in only 32 bits. They both take 32 bits and they both use techniques to rigorously contain the correct mathematical result. SORNs win on every count.
Besides the advantages of unums listed here, perhaps it deserves mention that the SORNs store decimal numbers whereas the IEEE 16-bit floats are binary and in general make rounding errors converting to and from human-readable form. Also, there are many problems that traditional intervals cannot solve because all their intervals are closed at both endpoints. Sometimes it is crucial to know whether the exact endpoint is included, or just approached. You cannot do proper set operations with traditional intervals. Like, if you ask for the set of strictly positive real numbers, you get [0, ∞] which incorrectly includes zero (not strictly positive) and infinity (not a real number). If you ask for the complement of that set, well, the best you can do is [–∞, 0]. How can it be the complement if both sets contain the same number, zero? The mathematical rigor claimed for traditional interval arithmetic is actually couched in lots of “gotcha” exceptions that make it even more treacherous to use than floats.
Which is why people stick with floats instead of migrating to intervals.
Just to let you know, [the debate with Kahan is over, while I can't find it online..] and I added info on Unum 2.0 implementeation (or modified called Pnum). I see there is an interview with Gustafson, I missed personally (and slides) [that are however not brand new], not sure if he has anything new to change your mind and his implementation, but Pnum might be different enough (just not looked too closely, if I recall not implementing SCORNs and other changes). comp.arch ( talk) 14:58, 13 July 2016 (UTC)
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There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Yamla ( talk) 11:38, 28 May 2017 (UTC)
Hi Vincent, I see you reverted my edit on the rounding article, the current phrasing is actually wrong, consider:
>>> x = 2**52 + 1
>>> round(x)
4503599627370497.0
>>> math.trunc(x + 0.5)
4503599627370498
Both should return 2**52 + 1
, but adding 0.5 and truncating does not.
Franciscouzo ( talk) 09:40, 1 November 2017 (UTC)
round()
function is not available (as assumed here), then nextafter()
is probably not available either.
Vincent Lefèvre (
talk) 15:40, 1 November 2017 (UTC)Vincent, you are correct that the three axioms for rounding are already too specific in order to encompass all types. Thank you for fixing it. In contrast, it is a pity that you don't like my idea to start the article with a formal definition of rounding (so with (R1) and (R2)?) and then specializing according to all types in use. Axiom0 ( talk) 13:38, 4 March 2018 (UTC)
Hello Mr. Lefèvre,
This is algoHolic. I stumbled across your Floating-point arithmetic Wikipedia page three days ago while I was refreshing my memory on some of the finer points of floating-point representation in computers. Thank you so much, sir, for taking the time yesterday to make that section a heck of a lot more understandable to "the common man" than it was three days ago.
I'm not a mathematician. Nor am I an electrical engineer. I proudly represent the everyday laymen and laywomen who read Wikipedia to learn new stuff — just for fun.
Every now and then I like to dust the cobwebs off my rusty high school algebra brain cells. So when I saw that summation of pi formula in your Floating-point numbers section, I thought that trying to solve it would be good mental exercise for me. Except, in the state that section was in 3 days ago, the worked equation there was as confusing as Chinese! And the textual explanation read like Greek to me!
My original confusion led me to Math Stack Exchange to ask for clarification from those whose math skills are fresher than mine. My layperson's understanding of summations, plus what I learned from the answers on that math.stackexchange page compelled me to make the changes I made to that one pi conversion sigma notation and its worked equation.
So, in the Wikipedia spirit of the broadest-possible inclusiveness, I would like to invite you (and any other Floating-point numbers contributors) to feedback on some of the questions asked in that math.stackexchange page. Being that you "wrote the book" on the subject, Mr. Lefèvre, I'm sure that if you offered your expert's take on the summation questions there, you could clear up a lot of cobwebs of mine and a lot of other math students' and enthusiast's heads regarding how mathematical notation is actually used outside of academia.
Please consider chiming in with your answers or comments if you ever have any spare time. I'm looking forward to hearing more from you, sir.
Thanks again,
algoHolic ( talk) 20:50, 8 November 2017 (UTC)
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In your reason for this massive deletion, you explained "wrong in various ways." Specifically, how is it wrong? This is not a valid criteria for deletion. See WP:DEL-REASON.
When you find errors in Wikipedia, the alternative is to correct the errors with citations. This edit was a good faith edit WP:GF.
Even if it is " badly presented", that is not a reason for deletion. Again, see WP:DEL-REASON.
And finally, "applied only to addition and subtraction (thus cannot be general)." Addition and subtraction are the major causes of floating point error. If you can make cases for adding other functions, such as multiplication, division, etc., then find a resource that backs your positions and add to the article.
I will give you some time to respond, but without substantive justification for your position, I am going to revert your deletion based on the Wikipedia policies cited. The first alternative is to reach a consensus. I am willing to discuss your point of view.
Softtest123 ( talk) 20:08, 19 April 2018 (UTC)
Hello. When you removed Bill Macy from the Golden Age list, you wrote: "due to the lack of references." What do you mean? I completely agree, the man started acting in films in the 1960s, but what exactly were you referring to by lack of references? I am just curious. :) Radiohist ( talk) 00:38, 15 November 2018 (UTC)
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I have an e-mail from David Hough saying that the drafts should be freely available, with the usual restriction of not changing any copyright notice. For years, it has been well known that the drafts of the Fortran standards (at least recent ones) are available for download, but you have to pay for the approved version. David Hough seems to believe that for IEEE 754, but others here claim WP:COPYLINK. I suppose the delegation to WG does complicate things. ucbtest.org seems to be owned by 754WG, and so convenient for posting them. I could ask David Hough for a signed notarized statement, but I don't think he would be too happy with me for that. Gah4 ( talk) 22:53, 8 March 2019 (UTC)
It looks to me like the DOI pages have a copyright notice. Links to actual articles have CCC notice with a dollar amount. I suspect someone is going to say that they should stay, and I think the link to ucbtest.org should stay. Thanks, Gah4 ( talk) 22:53, 8 March 2019 (UTC)
The Goldberg paper has the notice: Permission to copy without fee all or part of this material i sgranted provided that th ecopies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its data appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.@1991ACM0360-0300/91/0300-0005$01.50. What is the rule about ones like that? Thanks, Gah4 ( talk) 23:13, 8 March 2019 (UTC)
Please read MOS:FORMULA (the relevant part of the style guideline) before considering reverting again. Thanks. -- JBL ( talk) 12:58, 22 November 2019 (UTC)
Hi Vincent. I added a page o GNU MPC. Would you look it over when you have some time, please.
Jeffrey Walton ( talk) 00:10, 24 May 2020 (UTC)
Hi Vincent. I am adding SuperH back to Multimedia extensions template. Please do not uno, this is not a mistake as I explained in talk page. If you are still not convinced please voice your opinion. Dawzab ( talk) 20:21, 8 July 2020 (UTC)
the scientific community actually seems to fall into 2 categories: those who do not care and those who want to use the upright style – try to change this on WP, and you'll quickly hear from the third unmentioned category: those who do care and want it in the italic style, particularly in the WP mathematical community. My favourite complaint is that ex is used to denote exp(x) without disambiguation in contexts where this is ambiguous, which is pretty much anywhere outside of real analysis, e.g. with complex numbers. — Quondum 22:25, 16 August 2020 (UTC)
Hi Vincent,
in the Microsoft Binary Format#Technical details article we have a bit-level description of the MBF floating point number format. Further down, we even have a couple of example values including their binary representation derived from a byte-exact 6502 ROM disassembly using this format. And we have pieces of source code comments from a Borland document how to carry out conversions into/from IEEE 754. The values and the description in the article, however, do not seem to match up correctly in regard to the binary exponent value ranges and biased exponents, but, I think, it is important for historical reasons that we provide a bit-level accurate description of this format. It is also possible that I am just temporarily confused about it, therefore, if you have fun and time, I would appreciate a sharp eye on this so we get it right...
Thanks and greetings, -- Matthiaspaul ( talk) 12:12, 2 September 2020 (UTC)
You reverted my change, citing the C/C++ Users guide. However, the portion of the document that you cited refers to IEEE(HEX) compilation ( /info/en/?search=IBM_hexadecimal_floating_point). Extended precision with the FLOAT(HEX) compilation option (the default for 24-bit and 32-bit compilation modes) is also a 128-bit format (not x87), but has a 7 bit exponent (with a base 16 bias).
In the paragraph after the one you cited for rationale to revert my change, is the relevant text:
"z/OS XL C/C++ also supports IEEE 754 floating-point representation (base-2 or binary floating-point formats). By default, float, double, and long double values are represented in z/Architecture floating-point formats (base-16 floatingpoint formats). However, the IEEE 754 floating-point representation is used if you specify the FLOAT(IEEE) compiler option. For details on this support, see “FLOAT” on page 117."
z/OS floating point is confusing, but I've added an additional reference to substantiate my original edit.
Also see:
- /info/en/?search=Quadruple-precision_floating-point_format
- /info/en/?search=IBM_hexadecimal_floating_point
(the latter explains the FLOAT(HEX) extended precision format, which is the default long double representation in some compilation modes (but not for 64-bit.))
-- Peeter.joot ( talk)
What are the typos? I fixed the error forgetting to mention the endianness. Here is the recent update: https://commons.wikimedia.org/wiki/File:Single-precision_floating_point_diagram.png — Preceding unsigned comment added by Joeleoj123 ( talk • contribs) 20:41, 7 November 2020 (UTC)
I was disappointed that you reverted my edit. [9] The point was to make it clear to a casual reader, that they can expect their favourite programming language to do this, after I was surprised to see this behaviour myself. I never claimed GNU C set the default, I was just giving some common examples. Surely making the connection to actual programming languages improves the article, and so should be left in (or at least improved rather than deleted) according to WP:IAR? Adpete ( talk) 00:30, 5 December 2020 (UTC)
I have noticed that whenever I see an edit by you it really improves the article. I just wanted to drop you a line thanking you for all of the hard work. -- Guy Macon ( talk) 01:15, 29 March 2021 (UTC)
Hello, I’m confused as to where the 20th of December has come from as the website and sources such as IMDB have always said he was born on the 5th of March? Maryam01830 ( talk) 11:11, 10 April 2021 (UTC)
Thankyou so much for the feedback and the correction! Maryam01830 ( talk) 12:42, 10 April 2021 (UTC)
Hello again, I remembered I forgot to ask something; was his birthday updated to 20 December before or after the publishing of the times obituary and the guardian article? Many thanks. Maryam01830 ( talk) 18:09, 10 April 2021 (UTC)
Thanks so much for once again clearing that up, I had apprehensions about the guardian copying but having heard your positive experience with them It seems trustworthy. Oh I see, yes that could make sense! Especially as the other info that had been released has brought to light more truth. Thanks again for the info Maryam01830 ( talk) 21:15, 10 April 2021 (UTC)
Hi, I see that you reverted my edit from changing "licence" to "license". The American spelling of "license" and its derivatives are used everywhere else in the article. I am confused why you reverted changing it back to the British spelling when the usage of "license" is written in American English. Ordusifer ( talk) 21:25, 21 June 2021 (UTC)
{{Use British English|date=June 2012}}
template, thus uses British spelling, not American spelling. The reason is that ARM was originally a British company.Vincent,
Thank you for your interest in floating point and floating point error.
In my conversations with experts in the field I put the following explanation:
"*Note on the naming of BFP: We regret choosing the adjective “Bounded” to refer to our floating-point extension. Significant Bits Floating Point may have more accurately identified our work, since we are calculating, monitoring, and storing the number of significant bits available after a calculation."
Though it is possible to derive an interval with BFP (in general much tighter than interval arithmetic, IA) there are other important distinctions. To represent double precision intervals requires 128 bits while BFP this is accomplished with only 80 bits. BFP detects true zero when the significant bits of a result are all zero. And fundamentally, BFP does not blow up under catastrophic cancellation. We haven't built the hardware yet, but clearly BFP will out perform IA. I would hope that you would read the BFP literature and provide informed criticism.
I look forward to hearing from you.
Alan Softtest123 ( talk) 23:55, 19 October 2021 (UTC)
Hey you! Yes, you, Mr. Revert Man! I see from your talk page that you love reverts. So I reverted your revert to make even more reverts! Twice as many reverts! A revert bonanza! I thought you'd enjoy so just letting you know -- Mathnerd314159 ( talk) 19:32, 29 January 2022 (UTC)
Before you delete my work on Bounded Floating Point I would think it would be wise of you to understand BFP. There are many publications on Bounded Floating Point including the patents. It is a patented device and method for computing and retaining error during floating point computations. No other method of floating point calculation performs these functions. For example, it correctly performs the comparison operator A-B when the result is zero under all circumstances. Interval arithmetic does not do this and under certain circumstances blows up. You do floating point technology a disservice by deleting my work.
Your recent editing history shows that you are currently engaged in an edit war; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See the bold, revert, discuss cycle for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.
Being involved in an edit war can result in you being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you do not violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.
Softtest123 ( talk) 04:13, 14 February 2022 (UTC)
u[0] = 2; u[1] = -4; u[n+1] = 111 - 1130 / u[n] + 3000 / (u[n] * u[n-1]);
. It would be interesting to know how BFP behaves on it. You did not provide any clue to guess what one will get. —
Vincent Lefèvre (
talk) 21:44, 16 February 2022 (UTC)
X[0] = 2.000000000000000
X[1] = -4.000000000000000
X[2] = 18.50000000000007
X[3] = 9.37837837837878
X[4] = 7.801152737756
X[5] = 7.15441448103
X[6] = 6.8067847377
X[7] = 6.592632780
X[8] = 6.44946611
X[9] = 6.348454
X[10] = 6.27448
X[11] = 6.2193
X[12] = 6.187
X[13] = 6.32
X[14] = qNaN.sig
There is this quote from the ASTESJ paper: "If all of the significant bits are zero, the resulting value must be zero. BFP detects this condition and sets all fields of the BFP result to zero." So it seems that zero detection normalizes to a true / exact zero value. But it is not clear if this happens on each operation (e.g. each addition) or only at the end of the computation. And the comparison in section 8 seems somewhat misleading because the interesting value is the value before zero detection normalized to true zero. But I guess it would just be what you get with the floating point. The interesting part of BFP is the interval arithmetic with the C, D, and R fields. -- Mathnerd314159 ( talk) 06:44, 1 March 2022 (UTC)
approxEqual
function, and this surprised some users when this started to fail on some inputs. There was a long discussion in a French mailing-list about that, but the archive has unfortunately gone.MOS:TENSE suggests that descriptions should be present tense, except when describing events. Designed, built, sold, and such are actual events. Even when no hardware exists, though in most cases some actually does, the documentation should still exist and the descriptions are present tense. The recent edits were mostly related to documentation of some older processors. I think the Word article looks fine now. Gah4 ( talk) 05:25, 9 August 2022 (UTC)
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Please help group the new C2x features. I started some grouping. • Sbmeirow • Talk • 01:49, 24 December 2022 (UTC)
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I don't like this 'block warden mentality', it hinders progress in Wikipedia. If my edits don't meet your quality standards then improve them, or give me time to work on them and get better, don't switch back to technically WRONG information. My post was technically and historically much better than what is in now. Even if you may be formally right in details, IEEE 854 did not define the data format decimal64 but 'standardized the framework to use data types with e.g. root 10', it is completely stupid to continue to spread misinformation about decimal64 having 'broken significands' and wrong values for the exponents. YOU ARE FRUSTRATING WELL-INTENTIONED PEOPLE!!! Newbie002 ( talk) 10:43, 8 December 2023 (UTC)
Hi @ Vincent Lefèvre, I wonder if you have any time to spare / would be interested in helping figure out what content should belong at Computer arithmetic (previously a poorly chosen redirect), which was just made as a stub in response to some ongoing discussion at arithmetic. I don't feel like enough of an expert to properly organize or write an article at that title from scratch, but I'm happy to help with smaller tasks like discussing possible high-level organization, hunting for historical references, writing small pieces, ... – jacobolus (t) 18:47, 7 March 2024 (UTC)
hello @Vincent Lefèvre, reverting that changes shows that you don't know about the details of this format. Pls. learn and then correct acc. your style, as of now it's misleading.
Someone was adding a bit to IEEE 754-2008 about expression evaluation and a bit of the standard there struck me as worth querying.
My reading of the preferred width recommendations in IEEE 754-2008 is that if you have a statement
where x, y, z are all double but the block has preferred width extended then y and z should be added using extended precision and then assigned to x, so one would have double rounding. Is that correct do you think? Thanks Dmcq ( talk) 23:33, 6 April 2012 (UTC)
The Technical Barnstar | |
I am awarding you this Technical Barnstar for your work on IEEE floating point. Good Job! Guy Macon ( talk) 03:21, 13 November 2012 (UTC) |
Could you take a look at Quadruple-precision floating-point format#Double-double arithmetic an perhaps expand it a bit? In particular, many embedded processors have 32-bit floating point arithmetic, and there is a lot of interest in combining two, three or four 32-bit numbers to get extended precision. Yet double-single and quad-single don't seem to be covered anywhere on Wikipedia. Thanks! -- Guy Macon ( talk) 08:51, 15 November 2012 (UTC)
Why the formulas are incorrect? If you mean rounding half-integer always up (like MS Excel function EVEN() do), or always down - it is not bankers' rounding.
If the fraction of number is 0.5 (half-integer), then rounded number is the even integer nearest (maybe up, maybe down) to initial number.
0.5 rounded to 0; 1.5 to 2; 2.5 to 2; 3.5 to 4; 4.5 to 4 and so on.
-0.5 rounded to 0; -1.5 to -2; -2.5 to -2; -3.5 to -4; -4.5 to -4 and so on.
On the other hand each even number has two entries of half-integers: 0 has 0.5 and -0.5; 2 has 1.5 and 2.5; -2 has -1.5 and -2.5 an so on.
That is the point of banker's rounding - unbiased rounding.
It is almost the same arguments for rounding half to odd formula.
If you are confused with multiplier (factor) before floor brackets, or addend inside floor brackets, you should understand that the floor or ceiling brackets are not usual brackets (parentheses) - you can't carry out or in anything, except integer addend (subtrahend), as usual as you do with simple brackets. Floor and ceiling functions have some unique rules. Anyway, just try my formulas with few half-integer numbers and say where I have mistaken. :-)
P.S. Sorry for my English.
Borman05 ( talk) 16:49, 11 April 2014 (UTC)
You have removed my edit in that page qithout understanding what was posted. Please make sure to READ the relevant talk page for a deeper clarification. Only after you have debunked the claims in that page (if indeed they are wrong) is that you may remove my post. Talk:Pwd#PWD meaning. — Preceding unsigned comment added by JustToHelp ( talk • contribs) 05:38, 22 December 2014 (UTC)
Genepy Quantum (
talk) 01:57, 11 November 2015 (UTC)
Why are you reverting my correct changes?
You can calculate the range of data types in this way:
short int: 2 bytes i.e. 16 bits.
216 = 65536 possibilities.
Now let's consider number including zero: we have 65536 numbers from 0 to 65535 (including 0 and 65535).
If you split this range with the sign behaviour of the type you have: 32768 numbers from -32768 to -1 and 32768 numbers from 0 to 32767.
So for a 2 bytes signed data type the range is [-32768 ; 32767].
for a 4 bytes signed data type is [-2147483648 ; 2147483647]
etc...
If you still don't want to understand, compile and run this easy C source code, testing it with, for example, -32768 -32769 +32768.
you can also change the type of 'a' to test it more.
'#include <stdio.h>
int main()
{
short int a;
printf ("\nInsert a number: ");
scanf("%hi",&a);
printf ("\nYour number is: %hi \n\n", a);
return 0;
}
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Here's the way it is now:
unsigned char
the basic type used for arrays suitable to store arbitrary non-bit-field objects: its lack of padding bits and trap representations, the definition of object representation, and the possibility of aliasing.There are three clauses:
Number 1 is an something that is true of unsigned char arrays. They lack padding bits and trap representations. Number 3 is the opposite. There is no possible of aliasing in unsigned char arrays. You see how that's changing sides in the middle?
The first should be changed to "the possibility of padding bits and trap representations" exclusive-or the last should be changed to "the impossibility of aliasing". - Richfife ( talk) 02:07, 15 December 2015 (UTC)
unsigned char
arrays.
Vincent Lefèvre (
talk) 08:04, 15 December 2015 (UTC)restrict
(in C11, §6.7.3.1).
Vincent Lefèvre (
talk) 12:48, 3 May 2016 (UTC)High! You've just reverted an edit on page
C data types. I would like to discuss type ranges. Really, standard says that, for example, short should be from -32767 to 32767. But in fact any compiler (clang-3.6, gcc and microsoft according to msdn) allows you to set signed short
-32768 without any warnings ( -Wall, Wextra, -Wpedantic
, even with -std=iso9899:1990
). So I guess we should change range to from −(2N − 1) to +(2N − 1 − 1)
Yanpas (
talk) 20:23, 17 January 2016 (UTC)
short
and either sign-magnitude or ones' complement representation (both allowed by the C standard), the value −32768 is not possible and the range is [−32767,32767]. Such implementations existed in the past, and might still exist nowadays. There also exist implementations where a short
has more than 16 bits.
Vincent Lefèvre (
talk) 23:47, 17 January 2016 (UTC)FLT_RADIX
is still there. But now, decimal floating point tends to be implemented with _Decimal64
, etc. (not yet in the C standard). I'm not sure about the pocket calculators, though.
Vincent Lefèvre (
talk) 15:32, 26 April 2016 (UTC)Where does C standard tells about CHAR_BITS >= 8? — Preceding unsigned comment added by 86.57.146.226 ( talk) 09:47, 26 February 2016 (UTC)
CHAR_BIT
8", and the first paragraph of this section says: "Their implementation-defined values shall be equal or greater in magnitude (absolute value) to those shown, with the same sign." So, this means CHAR_BIT
≥ 8.
Vincent Lefèvre (
talk) 11:24, 26 February 2016 (UTC)
I'm ok with your . I even kind of like it (how "a bit more" is ambiguous). The sign bit is overhead that does not double.. [Mantissa is/could be larger, usually not double]. Note unums, that do actually have a sign bit in version 1, but he broke away with them in "Unums 2.0" (that is no separate + and - zero). This will make floating-point obsolete.. eventually (see his book, "End of error"). comp.arch ( talk) 14:31, 26 April 2016 (UTC)
u[0] = 2 u[1] = -4 u[n+1] = 111 - 1130 / u[n] + 3000 / (u[n] * u[n-1])
We can almost compare apples with apples by comparing traditional interval arithmetic, using 16-bit floats, with SORNs restricted to connected sets so that they can be stored in only 32 bits. They both take 32 bits and they both use techniques to rigorously contain the correct mathematical result. SORNs win on every count.
Besides the advantages of unums listed here, perhaps it deserves mention that the SORNs store decimal numbers whereas the IEEE 16-bit floats are binary and in general make rounding errors converting to and from human-readable form. Also, there are many problems that traditional intervals cannot solve because all their intervals are closed at both endpoints. Sometimes it is crucial to know whether the exact endpoint is included, or just approached. You cannot do proper set operations with traditional intervals. Like, if you ask for the set of strictly positive real numbers, you get [0, ∞] which incorrectly includes zero (not strictly positive) and infinity (not a real number). If you ask for the complement of that set, well, the best you can do is [–∞, 0]. How can it be the complement if both sets contain the same number, zero? The mathematical rigor claimed for traditional interval arithmetic is actually couched in lots of “gotcha” exceptions that make it even more treacherous to use than floats.
Which is why people stick with floats instead of migrating to intervals.
Just to let you know, [the debate with Kahan is over, while I can't find it online..] and I added info on Unum 2.0 implementeation (or modified called Pnum). I see there is an interview with Gustafson, I missed personally (and slides) [that are however not brand new], not sure if he has anything new to change your mind and his implementation, but Pnum might be different enough (just not looked too closely, if I recall not implementing SCORNs and other changes). comp.arch ( talk) 14:58, 13 July 2016 (UTC)
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There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Yamla ( talk) 11:38, 28 May 2017 (UTC)
Hi Vincent, I see you reverted my edit on the rounding article, the current phrasing is actually wrong, consider:
>>> x = 2**52 + 1
>>> round(x)
4503599627370497.0
>>> math.trunc(x + 0.5)
4503599627370498
Both should return 2**52 + 1
, but adding 0.5 and truncating does not.
Franciscouzo ( talk) 09:40, 1 November 2017 (UTC)
round()
function is not available (as assumed here), then nextafter()
is probably not available either.
Vincent Lefèvre (
talk) 15:40, 1 November 2017 (UTC)Vincent, you are correct that the three axioms for rounding are already too specific in order to encompass all types. Thank you for fixing it. In contrast, it is a pity that you don't like my idea to start the article with a formal definition of rounding (so with (R1) and (R2)?) and then specializing according to all types in use. Axiom0 ( talk) 13:38, 4 March 2018 (UTC)
Hello Mr. Lefèvre,
This is algoHolic. I stumbled across your Floating-point arithmetic Wikipedia page three days ago while I was refreshing my memory on some of the finer points of floating-point representation in computers. Thank you so much, sir, for taking the time yesterday to make that section a heck of a lot more understandable to "the common man" than it was three days ago.
I'm not a mathematician. Nor am I an electrical engineer. I proudly represent the everyday laymen and laywomen who read Wikipedia to learn new stuff — just for fun.
Every now and then I like to dust the cobwebs off my rusty high school algebra brain cells. So when I saw that summation of pi formula in your Floating-point numbers section, I thought that trying to solve it would be good mental exercise for me. Except, in the state that section was in 3 days ago, the worked equation there was as confusing as Chinese! And the textual explanation read like Greek to me!
My original confusion led me to Math Stack Exchange to ask for clarification from those whose math skills are fresher than mine. My layperson's understanding of summations, plus what I learned from the answers on that math.stackexchange page compelled me to make the changes I made to that one pi conversion sigma notation and its worked equation.
So, in the Wikipedia spirit of the broadest-possible inclusiveness, I would like to invite you (and any other Floating-point numbers contributors) to feedback on some of the questions asked in that math.stackexchange page. Being that you "wrote the book" on the subject, Mr. Lefèvre, I'm sure that if you offered your expert's take on the summation questions there, you could clear up a lot of cobwebs of mine and a lot of other math students' and enthusiast's heads regarding how mathematical notation is actually used outside of academia.
Please consider chiming in with your answers or comments if you ever have any spare time. I'm looking forward to hearing more from you, sir.
Thanks again,
algoHolic ( talk) 20:50, 8 November 2017 (UTC)
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In your reason for this massive deletion, you explained "wrong in various ways." Specifically, how is it wrong? This is not a valid criteria for deletion. See WP:DEL-REASON.
When you find errors in Wikipedia, the alternative is to correct the errors with citations. This edit was a good faith edit WP:GF.
Even if it is " badly presented", that is not a reason for deletion. Again, see WP:DEL-REASON.
And finally, "applied only to addition and subtraction (thus cannot be general)." Addition and subtraction are the major causes of floating point error. If you can make cases for adding other functions, such as multiplication, division, etc., then find a resource that backs your positions and add to the article.
I will give you some time to respond, but without substantive justification for your position, I am going to revert your deletion based on the Wikipedia policies cited. The first alternative is to reach a consensus. I am willing to discuss your point of view.
Softtest123 ( talk) 20:08, 19 April 2018 (UTC)
Hello. When you removed Bill Macy from the Golden Age list, you wrote: "due to the lack of references." What do you mean? I completely agree, the man started acting in films in the 1960s, but what exactly were you referring to by lack of references? I am just curious. :) Radiohist ( talk) 00:38, 15 November 2018 (UTC)
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I have an e-mail from David Hough saying that the drafts should be freely available, with the usual restriction of not changing any copyright notice. For years, it has been well known that the drafts of the Fortran standards (at least recent ones) are available for download, but you have to pay for the approved version. David Hough seems to believe that for IEEE 754, but others here claim WP:COPYLINK. I suppose the delegation to WG does complicate things. ucbtest.org seems to be owned by 754WG, and so convenient for posting them. I could ask David Hough for a signed notarized statement, but I don't think he would be too happy with me for that. Gah4 ( talk) 22:53, 8 March 2019 (UTC)
It looks to me like the DOI pages have a copyright notice. Links to actual articles have CCC notice with a dollar amount. I suspect someone is going to say that they should stay, and I think the link to ucbtest.org should stay. Thanks, Gah4 ( talk) 22:53, 8 March 2019 (UTC)
The Goldberg paper has the notice: Permission to copy without fee all or part of this material i sgranted provided that th ecopies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its data appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.@1991ACM0360-0300/91/0300-0005$01.50. What is the rule about ones like that? Thanks, Gah4 ( talk) 23:13, 8 March 2019 (UTC)
Please read MOS:FORMULA (the relevant part of the style guideline) before considering reverting again. Thanks. -- JBL ( talk) 12:58, 22 November 2019 (UTC)
Hi Vincent. I added a page o GNU MPC. Would you look it over when you have some time, please.
Jeffrey Walton ( talk) 00:10, 24 May 2020 (UTC)
Hi Vincent. I am adding SuperH back to Multimedia extensions template. Please do not uno, this is not a mistake as I explained in talk page. If you are still not convinced please voice your opinion. Dawzab ( talk) 20:21, 8 July 2020 (UTC)
the scientific community actually seems to fall into 2 categories: those who do not care and those who want to use the upright style – try to change this on WP, and you'll quickly hear from the third unmentioned category: those who do care and want it in the italic style, particularly in the WP mathematical community. My favourite complaint is that ex is used to denote exp(x) without disambiguation in contexts where this is ambiguous, which is pretty much anywhere outside of real analysis, e.g. with complex numbers. — Quondum 22:25, 16 August 2020 (UTC)
Hi Vincent,
in the Microsoft Binary Format#Technical details article we have a bit-level description of the MBF floating point number format. Further down, we even have a couple of example values including their binary representation derived from a byte-exact 6502 ROM disassembly using this format. And we have pieces of source code comments from a Borland document how to carry out conversions into/from IEEE 754. The values and the description in the article, however, do not seem to match up correctly in regard to the binary exponent value ranges and biased exponents, but, I think, it is important for historical reasons that we provide a bit-level accurate description of this format. It is also possible that I am just temporarily confused about it, therefore, if you have fun and time, I would appreciate a sharp eye on this so we get it right...
Thanks and greetings, -- Matthiaspaul ( talk) 12:12, 2 September 2020 (UTC)
You reverted my change, citing the C/C++ Users guide. However, the portion of the document that you cited refers to IEEE(HEX) compilation ( /info/en/?search=IBM_hexadecimal_floating_point). Extended precision with the FLOAT(HEX) compilation option (the default for 24-bit and 32-bit compilation modes) is also a 128-bit format (not x87), but has a 7 bit exponent (with a base 16 bias).
In the paragraph after the one you cited for rationale to revert my change, is the relevant text:
"z/OS XL C/C++ also supports IEEE 754 floating-point representation (base-2 or binary floating-point formats). By default, float, double, and long double values are represented in z/Architecture floating-point formats (base-16 floatingpoint formats). However, the IEEE 754 floating-point representation is used if you specify the FLOAT(IEEE) compiler option. For details on this support, see “FLOAT” on page 117."
z/OS floating point is confusing, but I've added an additional reference to substantiate my original edit.
Also see:
- /info/en/?search=Quadruple-precision_floating-point_format
- /info/en/?search=IBM_hexadecimal_floating_point
(the latter explains the FLOAT(HEX) extended precision format, which is the default long double representation in some compilation modes (but not for 64-bit.))
-- Peeter.joot ( talk)
What are the typos? I fixed the error forgetting to mention the endianness. Here is the recent update: https://commons.wikimedia.org/wiki/File:Single-precision_floating_point_diagram.png — Preceding unsigned comment added by Joeleoj123 ( talk • contribs) 20:41, 7 November 2020 (UTC)
I was disappointed that you reverted my edit. [9] The point was to make it clear to a casual reader, that they can expect their favourite programming language to do this, after I was surprised to see this behaviour myself. I never claimed GNU C set the default, I was just giving some common examples. Surely making the connection to actual programming languages improves the article, and so should be left in (or at least improved rather than deleted) according to WP:IAR? Adpete ( talk) 00:30, 5 December 2020 (UTC)
I have noticed that whenever I see an edit by you it really improves the article. I just wanted to drop you a line thanking you for all of the hard work. -- Guy Macon ( talk) 01:15, 29 March 2021 (UTC)
Hello, I’m confused as to where the 20th of December has come from as the website and sources such as IMDB have always said he was born on the 5th of March? Maryam01830 ( talk) 11:11, 10 April 2021 (UTC)
Thankyou so much for the feedback and the correction! Maryam01830 ( talk) 12:42, 10 April 2021 (UTC)
Hello again, I remembered I forgot to ask something; was his birthday updated to 20 December before or after the publishing of the times obituary and the guardian article? Many thanks. Maryam01830 ( talk) 18:09, 10 April 2021 (UTC)
Thanks so much for once again clearing that up, I had apprehensions about the guardian copying but having heard your positive experience with them It seems trustworthy. Oh I see, yes that could make sense! Especially as the other info that had been released has brought to light more truth. Thanks again for the info Maryam01830 ( talk) 21:15, 10 April 2021 (UTC)
Hi, I see that you reverted my edit from changing "licence" to "license". The American spelling of "license" and its derivatives are used everywhere else in the article. I am confused why you reverted changing it back to the British spelling when the usage of "license" is written in American English. Ordusifer ( talk) 21:25, 21 June 2021 (UTC)
{{Use British English|date=June 2012}}
template, thus uses British spelling, not American spelling. The reason is that ARM was originally a British company.Vincent,
Thank you for your interest in floating point and floating point error.
In my conversations with experts in the field I put the following explanation:
"*Note on the naming of BFP: We regret choosing the adjective “Bounded” to refer to our floating-point extension. Significant Bits Floating Point may have more accurately identified our work, since we are calculating, monitoring, and storing the number of significant bits available after a calculation."
Though it is possible to derive an interval with BFP (in general much tighter than interval arithmetic, IA) there are other important distinctions. To represent double precision intervals requires 128 bits while BFP this is accomplished with only 80 bits. BFP detects true zero when the significant bits of a result are all zero. And fundamentally, BFP does not blow up under catastrophic cancellation. We haven't built the hardware yet, but clearly BFP will out perform IA. I would hope that you would read the BFP literature and provide informed criticism.
I look forward to hearing from you.
Alan Softtest123 ( talk) 23:55, 19 October 2021 (UTC)
Hey you! Yes, you, Mr. Revert Man! I see from your talk page that you love reverts. So I reverted your revert to make even more reverts! Twice as many reverts! A revert bonanza! I thought you'd enjoy so just letting you know -- Mathnerd314159 ( talk) 19:32, 29 January 2022 (UTC)
Before you delete my work on Bounded Floating Point I would think it would be wise of you to understand BFP. There are many publications on Bounded Floating Point including the patents. It is a patented device and method for computing and retaining error during floating point computations. No other method of floating point calculation performs these functions. For example, it correctly performs the comparison operator A-B when the result is zero under all circumstances. Interval arithmetic does not do this and under certain circumstances blows up. You do floating point technology a disservice by deleting my work.
Your recent editing history shows that you are currently engaged in an edit war; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See the bold, revert, discuss cycle for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.
Being involved in an edit war can result in you being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you do not violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.
Softtest123 ( talk) 04:13, 14 February 2022 (UTC)
u[0] = 2; u[1] = -4; u[n+1] = 111 - 1130 / u[n] + 3000 / (u[n] * u[n-1]);
. It would be interesting to know how BFP behaves on it. You did not provide any clue to guess what one will get. —
Vincent Lefèvre (
talk) 21:44, 16 February 2022 (UTC)
X[0] = 2.000000000000000
X[1] = -4.000000000000000
X[2] = 18.50000000000007
X[3] = 9.37837837837878
X[4] = 7.801152737756
X[5] = 7.15441448103
X[6] = 6.8067847377
X[7] = 6.592632780
X[8] = 6.44946611
X[9] = 6.348454
X[10] = 6.27448
X[11] = 6.2193
X[12] = 6.187
X[13] = 6.32
X[14] = qNaN.sig
There is this quote from the ASTESJ paper: "If all of the significant bits are zero, the resulting value must be zero. BFP detects this condition and sets all fields of the BFP result to zero." So it seems that zero detection normalizes to a true / exact zero value. But it is not clear if this happens on each operation (e.g. each addition) or only at the end of the computation. And the comparison in section 8 seems somewhat misleading because the interesting value is the value before zero detection normalized to true zero. But I guess it would just be what you get with the floating point. The interesting part of BFP is the interval arithmetic with the C, D, and R fields. -- Mathnerd314159 ( talk) 06:44, 1 March 2022 (UTC)
approxEqual
function, and this surprised some users when this started to fail on some inputs. There was a long discussion in a French mailing-list about that, but the archive has unfortunately gone.MOS:TENSE suggests that descriptions should be present tense, except when describing events. Designed, built, sold, and such are actual events. Even when no hardware exists, though in most cases some actually does, the documentation should still exist and the descriptions are present tense. The recent edits were mostly related to documentation of some older processors. I think the Word article looks fine now. Gah4 ( talk) 05:25, 9 August 2022 (UTC)
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Please help group the new C2x features. I started some grouping. • Sbmeirow • Talk • 01:49, 24 December 2022 (UTC)
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I don't like this 'block warden mentality', it hinders progress in Wikipedia. If my edits don't meet your quality standards then improve them, or give me time to work on them and get better, don't switch back to technically WRONG information. My post was technically and historically much better than what is in now. Even if you may be formally right in details, IEEE 854 did not define the data format decimal64 but 'standardized the framework to use data types with e.g. root 10', it is completely stupid to continue to spread misinformation about decimal64 having 'broken significands' and wrong values for the exponents. YOU ARE FRUSTRATING WELL-INTENTIONED PEOPLE!!! Newbie002 ( talk) 10:43, 8 December 2023 (UTC)
Hi @ Vincent Lefèvre, I wonder if you have any time to spare / would be interested in helping figure out what content should belong at Computer arithmetic (previously a poorly chosen redirect), which was just made as a stub in response to some ongoing discussion at arithmetic. I don't feel like enough of an expert to properly organize or write an article at that title from scratch, but I'm happy to help with smaller tasks like discussing possible high-level organization, hunting for historical references, writing small pieces, ... – jacobolus (t) 18:47, 7 March 2024 (UTC)
hello @Vincent Lefèvre, reverting that changes shows that you don't know about the details of this format. Pls. learn and then correct acc. your style, as of now it's misleading.