User talk:Taylor Riastradh Campbell

Your submission at Articles for creation: Sterbenz lemma has been accepted

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SL93 (talk) 21:38, 21 November 2020 (UTC)

Your submission at Articles for creation: 2Sum has been accepted

2Sum, which you submitted to Articles for creation, has been created.

Congratulations, and thank you for helping expand the scope of Wikipedia! We hope you will continue making quality contributions.

The article has been assessed as Start-Class, which is recorded on its talk page. Most new articles start out as Stub-Class or Start-Class and then attain higher grades as they develop over time. You may like to take a look at the grading scheme to see how you can improve the article.

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If you have any questions, you are welcome to ask at the help desk. Once you have made at least 10 edits and had an account for at least four days, you will have the option to create articles yourself without posting a request to Articles for creation.

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SL93 (talk) 00:12, 27 November 2020 (UTC)

catastrophic cancellation

you reverted my comment ... why? — Preceding unsigned comment added by 77.0.112.186 (talk) 20:00, 4 February 2021 (UTC)

I moved it to the talk page where it seemed more appropriate for signed conversational exchanges: https://wiki.riteme.site/wiki/Talk:Catastrophic_cancellation Taylor Riastradh Campbell (talk) 20:25, 4 February 2021 (UTC)

On Rabin cryptosystem

Thanks for your recent edit. I added a related item in the discussion. Fgrieu (talk) 14:54, 23 August 2022 (UTC)

reverting changes on Floating-point arithmetic

hi, you reverted my improvements on Floating-point arithmetic, AFAIS without checking the facts. IEEE 754 understands binary floating point representations as 'normalized' significand, a binary fraction between 1 and nearly two, times sign and exponent. In engineering it's common to write floating point numbers in a xyz.uvw...Eab form, a decimal fraction with three leading integer digits. I - tried to - improve this shortcoming in the article, pls. put it back in or provide this relevant info in an appropriate form. Pls. do not! suppres spreading the word about facts. 176.4.177.23 (talk) 00:07, 13 November 2024 (UTC)

Both perspectives of significands are endorsed by IEEE 754:

significand: A component of a finite floating-point number containing its significant digits. The significand can be thought of as an integer, a fraction, or some other fixed-point form, by choosing an appropriate exponent offset. A decimal or subnormal binary significand can also contain leading zeros, which are not significant. —IEEE 754-2019, p. 15

But for the introduction of the article, the integer perspective—that a significand in $p$-digit base-$\beta$ FP is a $p$-digit integer in base $\beta$—is easier to state and more important to focus on without unnecessary jargon like normalized/integral distinction. While it's not wrong that you can view a significand as an element of $[0,\beta -\beta ^{-p+1}]$, it is not an arbitrary element of this real interval. Floating-point arithmetic is fundamentally just fixed-precision integer arithmetic under the hood, as in $$n_{1}\cdot \beta ^{e_{1}}\times n_{2}\cdot \beta ^{e_{2}}=(n_{1}\times n_{2})\cdot \beta ^{e_{1}+e_{2}}$$ with rounding as needed to stay within the fixed precision.

You also replaced material central to the article, about interpreting floating-point formats, by digressions into examples of scientific/engineering notation. And there were a lot of other issues with your changes which I didn't review at first—I only noticed and reverted the changes to the introduction. Some of your changes had typographical errors like ( extraneous spacing in parentheses ) and 'quotation marks' around non-quotations; some of the terminology you added was obsolete, like denormal instead of the modern term subnormal; some of what you added was already said in multiple places in the article, like decimal 0.1 not being a binary floating-point number; some of the material had WP:NPOV issues. Taylor Riastradh Campbell (talk) 11:04, 13 November 2024 (UTC)

'both alternatives' - as you now know about this, and as you are more experienced in wikipedia styling, I'd like to ask you to put it in the article in an appropriate way and place. IMHO it's quite important, in human writing you usually have an explicit radix point, in computer formats it's mostly implicit, and chosing a not fitting bias will falsify values and trash calculations. 176.4.201.218 (talk) — Preceding undated comment added 14:57, 13 November 2024 (UTC)

The body of the article already discusses different perspectives of significand, how the radix point floats according to the exponent with a factor of $\beta ^{p-1}$ implied for normalized significands, and how this is related to scientific notation with a worked example. The body of the article is a good place for going into all this detail. The WP:LEAD section, however, should be strictly limited to a high-level overview of the key points. Taylor Riastradh Campbell (talk) 15:31, 13 November 2024 (UTC)

But it should not start with stating a clear wrong point - 'integer'. 176.4.201.218 (talk) 01:08, 14 November 2024 (UTC)

Again a silly and technically wrong edit on 'Floating-point arithmetic', pls. re-put-in the technically relevant and big difference information that the significand is not! scaled by an exponent, but by a factor calculated as an integral power of the base to the stored exponent ( often minus some bias ). And pls. consider to understand the technical content before reverting reg. format nitpicking. 'Improve rather the revert!'.

176.4.188.149 (talk) 07:51, 23 November 2024 (UTC)

You are correct that the significand is not scaled by the exponent like −3 in the example. But it is scaled by an exponent of the base like 10⁻³ in the example. This concise phrasing is normal in English-language mathematics, and the lead now introduces the important terms (significand, exponent) while avoiding unnecessary jargon like integral power or fixed-point. Exactly what is scaled by what is clarified immediately afterward in the displayed example for anyone to whom the phrasing is not perfectly unambiguous.

The bias is an implementation detail of storage formats with limited exponent ranges, not part of the concept of the set of floating-point numbers or arithmetic on them, it's best to put it in the article body about details of formats; keep the lead concise and to the point.

Regarding format: A number is or is not a floating-point number in some base, precision, and exponent range no matter how you write the number. In base ten, 1/3 is not a floating-point number, but 1/2 is, whether you write it as 1/2, as 2⁻¹, as $0.5\times 10^{0}$, as $5.0\times 10^{-1}$, as $\textstyle (1/{\sqrt {\pi }})\int _{0}^{\infty }e^{-t^{2}}\;dt$, or stored as the binary64 representation 0x3fe0000000000000. Programming languages may tag certain objects in memory differently as int or float, and display data differently depending on the tag, but the mathematical integer 2 is a floating-point number in just about any floating-point system.

Now $\operatorname {FP} (r,p,a)$ will denote a system comprised of a set $S$ of numbers which we shall call floating-point numbers… When $r$ and $p$ are not fixed by context, we shall write $S(r,p)$ instead of $S$. The set $S(r,p)$ contains zero and all numbers of the form $$x=r^{e}m$$ where $e$ is any integer and $m$ is any positive or negative fraction satisfying $$r^{-1}\leq \left|m\right|<1$$ whose absolute value can be expressed in the base $r$ using at most $p$ digits. That is, $$\left|m\right|=r^{-p}M$$ where $M$ is an integer in the range $r^{p-1}\leq M<r^{p}$… Since every floating-point number is a real number, we can perform the standard arithmetic operations of addition, subtraction… However, it is quite possible that these operations will produce numbers not in $S$. —Sterbenz, Floating-Point Computation, 1974, p. 10

(Note that not everyone agrees how the significand is normalized: Sterbenz takes it to lie in $[r^{-1},1)$, while the Handbook of Floating-Point Arithmetic takes it to be $[1,r)$—but everyone agrees there is integer somewhere in $[0,r^{p})$ that can be scaled into the normalized interval.) Taylor Riastradh Campbell (talk) 14:38, 23 November 2024 (UTC)

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