<![CDATA[Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing?]]>Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? (Not the spacing of IEEE floats, the values themselves!

]]>https://board.circlewithadot.net/topic/0b60b28f-3e99-440f-b44b-9385ee1bc58f/does-anyone-know-of-paper-s-that-discuss-the-distribution-of-numerical-values-in-scientific-computingRSS for NodeFri, 01 May 2026 06:31:52 GMTSat, 25 Apr 2026 01:50:22 GMT60<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 17:59:27 GMT]]>@whophd @BoydStephenSmithJr @rk

I do not use AI because you spend more time verifying the output (or being annoyed at it) than actually using it. But just for the sake of argument, I tried. The answer I got:

[starts by repeating the question, but getting it from the wrong end] The statistical distribution of floating-point magnitude in computation is influenced by the precision and range of the floating-point representation used.

[Follows:] The IEEE 754 Standard, [then 10 more irrelevant lines, and 5 more about how floats work]

[ends with] Understanding the statistical distribution of floating-point magnitude is crucial for developers to design code that is less susceptible to the pitfalls of floating-point computation and to implement techniques for statistical analysis to ensure numerical stability in scientific software. [True, but that given the question is the converse...]

Then gives me a link to an unpublished, unreviewed paper that looks at how many projects use floats on github.

]]>https://board.circlewithadot.net/post/https://mstdn.ca/users/steven_pigeon/statuses/116466644936597455https://board.circlewithadot.net/post/https://mstdn.ca/users/steven_pigeon/statuses/116466644936597455Sat, 25 Apr 2026 17:59:27 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 14:46:26 GMT]]>@whophd @steven_pigeon @BoydStephenSmithJr @rk Good grief no.

]]>https://board.circlewithadot.net/post/https://scribili.masto.host/ap/users/116268791300985227/statuses/116465885921472247https://board.circlewithadot.net/post/https://scribili.masto.host/ap/users/116268791300985227/statuses/116465885921472247Sat, 25 Apr 2026 14:46:26 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 11:39:03 GMT]]>@steven_pigeon @BoydStephenSmithJr @rk For this kind of topic especially, and at this stage in your research, I would suggest Gemini and ChatGPT, just because you can phrase your query into something harder to find than a search engine can handle. The LLMs can get you URLs for research and further reading if that’s how you work with them. Treat them as junior researchers — but there’s multiple talents, and multiple variants within each brand.

]]>https://board.circlewithadot.net/post/https://ioc.exchange/users/whophd/statuses/116465149101913782https://board.circlewithadot.net/post/https://ioc.exchange/users/whophd/statuses/116465149101913782Sat, 25 Apr 2026 11:39:03 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 02:32:55 GMT]]>@BoydStephenSmithJr @rk Clearly not all inputs are Zipf- or Benford-like. Weights in NN seem to be vaguely gaussian.

I'm trying to figure out what the literature on the topic is.

(and, no, Google doesn't help, it's being as stupid as usual, giving me links on how floats work instead of something actually useful)

]]>https://board.circlewithadot.net/post/https://mstdn.ca/users/steven_pigeon/statuses/116463001641739144https://board.circlewithadot.net/post/https://mstdn.ca/users/steven_pigeon/statuses/116463001641739144Sat, 25 Apr 2026 02:32:55 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 02:22:59 GMT]]>@steven_pigeon @rk There's a criteria https://en.wikipedia.org/wiki/Benford's_law#Benford's_law_compliance_theorem though I don't know why it would apply to "inputs to a FPU" in general -- it seems like you'd have to assume (or prove) something about what is generating those inputs (the workload or programs).

]]>https://board.circlewithadot.net/post/https://hachyderm.io/users/BoydStephenSmithJr/statuses/116462962570994599https://board.circlewithadot.net/post/https://hachyderm.io/users/BoydStephenSmithJr/statuses/116462962570994599Sat, 25 Apr 2026 02:22:59 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 01:53:49 GMT]]>@rk The distribution of float values a computer might process in a day. Not sure why it would be Zipf- or Benford-like.

]]>https://board.circlewithadot.net/post/https://mstdn.ca/users/steven_pigeon/statuses/116462847910337993https://board.circlewithadot.net/post/https://mstdn.ca/users/steven_pigeon/statuses/116462847910337993Sat, 25 Apr 2026 01:53:49 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 01:53:45 GMT]]>@steven_pigeon Benford's Law?

]]>https://board.circlewithadot.net/post/https://scribili.masto.host/ap/users/116268791300985227/statuses/116462847592951229https://board.circlewithadot.net/post/https://scribili.masto.host/ap/users/116268791300985227/statuses/116462847592951229Sat, 25 Apr 2026 01:53:45 GMT<![CDATA[Reply to Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing? on Sat, 25 Apr 2026 01:51:06 GMT]]>@steven_pigeon

Like Zipfian distribution or something else?

]]>https://board.circlewithadot.net/post/https://mastodon.well.com/users/rk/statuses/116462837197477745https://board.circlewithadot.net/post/https://mastodon.well.com/users/rk/statuses/116462837197477745Sat, 25 Apr 2026 01:51:06 GMT