Does anyone know of paper(s) that discuss the distribution of numerical values in (scientific) computing?
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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!
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R relay@relay.mycrowd.ca shared this topic
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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!
Like Zipfian distribution or something else?
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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!
@steven_pigeon Benford's Law?
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Like Zipfian distribution or something else?
@rk The distribution of float values a computer might process in a day. Not sure why it would be Zipf- or Benford-like.
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@rk The distribution of float values a computer might process in a day. Not sure why it would be Zipf- or Benford-like.
@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).
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@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).
@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)
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@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)
@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.
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@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.
@whophd @steven_pigeon @BoydStephenSmithJr @rk Good grief no.
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@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.
@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.
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