I think you're missing the reason why the GPU kicks you out of the fast path when you need that special function. The special function evaluation is fundamentally more expensive in energy, whether that cost is paid in area or time. Evaluation of the special functions with throughput similar to the arithmetic throughput would require much more area for the special functions, which for most computation isn't a good tradeoff. That's why the GPU's designers chose to make your exp2 slow.

Replacing everything with dozens of cascaded special functions makes everything uniform, but it's uniformly much worse. I feel like you're assuming that by parallelizing your "EML tree" in dedicated hardware that problem goes away; but area isn't free in either dollars or power, so it doesn't.

The fact that addition, subtraction, and multiplication run quickly on typical processors isn't arbitrary--those operations map well onto hardware, for roughly the same reasons that elementary school students can easily hand-calculate them. General transcendental functions are fundamentally more expensive in time, die area, and/or power, for the same reasons that elementary school students can't easily hand-calculate them. A primitive where all arithmetic (including addition, subtraction, or negation) involves multiple transcendental function evaluations is not computationally faster, lower-power, lower-area, or otherwise better in any other practical way.

The comments here are filled with people who seem to be unaware of this, and it's pretty weird. Do CS programs not teach computer arithmetic anymore?

Of course the redundant primitives aren't free, since they add code size or die area. In choosing how many primitives to provide, the designer of a numerical library aims to make a reasonable tradeoff between that size cost and the speed benefit.

This paper takes that tradeoff to the least redundant extreme because that's an interesting theoretical question, at the cost of transforming commonly-used operations with simple hardware implementations (e.g. addition, multiplication) into computational nightmares. I don't think anyone has found a practical application for their result yet, but that's not the point of the work.

Efficient numerical libraries likewise contain lots of redundancy. For example, sqrt(x) is mathematically equivalent to pow(x, 0.5), but sqrt(x) is still typically provided separately and faster. Anyone who thinks that eml() function is supposed to lead directly to more efficient computation has missed the point of this (interesting) work.

If you own an ETF that buys SpaceX but without overweighting vs. float, then you're not contributing to the inflated price in that sense. You're still buying at the inflated price though, so the NASDAQ rule change still affects you indirectly.

I guess the point of the "wealth tax" comment is that any higher taxation of the wealthiest individuals would reduce their power to shape the rules to their favor, and a wealth tax is potentially harder to avoid than income taxes. I think most prior attempts just made them emigrate, though.

If you think there's any practical difference between a stream of true randomness and a modern CSPRNG seeded once with 256 bits of true randomness, then you should be able to provide a numerical simulation that detects it. If you (and, again, the world's leading cryptographers) are unable to adversarially create such a situation, then why are you worried that it will happen by accident?

SHA-1 is practically broken, in the sense that a practically relevant chosen-prefix attack can be performed for <$100k. This has no analogy with anything we're discussing here, so I'm not sure why you mentioned it.

You wrote:

> There are concepts like "k-dimensional equidistribution" etc. etc... where in some ways the requirements of a PRNG are far, far, higher than a cryptographically sound PRNG

I believe this claim is unequivocally false. A non-CS PRNG may be better because it's faster or otherwise easier to implement, but it's not better because it's less predictable. You've provided no reference for this claim except that PCG comparison table that I believe you've misunderstood per mananaysiempre's comments. It would be nice if you could either post something to support your claim or correct it.

For example, the turkeys could be randomized by generating 256 bits of randomness per turkey, then sorting by that and taking the first half of the list. By a counting argument this must be biased (since the number of assignments isn't usually a power of two), but the bias is negligible.

The rejection methods may be faster, and thus beneficial in something like a Monte Carlo simulation that executes many times. Rejection methods are also often the simplest way to get distributions other than uniform. The additional complexity doesn't seem worthwhile to me otherwise though, more effort and risk of a coding mistake for no meaningful gain.

Your numbers don't make sense. Your number of assignments is way fewer than 2^256, so the problem the author is (mistakenly) concerned about doesn't arise--no sane method would result in any measurable deviation from equiprobable, certainly not "twice as likely".

With a larger number of turkeys and thus assignments, the author is correct that some assignments must be impossible by a counting argument. They are incorrect that it matters--as long as the process of winnowing our set to 2^256 candidates isn't measurably biased (i.e., correlated with turkey weight ex television effects), it changes nothing. There is no difference between discarding a possible assignment because the CSPRNG algorithm choice excludes it (as we do for all but 2^256) and discarding it because the seed excludes it (as we do for all but one), as long as both processes are unbiased.

Perhaps it would help to think of the randomization in two stages. In the first, we select 2^256 members from the set of all possible permutations. (This happens when we select our CSPRNG algorithm.) In the second, we select a single member from the new set of 2^256. (This happens when we select our seed and run the CSPRNG.) I believe that measurable structure in either selection would imply a practical attack on the cryptographic algorithm used in the CSPRNG, which isn't known to exist for any common such algorithm.

Computational feasibility is what matters. That's roughly what I meant by "measurable", though it's better to say it explicitly as you did. I'm also unaware of any computationally feasible way to distinguish a CSPRNG seeded once with true randomness from a stream of all true randomness, and I think that if one existed then the PRNG would no longer be considered CS.

For emphasis, an empirically measurable deviation from k-equidistribution would be a cryptographic weakness (since it means that knowing some members of the k-tuple helps you guess the others). So that would be a strong claim requiring specific support.

> The point is, if you’re gonna go to all this trouble collecting your data, be a bit more careful in the analysis!

I read that as a complaint about the analysis, not a claim that the study shouldn't have been conducted (and analyzed correctly).

Gelman's blog has exposed bad statistical research from many authors, including the management scientists under discussion here. I don't see any evidence that they applied a harsher standard to Ioannidis.

It's also hard to determine whether that serosurvey (or any other study) got the right answer. The IFR is typically observed to decrease over the course of a pandemic. For example, the IFR for COVID is much lower now than in 2020 even among unvaccinated patients, since they almost certainly acquired natural immunity in prior infections. So high-quality later surveys showing lower IFR don't say much about the IFR back in 2020.

https://sites.stat.columbia.edu/gelman/research/unpublished/...

I don't think Gelman walked anything back in his P.S. paragraphs. The only part I see that could be mistaken for that is his statement that "'not statistically significant' is not the same thing as 'no effect'", but that's trivially obvious to anyone with training in statistics. I read that as a clarification for people without that background.

We'd already discussed PCR specificity ad nauseam, at

https://news.ycombinator.com/item?id=36714034

These test accuracies mattered a lot while trying to forecast the pandemic, but in retrospect one can simply look at the excess mortality, no tests required. So it's odd to still be arguing about that after all the overrun hospitals, morgues, etc.

https://statmodeling.stat.columbia.edu/2020/04/19/fatal-flaw...

That said, I'd put both his serosurvey and the conduct he criticized in "Most Published Research Findings Are False" in a different category from the management science paper discussed here. Those seem mostly explainable by good-faith wishful thinking and motivated reasoning to me, while that paper seems hard to explain except as a knowing fraud.

The biggest downside is all the dark patterns at Merrill trying to sell you advisory services. That seems to be only upon account opening, though.

I guess I'm lucky they rejected me before any money changed hands. I've heard horror stories from people with significant assets at their bank, locked out until an actual lawsuit (the letter from a lawyer didn't work) finally got their attention. I think it's like Google support, usually fine but catastrophic when it's not.

That said, I believe optical isolation is typical for these "data diode" applications, even between two computers in the same rack. I don't think it provides any security benefit, but it's cheap and customers expect it; so there's no commercial incentive to do anything else.