The tone of the GP is such because it's a quote from the rules/guidelines. However, applying that rule to what you said makes no sense to me, fwiw.

I don't want to go too heavy on the negatives, but what's nuts is Python going for trust-the-programmer style multithreading. The risk is that extension modules could cause a lot of crashes.

My understanding is that many extension modules are already written to take advantage of multithreading by releasing the GIL when calling into C code. This allows true concurrency in the extension, and also invites all the hazards of multithreading. I wonder how many bugs will be uncovered in such extensions by the free threaded builds, but it seems like the “nuts” choice actually happened a long time ago.

How did you get that diploma/plaque, is that something every patent author will have?

You can buy them from various manufacturers that make them; you often get unsolicited mail from them as your name and address is on the patent filings.

The plaque was a personal order from one of the many companies that make them. What you actually get from the USPTO looks like this: https://x.com/EricLengyel/status/1159917092331642880/photo/1

How did you find out that his optimization was done for a different equation, just by trial?

Just looking at the formula in the code (and the book it came from), we see that the approximation is of form arcsin(x) = π/2 - P(x)*sqrt(1-x). It is called a minimax solution in both, and the simplest form of minimax optimization is for polynomials. So we look at P(x) = (π/2 - arcsin(x))/sqrt(1-x): plotting out its error function with the original coefficients, it has the clear equioscillations that you'd expect from an optimized polynomial, i.e., each local peak has the exact same height, which is the max error. But if we look at the error curve in terms of arcsin(x), then its oscillations no longer have the same height, which indicates that the approximation can be improved.

Thank you for elaborating!

yes, Estrin's method is the update

Sorry, I said that wrong. Estrin's doesn't reduce the number of multiplications.

If your goal is reducing the number of multiplications, I imagine it would make sense to factor that polynomial into degree-1 and degree-2 factors.

They list a bunch of companies under the heading "All these companies work with the same technology" on their landing page. I think it's quite scummy, and very non-impressive when you see it.

Simple rule to keep in mind that even math savvy people seem to forget about is that: sqrt(x²) = |x| with bars for absolute value.

For a programmer, it's clear that we have lost the sign information but not the magnitude.

Simple. Makes most sign and solution reasoning explicit instead of implicit when solving quadratics or otherwise working with square roots.

> Simple rule to keep in mind that even math savvy people seem to forget about is that: sqrt(x²) = |x| with bars for absolute value.

i would disagree with that (pun intended).

We can try the same with "oil production"

Do you know if the other 20% is oxygen (as was claimed) or if it's air? I just think the latter seems cheaper and more likely.

I think it may be CO2. CO2 in the gas would cause all sorts of unpleasant effects that would discourage continuing to breath it, and CO2 is probably cheaper to store and transport than oxygen.

It is open source, there are just many different ways to do open source code. One example is Lua, which is released as open source but the project is not open - they will not accept contributions from others.