sfpotter

16 ms·

241.
by sfpotter 2y ago
IEEE floats are an incredible feat of engineering. The people who designed them were geniuses. We should be appreciative of the fact that we have a consistent and portable way to do numerics. I'm glad we've got IEEE 754 and don&#x
242.
by sfpotter 2y ago
The only real place for quad precision is when you're working with numbers that truly require you to be able span a massive difference in magnitudes without round-off error accumulating. For some context, an electron "has structur
243.
by sfpotter 2y ago
Basically guaranteed that you don't need quad for this.
244.
by sfpotter 2y ago
A "high income" is relative. They might actually have a well-calibrated expectation for what "high" means based on being close to people who don't have high incomes---that is, being in the top 25% should be high b
245.
by sfpotter 2y ago
They link to three of their papers that have more details.
246.
by sfpotter 2y ago
There are tons of different games to play. Designing a preconditioner that's specific to the problem being solved can help you beat incomplete LU, often by a substantial (even asymptotic) margin. If you have a problem that's small
247.
by sfpotter 2y ago
It it were really "just for fun", would you really feel the need to make a website spelling it out?
248.
by sfpotter 2y ago
I think you have a poor understanding of what most of the world looks like. Most people on the planet exist in tenuous circumstances which do not allow them to simply go find another job, let alone an employer that isn't abusive, etc.
249.
by sfpotter 2y ago
Sounds like you live in a world of incredible privilege. Not everyone is so lucky.
250.
by sfpotter 2y ago
That seems plausible. I actually spent a little time digging into this, and I'm not sure if this method is actually due to Chebyshev! This link has the most extensive references I found: https://encyclopediaofmath.org&#
251.
by sfpotter 2y ago
Why is that bad? Are there any cases where Chebyshev iteration is the best option? It seems like acquiring the necessary information about the spectrum would be prohibitive in practice, although I have never tried it out.
252.
by sfpotter 2y ago
Python isn't simple.
253.
by sfpotter 2y ago
A nice way to approximate the median: https://www.stat.berkeley.edu/~ryantibs/papers/median.pdf
254.
by sfpotter 2y ago
Take whatever drugs you like. You just seem a little bewildered why people aren't more fired up about what you have to say about the halting problem. Just trying to suggest that it may be because this isn't the right venue for it.
255.
by sfpotter 2y ago
You're getting hung up on a logical point which, while correct, isn't particularly salient to the context in which this conversation is occurring (CAD and graphics). The original article, while mathematically interesting, is also
256.
by sfpotter 2y ago
This is a little mixed up. If you write the arc length as an elliptic integral and evaluate it using a special function library, you may just be evaluating a Chebyshev series or some rational approximation (or some piecewise combination). I
257.
by sfpotter 2y ago
No, I'm not getting this confused at all. I understand the point. What I'm saying is that because the general elliptic integral corresponding to sqrt(quartic) doesn't have a closed form, and because this (or maybe a slightl
258.
by sfpotter 2y ago
We're talking about Bezier curves in the context of CAD and graphics. In this case, I believe there is no reason to assume that these curves will have a more special form than sqrt(arbitrary quartic). Do you think that they do have a m
259.
by sfpotter 2y ago
The specific form in question is basically sqrt(any quartic). Seems like almost all of these will be able to be expressed in terms of elliptic integrals and that's it. Outer post summarizes this just fine.
260.
by sfpotter 2y ago
I'm not sure how much more "closed form" you need than elliptic integrals. For another approach, expand sqrt(1 + B'(t)^2) in a Chebyshev series and you're off to the races.
261.
by sfpotter 2y ago
Second paragraph of the Wikipedia article on elliptic integrals: https://en.wikipedia.org/wiki/Elliptic_integral
262.
by sfpotter 2y ago
Experience of the world, not HN...
263.
by sfpotter 2y ago
It's easy to infer which is normal based on one's experience of the world. The world would be very different if it were otherwise.
264.
by sfpotter 2y ago
This is just normal. I wouldn't overthink it. If you were truly "aphantasic", you'd know; if you truly had preternatural visualization abilities, you'd know.
265.
by sfpotter 2y ago
I think this is a really good way to put it. It feels like there's a rush to label and self-diagnose which ultimately results in a ton of pathologization of relatively normal behaviors. That is: "normal" as in we expect to se
266.
by sfpotter 2y ago
"Nobody has anything more to say about Fourier series than what Walter Rudin figured out long ago."
267.
by sfpotter 2y ago
Uhh... there is a lot more to say about Fourier series than "just that they're defined for any locally compact abelian group". Give me a break.
268.
by sfpotter 2y ago
I think the response gets right to the point! Using something like Haskell for ROOT is ridiculous for a lot of obvious reasons. A simple and dismissive "no" invites the cautious reader to discover them on their own rather than was
269.
by sfpotter 2y ago
I'm not sure how TIOBE works, but I wonder how much of the rise can be attributed to old Fortran projects getting thrown up on GitHub. Fortran is a fine language, and it has its strengths, but I don't think "native computatio
270.
by sfpotter 2y ago
I'm under the impression "big" here might mean a 10-20% improvement if you're lucky. Good to back this claim up with hard data.

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