arb VS julia

You can instead list your criteria for good number format and look at alternatives with those lenses. Floating point is designed for a good balance between dynamic range and precision, and IEEE 754 binary formats can be seen as a FP standard particularly optimized for numerical calculation.

There are several other FP formats. The most popular one is IEEE 754 minus subnormal numbers, followed by bfloat16, IEEE 754 decimal formats (formerly IEEE 854) and posits. Only first two have good hardware supports. The lack of subnormal number means that `a <=> b` can't be no longer rewritten to `a - b <=> 0` among others but is widely believed to be faster. (I don't fully agree, but it's indeed true for existing contemporary hardwares.) IEEE 754 decimal formats are notable for lack of normalization guarantee. Posits are, in some sense, what IEEE 754 would have been if designed today, and in fact aren't that fundamentally different from IEEE 754 in my opinion.

Fixed-point formats share pros and cons of finitely sized integer numbers and you should have no difficulty to analyze them. In short, they offer a smaller dynamic range compared to FP, but its truncation model is much simpler to reason. In turn you will get a varying precision and out-of-bound issues.

Rational number formats look very promising at the beginning, but they are much harder to implement efficiently. You will need a fast GCD algorithm (not Euclidean) and also have to handle out-of-bound numerators and denumerators. In fact, many rational number formats rely on arbitrary-precision integers precisely for avoiding those issues, and inherit the same set of issues---unbounded memory usage and computational overhead. Approximate rational number formats are much rarer, and I'm only aware of the Inigo Quilez's floating-bar experiment [1] in this space.

[1] https://iquilezles.org/articles/floatingbar/

Interval/ball/affine arithmetics and others are means to automatically approximate an error analysis. They have a good property of being never incorrect, but it is still really easy for them to throw up and give a correct but useless answer like [-inf, inf]. Also they are somewhat awkward in a typical procedural paradigm because comparisons will return a tri-state boolean (true, false, unsure). Nevertheless they are often useful when correctly used. Fredrik Johansson's Arb [2] is a good starting point in my opinion.

[2] https://arblib.org/

Finally you can model a number as a function that returns a successively accurate approximation. This is called the constructive or exact real number, and simultaneously most expensive and most correct. One of the most glaring problems is that an equality is not always decidable, and practical applications tend to have various heuristics to get around this fact. Amazingly enough, Android's built-in calculator is one of the most used applications that use this model [3].

[3] https://dl.acm.org/doi/pdf/10.1145/2911981

https://github.com/JuliaMath/Bessels.jl/blob/master/src/bess...

Thanks! I love it, so easy to understand and follow.

My favourite work on the subject is Fredrik Johansson's:

https://github.com/fredrik-johansson/arb

Whenever I feel down and without energy I just read something in there

Probably the most popular package for dealing with error propagation and arbitrary precision arithmetic in Python is mpmath, more specifically the mp.iv module. For more serious applications I'd take a look at MPFR and Arb, both in C. And there are tons of ball arithmetic and interval arithmetic libraries in Fortran.

You're in good company too. Using intervals to bound error is the entire idea behind the arb library.

The error bounds approach is probably what you’re looking for. A better search term for that is “interval arithmetic.” There are many good software packages for interval arithmetic, like Arb.

I do agree with your list, so that is something! I will add, balls are underrated, ditto intervals (nominally more efficient, but on x86 switching rounding modes is 20-30 cycles...)

Ball arithmetic looks interesting. As far as I know, arb is the primary implementation.

34. Julia - $74,963

I don't believe there is any official documentation on this, but https://github.com/JuliaLang/julia/pull/49430 for example added prefetching to the marking phase of a GC which saw speedups on x86, but not on M1.

3. dispatch on all the arguments

the first solution is clean, but people really like dispatch.

the second makes calling functions in the function call syntax weird, because the first argument is privileged semantically but not syntactically.

the third makes calling functions in the method call syntax weird because the first argument is privileged syntactically but not semantically.

the closest things to this i can think of off the top of my head in remotely popular programming languages are: nim, lisp dialects, and julia.

nim navigates the dispatch conundrum by providing different ways to define free functions for different dispatch-ness. the tutorial gives a good overview: https://nim-lang.org/docs/tut2.html

lisps of course lack UFCS.

see here for a discussion on the lack of UFCS in julia: https://github.com/JuliaLang/julia/issues/31779

so to sum up the answer to the original question: because it's only obvious how to make it nice and tidy like you're wanting if you sacrifice function dispatch, which is ubiquitous for good reason!

https://github.com/JuliaLang/julia/blob/release-1.10/NEWS.md

Visit official site: https://julialang.org/

No. It runs natively on ARM.

julia> versioninfo() Julia Version 1.9.3 Commit bed2cd540a1 (2023-08-24 14:43 UTC) Build Info: Official https://julialang.org/ release

https://github.com/JuliaLang/julia/issues/51086#issuecomment...

So while this "fixes" the issue, it'll introduce a confusing time delay between you freeing the memory and you observing that in `htop`.

But according to https://jemalloc.net/jemalloc.3.html you can set `opt.muzzy_decay_ms = 0` to remove the delay.

Still, the musl author has some reservations against making `jemalloc` the default:

https://www.openwall.com/lists/musl/2018/04/23/2

> It's got serious bloat problems, problems with undermining ASLR, and is optimized pretty much only for being as fast as possible without caring how much memory you use.

With the above-mentioned tunables, this should be mitigated to some extent, but the general "theme" (focusing on e.g. performance vs memory usage) will likely still mean "it's a tradeoff" or "it's no tradeoff, but only if you set tunables to what you need".

I have asked about Julia's reproducibility story on the Guix mailing list in the past, and at the time Simon Tournier didn't think it was promising. I seem to recall Julia itself didnt have a reproducible build. All I know now is that github issue is still not closed.

https://github.com/JuliaLang/julia/issues/34753

I don't really know what kind of rebuttal you're looking for, but I will link my HN comments from when this was first posted for some thoughts: https://news.ycombinator.com/item?id=31396861#31398796. As I said, in the linked post, I'm quite skeptical of the business of trying to assess relative buginess of programming in different systems, because that has strong dependencies on what you consider core vs packages and what exactly you're trying to do.

However, bugs in general suck and we've been thinking a fair bit about what additional tooling the language could provide to help people avoid the classes of bugs that Yuri encountered in the post.

The biggest class of problems in the blog post, is that it's pretty clear that `@inbounds` (and I will extend this to `@assume_effects`, even though that wasn't around when Yuri wrote his post) is problematic, because it's too hard to write. My proposal for what to do instead is at https://github.com/JuliaLang/julia/pull/50641.

Another common theme is that while Julia is great at composition, it's not clear what's expected to work and what isn't, because the interfaces are informal and not checked. This is a hard design problem, because it's quite close to the reasons why Julia works well. My current thoughts on that are here: https://github.com/Keno/InterfaceSpecs.jl but there's other proposals also.

Doesn't musl have the same issue? https://github.com/JuliaLang/julia/issues/34726#issuecomment...

I also wonder about OSX's libc. Newer versions seem to have some sort of locking https://github.com/apple-open-source-mirror/Libc/blob/master...

but older versions (from 10.9) don't have any lockign: https://github.com/apple-oss-distributions/Libc/blob/Libc-99...