stephencanon

8 ms·

61.
by stephencanon 2y ago
(For that matter, though, most modern FP/SIMD units have a direct approximate-reciprocal instruction that is single-cycle throughput or better and much more accurate--generally around 10-12 bits, so there's no need for this sort o
62.
by stephencanon 2y ago
There are basic integer operations in the FP/SIMD units on most CPUs, so there’s no generally need to “move back and forth” unless you need to branch on the result of a comparison, use a value as an address, or do some more specialized
63.
by stephencanon 2y ago
The purely geometric proof works just fine without the case analysis if you use the oriented area.
64.
by stephencanon 2y ago
I'd just like to interject for a moment. What you're referring to as Fort Dix, is in fact, Joint Base McGuire–Dix–Lakehurst, or as the DOD has recently taken to calling it, JB MDL. Fort Dix is not an army base unto itself, but rat
65.
by stephencanon 2y ago
Nah, Dell sells less than 2x as many computers as Apple does (40 million in 2023 vs 22 million for Apple).
66.
by stephencanon 2y ago
I went to a rural public school in the US, we did fractions in 4th grade (~9-10 years old). 9th graders learning fractions sounds highly unusual.
67.
by stephencanon 2y ago
What’s the power draw of however many zen 5 cores you have to tie up to hit, say, 1.5tflop/s on sgemm? (Also, that’s a M2 number, since that’s what OP was talking about. Someone will presumably post M4 benchmarks for BLAS sometime soon
68.
by stephencanon 2y ago
Apple's matrix unit supports FP16, 32, and 64 sources and accumulators.
69.
by stephencanon 2y ago
Right. So, like I said, using one CPU core, you can exceed 1 TFLOP/s, leaving all the other CPU cores and the GPU free for other work.
70.
by stephencanon 2y ago
Sure, but still on each tile, you do O(k^3) compute with O(k^2) memory, and you generally arrange things so that at least one tile is in L1 and at least one other is in L2/LLC (using CPU idioms), so again, you have plenty of bandwidth
71.
by stephencanon 2y ago
For sufficiently large GEMM you should never run out of bandwidth before you max out FLOPS if your blocking is organized correctly, because the arithmetic scales like O(n^3) while the memory access scales like O(n^2).
72.
by stephencanon 2y ago
Probably more relevant here is that a single CPU core on that computer exceeds 1 tflop/s on gemm with plenty of margin using a single lib call, and leaves the rest of the CPU cores and all of the GPU free to do other work.
73.
by stephencanon 2y ago
Yeah. Kahan was involved in the design of the 8087, so he’s always wanted to _have_ extended precision available. What he (and I, and most other numerical analysts) are opposed to is the fact that (a) language bindings historically had no m
74.
by stephencanon 2y ago
Note here is a good starting point for the issue itself: http://www.cs.cmu.edu/~quake/triangle.exact.html References for the actual methods used in Triangle: http://www.cs.cmu.edu/~quake/robust.htm
75.
by stephencanon 2y ago
Binding float to the IEEE 754 binary32 format would not preclude use of decimal formats; they have their own bindings (e.g. _Decimal64 in C23). (I think they're still a TR for C++, but I haven't been keeping track).
76.
by stephencanon 2y ago
The first 754 standard (1985) was essentially formalization of the x87 arithmetic; it defines a "double extended" format. It is not mandatory: > Implementations should support the extended format corresponding to the widest bas
77.
by stephencanon 2y ago
It’s absolutely harmful. It turns computations that would be guaranteed to be exact (e.g. head-tail arithmetic primitives used in computational geometry) into “maybe it’s exact and maybe it’s not, it’s at the compiler’s whim” and suddenly y
78.
by stephencanon 2y ago
Numerical analysis people do not like it. Having _explicitly controlled_ wider accumulation available is great. Having compilers deciding to do it for you or not in unpredictable ways is anathema.
79.
by stephencanon 2y ago
> J.J. and D.H. led the research Hey, I wonder who these mysterious "J.J." and "D.H." might be?
80.
by stephencanon 2y ago
I'm really curious about who "most folks" you refer to are; no one in my extended family does this normally, and I don't know of any friends or neighbors who do it either (we all microwave a snack here and there, sometim
81.
by stephencanon 2y ago
The answer you link to there is from the Swift 1 days in 2014. It was absolutely true then, but array has had true value semantics since shortly after that answer was written.
82.
by stephencanon 2y ago
> It's confusing that arrays and dicts are structs, which have different rules from regular objects As a long-time assembly and C programmer and now Swift programmer, I would say that structs _are_ regular objects, and things with r
83.
by stephencanon 2y ago
(Author and implementer of the Swift Int128 proposal here) There's lots of one-off uses for 128-bit integers scattered around systems programming (and programming in general, I just happen to come from more of a systems background). In
84.
by stephencanon 2y ago
FWIW, that answer (to the second link, after edit) is really old, and you can do string.firstRange(of: substring) since Swift 5.7. The top answer to your third question gives a pretty good explanation of why Swift string indices work the wa
85.
by stephencanon 2y ago
Swift had made this available for a long time via multipliedFullWidth (SE-0104, implemented in Swift 4.0), no Int128 required. E.g.: https://godbolt.org/z/dvMefahdq
86.
by stephencanon 2y ago
Easy fix, just price out an Olympia Mina and then the other hand pumps will seem cheap by comparison.
87.
by stephencanon 2y ago
For IEEE 754-2019 basic formats, subnormal and denormal are synonyms. There are formats (like x87 80-bit as implemented in pre-387 hardware¹) that are not 754 basic formats which admit non-normal encodings that are not subnormal (i.e. not s
88.
by stephencanon 2y ago
OP’s watch appears to be a customized variant of the annual calendar LIGHT, which was introduced in 2016. The 36mm case is unusual, not one of the standard sizes, but O&J has been willing to do 36mm cases on request since ~2010 with cer
89.
by stephencanon 2y ago
FWIW, I’ve worn my O&J every day for seven years, banged it against all sorts of things, and never had any issue (and mine is 42mm and silver, so both less durable than OP’s titanium and much larger and more likely to get banged on stuf
90.
by stephencanon 2y ago
As an American (New Englander), I would say that if it's better to drive than walk or take transit, you are not actually in a city, you're in the suburbs. So this definitely isn't a universal American perspective.

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