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01:33:36 <Corbin> Folklore is that integration is computable; given a computable (continuous) function on the reals, the Riemann sums over an interval can be computed. Is there a neat trick to this, or is it quite literally done by drawing the little Riemann-style boxes and making ever-thinner slices?
01:47:07 <b_jonas> Corbin: I'd guess the latter. note that if it's a continuous function on a compact set then you can just pick Riemann-style boxes of equal sizes and they will converge, so that's like easy mode.
01:47:47 <Corbin> b_jonas: Yeah, good point.
01:48:02 <Corbin> They computably converge? That's a little surprising, but yeah, I'd believe it.
01:48:31 <b_jonas> I don't know much about computable reals and that sort of thing
01:49:25 <Corbin> I want to believe that they're the future. But every time I've implemented them, it's been like rolling the rock up the hill.
01:51:09 <Corbin> Of numerical work, I suppose. Like, we could be computing exact answers for a lot of engineering and physics work, but floats have limits on precision for operations like sqrt or division.
01:51:55 <b_jonas> anyway, the function is uniformly continuous which is why the Riemann-sum converges: for every 0<epsilon there's a N such that if you divide to N equal boxes then within each box the value of the function is within an epsilon tall interval, so the upper and lower Riemann-sum differs by at most epsilon times the length of the domain
01:52:15 <b_jonas> maybe if you understand computable reals you can tell if that translates to a proof
01:54:02 <b_jonas> as for the general thing, isn't the problem that if you try to compute something with computable reals, you might need like double exponential time or worse, so they can't just avoid you all the difficult numerical analysis tricks to bound errors of floating point computation properly
01:54:43 <b_jonas> and double exponental memory too obviously
01:54:54 <Corbin> Kind of. I guess that there's a continued-fraction proof that's not too bad. Let the upper and lower bounds for N boxes give two sequences of continued fractions. Consider the sequence P of rational numbers which arise as common prefixes; P_N agrees with upper_N and lower_N on the first few coefficients of the continued fractions.
01:57:08 <Corbin> Now, by fun facts about continued fractions, every element of P is a Padé approximant and thus a best possible approximation to some real number; but Riemann already showed that upper and lower already converge to a real number, and P is sandwiched between them. So P uniquely determines a real, and we can read off its continued fraction by one of Gosper's algorithms.
01:57:45 <b_jonas> does this really need to involve continued fractions?
01:58:56 <Corbin> No, that's just the model that I'm used to using.
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04:11:41 <esolangs> [[E]] N https://esolangs.org/w/index.php?oldid=94745 * Lemonz * (+3466) Created page with "'''E''' is a esoteric based off of [[E]]. But you can #s to change from Main use to secondary use. However since there are two per command, <code>E##</code> acts the same a..."
04:12:59 <esolangs> [[E]] https://esolangs.org/w/index.php?diff=94746&oldid=94745 * Lemonz * (+99)
04:50:26 <Corbin> https://i.imgur.com/lU62xDx.png This took hours, but it works. I want it to take seconds. Compilers are hard.
05:25:00 <b_jonas> Corbin: is that some kind of fractal?
05:25:35 <Corbin> b_jonas: Yeah, it's a closeup of the Burning Ship fractal.
05:28:39 <b_jonas> I see. that one is probably famous enough that there's probably optimized code for it somewhere.
05:29:42 <Corbin> There certainly is. Right now, I'm enjoying finding optimized code for such difficult expressions as "256" and "x + y". Primitive recursion is *very* primitive.
05:30:23 <Corbin> So, after putting it off for months, I'm trying out "jets"; I'm replacing short chunks of library code with single optimized bytecodes.
05:34:18 <b_jonas> so you were implementing everything directly in primitive recursion?
05:35:21 <b_jonas> short enough ones I guess that it doesn't generate to writing an interpreter that interprets a biggere interpreter
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13:13:43 <int-e> "sign-in from new location" ...no I'm pretty sure it's the same location as last time.
13:14:00 <HackEso> A device is a browser session. Please verify your device.
13:24:30 <HackEso> device manager? ¯\(°_o)/¯
13:24:37 <fizzie> `le//rn device manager//The device manager can perform low-level device functions such as reboot and factory reset.
13:24:40 <HackEso> Learned 'device manager': The device manager can perform low-level device functions such as reboot and factory reset.
13:24:52 <fizzie> Useless factoids since [insert an early year].
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15:42:08 <esolangs> [[ONE WAY]] M https://esolangs.org/w/index.php?diff=94747&oldid=94743 * DigitalDetective47 * (+1603) /* Examples */
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16:19:30 <esolangs> [[]] M https://esolangs.org/w/index.php?diff=94748&oldid=94710 * PythonshellDebugwindow * (+4) Add link
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20:35:40 <fizzie> Just realized (from a different channel's discussion) that if you use the INTERCAL character names (that is, the correct character names), scripts start with a meshwow line to indicate the interpreter.
21:25:37 <zzo38> Does any implementation of INTERCAL can work if it has such a line at first?
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22:37:49 <esolangs> [[Uzumaki]] N https://esolangs.org/w/index.php?oldid=94749 * Zero player rodent * (+4949) Created page with "{{infobox proglang |name=Uzumaki |paradigms=imperative |author=[[User:Zero player rodent]] |year=[[:Category:2022|2022]] |memsys=[[:Category:Queue-based|Queue-based]] |dimensi..."
22:38:16 <fizzie> I don't know of any at least.
22:54:45 <esolangs> [[User:Zero player rodent]] https://esolangs.org/w/index.php?diff=94750&oldid=94374 * Zero player rodent * (+15)
23:00:28 <esolangs> [[Language list]] M https://esolangs.org/w/index.php?diff=94751&oldid=94641 * Zero player rodent * (+14)
23:36:13 <zzo38> Do you know if any PostScript interpreter does? (This can be done by defining a procedure named #! before the file is executed)
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23:43:09 <zzo38> Is there C interpreter that does? (Usually C is compiled but might also be an interpreter)
23:45:16 <shachaf> I don't know whether you'd call it an interpreter. It compiles your program into memory and jumps to it.
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