| --- Log opened Thu May 26 00:00:04 2016 |
| 00:07 | | Turaiel[Offline] is now known as Turaiel |
| 00:14 | < Azash> | Reiv: Not necessarily pre-installed, slackbot is the name they use for the core one but you can develop your own with that websocket+REST API' |
| 00:15 | <@Reiv> | there you go then |
| 00:15 | <@Reiv> | I hadn't seen a slack instance without it, so |
| 00:17 | < Azash> | Yeah it's more of an interface for the core functionaly |
| 00:17 | < Azash> | Compare to FooServ vs. IRC bots |
| 00:17 | < Azash> | s/y$/ity/ |
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| 04:07 | < yardboy> | anybody still awake over there? |
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| 04:27 | <~Vornicus> | noone ever |
| 04:32 | < [R]> | Aynone else find him really annoying? |
| 04:32 | <~Vornicus> | eh |
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| 10:24 | <@TheWatcher> | I think my comment for the day: # It's gone well so far, try to make a hash of it! |
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| 12:42 | < abudhabi> | What proportion of decimal fractions cannot be represented precisely in binary notation? |
| 12:45 | <@TheWatcher> | Are you using fixed or floating point? Because for floating point hte answer is "none of them can be represented precisely" |
| 12:51 | < abudhabi> | Floating point. Um, I'm pretty sure that "0.5" can be represented precisely in both binary and decimal. |
| 12:51 | < abudhabi> | (Or am I hallucinating?) |
| 12:54 | <@TheWatcher> | The instant you touch IEEE 754, you have no such thing as an exact representation. |
| 13:00 | < abudhabi> | OK. |
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| 13:02 | <@gnolam> | Also, the proportion is roughly lim -> 0, given that the number of decimal fractions is infinite.~ |
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| 13:14 | < abudhabi> | gnolam: Yeah, this is what I wanted to know; the limit towards which unrepresentable fractions tend. |
| 13:17 | < pjdelport> | abudhabi: Good question. |
| 13:18 | < pjdelport> | abudhabi: You could formalise that as the density of binary fractions in the Stern-Brocot tree or Farey sequence, up to various depths. |
| 13:26 | < pjdelport> | abudhabi: I just did a quick experiment: it looks like it approaches ~0.5 for increasing lengths of the Farey sequence. |
| 13:26 | < pjdelport> | It alternates on either side, approaching closer. |
| 13:34 | < pjdelport> | abudhabi: So the density of rationals with divisors congruent to 2 seems to be about a half. |
| 13:35 | < pjdelport> | Congruent to 3 seems to be about a third |
| 13:36 | < pjdelport> | Congruent to 5 seems about a fifth |
| 13:37 | < pjdelport> | Curiously, 4 also seems to be around ~0.2... |
| 13:37 | < pjdelport> | Not a quarter as you might expect. |
| 13:38 | < pjdelport> | All the other primes seem to have a rational divisor density of 1/n |
| 13:39 | < pjdelport> | The compounds seem to have weirder densitities |
| 13:40 | < pjdelport> | Congruent to 6 is ~0.0908 |
| 13:42 | < abudhabi> | I have no idea what you are doing! ;) |
| 13:43 | < pjdelport> | abudhabi: I just hacked a quick thing to enumerate the rationals up to a certain depth with the Farey sequence, and then count the density of rationals with a certain divisor congruence. |
| 13:43 | < pjdelport> | Which is maths-speak for what you were discussing above. |
| 13:45 | < pjdelport> | IOW, the fractions that you can express in binary notation is the same as the proportion of fractions that have a divisor divisible by two. |
| 13:45 | < abudhabi> | OK. The maths speak is what I don't parse. |
| 13:45 | < pjdelport> | "divisible by two" = "congruent to two" more or less. |
| 13:46 | < pjdelport> | Oh, I see you actually asked about decimal fractions, not all fractions. |
| 13:46 | < pjdelport> | That's also easy to work out. |
| 13:50 | < pjdelport> | Oh, whoops |
| 13:50 | < pjdelport> | I made a calculation error earlier. |
| 13:52 | < abudhabi> | Yeah, the point is to see how many are unrepresentable in binary like 0.1 and how many are representable like 0.25. |
| 13:53 | < pjdelport> | 0.25 is representable in binary. |
| 13:53 | < pjdelport> | (Oh, nevermind, read that wrong) |
| 13:54 | < pjdelport> | Okay, so for arbitrary rationals, the proportion seems to be 1/(1+n) for primes |
| 13:54 | < pjdelport> | So ~1/3 of rationals are binary, ~1/4 are ternary, and so on. |
| 13:56 | < pjdelport> | Okay, so considering 0.00⦠to 0.99⦠|
| 14:01 | < pjdelport> | For various lengths of digits, the density of binary-representable ones seems to approach 1: |
| 14:01 | < pjdelport> | 0.5, 0.75, 0.875, 0.9375, 0.96875, 0.984375, 0.9921875 |
| 14:02 | < pjdelport> | So that's a density of 0.5 for 0.0 to 0.9 |
| 14:02 | < pjdelport> | 0.75 for 0.00 to 0.99, and so on. |
| 14:03 | < pjdelport> | So the general rule seems to be that for n decimal digits of precision, 1 / 2^n will not be binary-representable. |
| 14:04 | < pjdelport> | A proportion of 1/2^n that is. |
| 14:04 | < pjdelport> | So 1 - 1/2^n will be representable |
| 14:06 | < abudhabi> | Huh. That's actually quite different from the ballpark gnolam gave. |
| 14:08 | <@gnolam> | Because my ballpark is not assuming that floats are infinitely large, but rather 32 or 64 bits. |
| 14:08 | <@gnolam> | A.k.a. the real world.~ |
| 14:15 | <@TheWatcher> | Like I said, when you're using IEEE 754, you're fucked if you need exact representation for anything other than 0, NaN, negative infinity, and positive infinity; essentially everything else should be treated as an approximation, especially the instant you start actually using them in calculations. |
| 14:18 | <@TheWatcher> | (+0 and -0 is supported as the sign bit can be 1 or 0 when the exponent and mantissa are both 0, but hey) |
| 14:47 | < pjdelport> | TheWatcher: IEEE 754 does have exact representations; numeral analysis can get pretty involved, though. |
| 14:47 | < pjdelport> | "Treat everything as approximate" is a good defensive first approximation, but you can do better. :) |
| 14:47 | < pjdelport> | If you're careful. |
| 14:59 | < catadroid> | I once did better |
| 15:37 | < catadroid> | I find myself agreeing rather a lot with Hyrum Wright and Titus Winters on what makes good and bad tests |
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| 16:16 | < ToxicFrog> | TheWatcher: integers are exact depending on how many sig figs there are, and in particular anything that will fit into a [u]int32_t is exactly representable in a double. |
| 16:17 | <@celticminstrel> | So a double has >+ 32 significant figures. |
| 16:17 | <@celticminstrel> | ^ >= |
| 16:19 | < ToxicFrog> | celticminstrel: a double has 52 bits mantissa (== 53 bits precision), 11 bits exponent and 1 sign bit. |
| 16:20 | <@celticminstrel> | I guess that means [u]int64_t will fit in a quad-float. |
| 16:22 | < ToxicFrog> | Yes. |
| 16:23 | <@celticminstrel> | I wonder if 80-bit floats exist anymore outside of legacy stuff. |
| 16:37 | < catadroid> | Today I am mentoring a new programmer |
| 16:37 | < catadroid> | Entirely accidentally |
| 16:37 | < catadroid> | He thinks our tools are, and I quote "cool" |
| 16:37 | | * catadroid beams excessively |
| 16:43 | < ToxicFrog> | neat! |
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| 21:08 | | * McMartin eyes the Rust patchnotes. |
| 21:08 | <&McMartin> | "The time complexity of comparing variables for equivalence during type unification is reduced from O(n!) to O(n). As a result, some programming patterns compile much, much more quickly." |
| 21:08 | <&McMartin> | ... yeah, I bet. |
| 21:08 | <@celticminstrel> | Whaaat! |
| 21:09 | <&McMartin> | I'm assuming they've moved from "brute force" to "do it right" |
| 21:09 | <&McMartin> | I super-vaguely recall that a full type-inference pass in ML-like languages is O(n^3), so unifying two variables being O(n) with The Right Algorithm doesn't strike me as implausible |
| 21:10 | <&McMartin> | But I'm going on vague recollection and ass-pulls here, so~ |
| 21:31 | <~Vornicus> | O(n!). |
| 21:31 | <~Vornicus> | What the hell were they doing |
| 21:36 | <&McMartin> | Testing all possible permutations of something by brute force, I'd guess |
| 21:36 | <&McMartin> | Still cheaper than all possible subsets! |
| 22:10 | <~Vornicus> | it's the other way around actually |
| 22:11 | < Azash> | Google won, so yay |
| 22:15 | <&McMartin> | Oh, wait, right |
| 22:15 | <&McMartin> | All subsets is 2^n |
| 22:15 | <&McMartin> | What am I thinking of that's the canonical n^n problem |
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| 22:33 | <~Vornicus> | yeah, this is like -- 1e9 vs 3e32 vs 2e44 |
| 22:38 | <@Reiv> | what |
| 22:39 | <&McMartin> | Reiv: Latest Rust release notes indicate one of the processes run during compilation has been sped up to linear time from, er, factorial time |
| 22:41 | <@Reiv> | Wait /what/ |
| 22:45 | < Azash> | Hahahah |
| 22:52 | <~Vornicus> | You are officially the fourth person to have that reaction |
| 22:55 | <&McMartin> | We may assume that n was generally very small |
| 22:55 | <@Tamber> | s/assume/hope/ ? |
| 22:59 | <&McMartin> | No, I mean |
| 22:59 | <&McMartin> | I've used it for projects on the scale of thousands of lines of code |
| 22:59 | <&McMartin> | And it compiled at a speed comparable to similarly-sized Java programs |
| 23:00 | <&McMartin> | As opposed to "life of the universe" |
| 23:01 | <@Tamber> | Ah, can't be that bad, then~ |
| 23:01 | <&McMartin> | Certain programming strategies apparently were very slow to compile |
| 23:01 | <&McMartin> | Not anymore, because this is after all a thing we know how to do |
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| 23:38 | <@Reiv> | I think the bit that makes me pause |
| 23:39 | <@Reiv> | Is that if you *ever* find yourself writing factorial-time code, you want to double check you really can't do it a better way |
| 23:39 | <@Reiv> | Then |
| 23:39 | <@Reiv> | To have that reduced to LINEAR |
| 23:40 | <@Reiv> | I mean, factorial to polynomial would be "Oh thank goodness, we have sanity back in the system" |
| 23:40 | <@Reiv> | to nlogn would be "Wow, guys did a great job there" |
| 23:40 | <@Reiv> | to n? "Wait, what the fuck were you doing the first time round" |
| 23:42 | < pjdelport> | It really depends on the expected range of N too. |
| 23:42 | <@Reiv> | Well, sure, granted |
| 23:43 | < Azash> | Reiv: Reminds me a little of the guy who was head of the CS dept when I studied actively, one of the two people here who have an algorithm named after them |
| 23:43 | <@Reiv> | sweet |
| 23:43 | < Azash> | Designed a suffix tree algorithm and took the state of the art from n^2 or n^3 to n, iirc |
| 23:43 | <@Reiv> | very sweet |
| 23:43 | <@Reiv> | But then, polynomial to n is... hm, how to put it |
| 23:44 | <@Reiv> | "Congratulations on an exciting algorathm that took a perfectly reasonable runtime and obliterated it through cunning" |
| 23:44 | <@Reiv> | Factorial to n |
| 23:45 | <@Reiv> | That starts to have me eye the Factorial part askance >_> |
| 23:45 | < Azash> | Is less impressive and more "what were you doing to begin with" ? |
| 23:46 | <@Reiv> | Correct |
| 23:46 | <@Reiv> | I mean, if it really was best practice routines that we were trapped in one of the worst scaling designs imaginable, but little progress had been made, sure |
| 23:46 | < Azash> | Reiv: On a trivia note http://stackoverflow.com/questions/9452701/ukkonens-suffix-tree-algorithm-in-pla in-english/9513423#9513423 |
| 23:47 | <@Reiv> | But, you know, factorial runtimes are the kind of thing where people will usually try to at least come up with a polynomial |
| 23:47 | < Azash> | Yeah |
| 23:47 | <@Reiv> | And if you find it, you celebrate |
| 23:47 | <@Reiv> | Finding a sodding linear makes one wonder if someone hadn't been lazy >_> |
| 23:50 | <&McMartin> | Oh uh |
| 23:50 | <&McMartin> | This is a long-solved problem |
| 23:50 | <&McMartin> | They were really obviously being lazy |
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| 23:54 | < Azash> | McMartin: That was the whole point, yeah |
| 23:56 | <@Reiv> | Thank you for confirming my suspicions. |
| --- Log closed Fri May 27 00:00:20 2016 |