--- Log opened Tue Feb 01 00:00:12 2011 |
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14:24 | <@TheWatcher> | Well fuck |
14:24 | < gnolam> | ? |
14:25 | <@TheWatcher> | With "use utf8;": BEGIN not safe after errors--compilation aborted at /usr/lib/perl5/5.12.2/Carp.pm line 113. With "use ut8;" commented out, it gets as far as reporting some unrelated errors |
14:25 | <@TheWatcher> | from some digging it appears that use utf8 has some Very Interesting and completely broken interactions with Carp under perl 5.12.x |
14:38 | | * Rhamphoryncus lights it on fire |
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18:59 | < gnolam> | http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-30 8/ |
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20:47 | <@ToxicFrog> | How do I start tackling the equation n/ln(n) == k, for known k? |
20:47 | <@ToxicFrog> | I mean, I have a program that will solve it with binary search, but that seems...crude. |
20:52 | <@jerith> | Iteratively, start with n=k*ln(k) or somesuch? |
20:52 | <@jerith> | Hrm. n = k*ln(n) |
20:53 | | * jerith tries to remember exponentials. |
21:06 | < RichardBarrell> | Is there any good way to find n-ln(n) = k, for some k? |
21:11 | <@jerith> | n**(1/n) = e**(1/k) fwiw |
21:12 | <@jerith> | But I'm just playing with identities. Matbe ask in #math. |
21:12 | <@jerith> | *Maybe |
21:13 | < RichardBarrell> | I am scared by the notion that perhaps that most actual numerical work is either iterative, or the first four of five terms of a Taylor expansion. |
21:14 | <@jerith> | Iterative algorithms are usually the easy way to solve numerical problems. |
21:15 | <@jerith> | They're certainly what we did the most of in my various engineering classes. |
21:16 | <@jerith> | In fact, the "Numerical Methods" course was pretty much all iterative with a little bit of background analysis to show where some of the good starting points are. |
21:35 | < RichardBarrell> | Newton-Rhapson works just fine for this. |
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21:56 | < RichardBarrell> | ToxicFrog: If you'll pardon my Haskell: newtonRhapson f f' x iterations = if iterations == 0 then x else newtonRhapson f f' (x - (f x / f' x)) (n-1) |
21:56 | | Kindamoody|out is now known as Kindamoody|noms |
21:57 | < gnolam> | RichardBarrell: Raphson. :) |
21:57 | < RichardBarrell> | gnolam: thanks, but I'm going to continue with my spelling error because I defined it earlier |
21:57 | < RichardBarrell> | ;D |
22:00 | < RichardBarrell> | ToxicFrog: froxicTog k = newtonRhapson (\n -> (n / log n) - k) (\n -> (log n - 1) / (log n * log n)) k 5 -- ((\n -> (n / log n)) . froxicTox) is a close approximation to "id :: Double -> Double". |
22:00 | <@TheWatcher> | Sounds like a particularly geeky norwegian singer's name... |
22:01 | < RichardBarrell> | gnolam: thank you, by the way. x_x |
22:05 | | * Vornicus really likes the iterative method for logarithm. |
22:05 | < Vornicus> | (which is Emphatically Not taylor series.) |
22:06 | < RichardBarrell> | There's another method which I think is probably faster. |
22:07 | < Vornicus> | "probably faster" he says. Let me tell you: the 10,000th iteration of the taylor series for the logarithm has a denominator of 10,000. |
22:07 | < RichardBarrell> | Using the newtonRaphson above, but: groxicTog k = let lk = log k in exp $ nr (\a -> a - log a - lk) (\a -> 1 - (1/a)) lk 5 |
22:08 | < RichardBarrell> | Vornicus: I meant faster than the "froxicTog" monstrosity that I posted above, which required taking a logarithm twice on every iteration. |
22:10 | < Vornicus> | oh, oh. |
22:10 | < Vornicus> | Oh, oh, you're solving n/ln(n) = k, I see. |
22:10 | < RichardBarrell> | There's a real damn fast way of doing logarithms, too. I call it a "one-element-LUT". Precision is a bit of a bummer, though. ;) |
22:12 | < RichardBarrell> | Vornicus: yeah, that was the puzzle that TF posted earlier. I scribbled on paper for a few minutes but couldn't find a non-iterative solution, so I resorted to Newton-Raphson. |
22:14 | < RichardBarrell> | ToxicFrog: http://pastebin.starforge.co.uk/451 if you want something actually readable. :) |
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22:18 | < RichardBarrell> | groxicTog's about twice as fast under GHC 6.12.1 with -O2. Yay. |
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--- Log closed Wed Feb 02 00:00:13 2011 |