code logs -> 2011 -> Tue, 01 Feb 2011< code.20110131.log - code.20110202.log >
--- 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. :)
22:17 Kindamoody|noms is now known as Kindamoody
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
code logs -> 2011 -> Tue, 01 Feb 2011< code.20110131.log - code.20110202.log >