Re: [Haskell-cafe] Another optimization question

18 May 2008


      Am Sonntag, 18. Mai 2008 14:50 schrieb anton muhin:
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On Sun, May 18, 2008 at 2:00 AM, Daniel Fischer
 wrote:
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Am Samstag, 17. Mai 2008 22:48 schrieb anton muhin:
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Why not -O3?
As far as I know - and Brandon S.Allbery said so, too - -O3 isn't better
than -O2.
I didn't know that, sorry.
No need to apologise. It was a perfectly reasonable question. Fortunately, 
Brandon just a few minutes before confirmed that my recollection was probably 
correct, otherwise I would've added "must check that, though".
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Using a real list of primes,
What's the size of the real list?
arbitrary, however, since it's [Int], it will actually be at most
105097565 primes long, but since only numbers up to 5000 are checked,
only 670 primes will ever be considered - When I check numbers 1 to 50000
(5133 primes, so 5134 primes evaluated),
So it's just a relatively sparsed sorted list of 5134 numbers and the
greatest of them still fits into Int, correct?
Technically, I think, it's a partially evaluated list with a thunk at the end 
that says how to get more when needed. But at the end, it's basically a list 
of 5134 Ints.
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with -O0 / -O2, it's
Jeroen 1 : 14.5 s / 2.4 s
Jeroen 2 : 52.5 s / 49.7 s
probably Jeroen's hypothesis about temporary list built might explain
that slowdown, what do you think?
Probably, but I'm a bit surprised how much that building of lists costs.
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(== x) . head . dropWhile (< x) : 8.2 s /4.1 s
go primes : 5.5 s / 2.5 s
So Jeroen 1 is the best to be optimised :)
:)
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but another
implementation of isPrime:
isPrime x = (== x) $ head $ dropWhile (< x) primes
With -O2, this is about 20% slower than the Jeroen's first version,
without optimisations 50% faster.
Strange.
Well, head has its overhead as well.  Cf. two variants:
firstNotLess :: Int -> [Int] -> Int
firstNotLess s (x:xs) = if x < s then firstNotLess s xs else x
dropLess :: Int -> [Int] -> [Int]
dropLess s l@(x:xs) = if x < s then dropLess s xs else l
isPrime :: Int -> Bool
isPrime x = x == (firstNotLess x primes)
isPrime' :: Int -> Bool
isPrime' x = x == (head $ dropLess x primes)
On my box firstNotLess gives numbers pretty close (if not better) than
for primes up to 50000, that's
6.8 s / 2.1 s with -O0 / -O2 respectively on mine
So it seems to be reproducible.
Yes, though with -O0 there's a big difference.
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Jeroen's first variant, while head $ dropLess notably worse.
5.8 s / 2.4 s here.
So that doesn't perform notably worse than Jeroen's first variant on my box
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isPrime :: Int -> Bool
isPrime x = go primes
     where
       go (p:ps) = case compare x p of
                       LT -> False
                       EQ -> True
                       GT -> go ps
does best (on my box), with and without optimisations (very very
slightly with -O2) for a list of real primes, but not for [1 .. ].
And what happens for [1..]?
With -O2, Jeroen 1 was best (1.62), nex firstNotLess (1.63), head .
dropLesst (1.74), then in close succesion Jeroen 2 (1.92), go primes
(1.96) and head . dropWhile (1.99),
go primes ran 1.96?  Indeed weird, does anybody know if it's due to
pattern matching?
I also tried a version with
go (p:ps)
	| p < x     = go ps
	| otherwise = p == x
that did worse (not much).
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with -O0, it's
head . dropWhile (1.7 s, YES, that actually is faster with -O0 than with
-O2!), head . dropLess (2.0), Jeroen 2 and firstNotLess (2.1 s), go
primes (2.3 s), Jeroen 1 (3.2 s).
Weirder and weirder.
agree
yours,
anton
Cheers,
Daniel