[Long, probably not-beginners anymore] Parallel folds and folds as
arrows (was: Re: [Haskell-beginners] Re: When, if ever, does Haskell
"calculate once"?)
Maciej Piechotka
uzytkownik2 at gmail.com
Thu May 6 21:15:19 EDT 2010
On Thu, 2010-05-06 at 23:46 +0200, Daniel Fischer wrote:
> Share.share :: GHC.Types.Int
> GblId
> [Str: DmdType]
> Share.share =
> case GHC.List.$wlen @ GHC.Integer.Type.Integer Share.share_a 0
> of ww_amc { __DEFAULT ->
> GHC.Types.I# (GHC.Prim.+# ww_amc ww_amc)
> }
>
Hmm. What's the name of this form and how to get it?
>
> No.
>
> cFoldl' f g (b0,c0) xs0 = lgo b0 c0 xs0
> where
> lgo b c [] = (b,c)
> lgo !b !c (x:xs) = lgo (f b x) (g c x) xs
>
Ok. Fixed (I tried fast rewrite from foldr')
>
> 64-bit system? I get
>
64 bit, GHC 6.12.2.
% ghc -V
The Glorious Glasgow Haskell Compilation System, version 6.12.2
% file a.out
a.out: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dynamically
linked (uses shared libs), for GNU/Linux 2.6.9, not stripped
>
> And that is strange, because I get the same figures for that one as for the
> first (times differ by a few hundredths of a second).
Fixed or non-fixed version?
> Is that a difference between 32-bit code generator and 64-bit or between
> GHC versions (6.12.2 here, but 6.10.3 gives roughly the same results)?
>
Hmm. Compiler and platform matches. Unless you use some other 64-bit
platform - not x86-64 ;)
>
> > > main =
> > > print $! uncurry (+) (cFoldl' lengthFold lengthFold
> > > (0, 0) [1..size])
>
> And that gives the same figures as the other two (plus/minus 0.05s).
>
> >
> > All are compiled with optimizations.
>
> All compiled with -O2.
>
Hmm. Difference between -O1 and -O2
Fixed versions and with sum (and -O2):
> main = let a = [1..size]
> l = length a + sum a
> in print $! l
Lot's of memory(Over 3 GiB). I voluntarily killed process
> main = print $! length [1..size] + sum [1..size]
Lot's of memory(Over 3 GiB). I voluntarily killed process.
So far as being inplace.
> main = print $! uncurry (+) (cFoldl' lengthFold (+) (0, 0) [1..size])
5000000150000000
16,889,753,976 bytes allocated in the heap
3,356,480 bytes copied during GC
1,976 bytes maximum residency (1 sample(s))
28,200 bytes maximum slop
1 MB total memory in use (0 MB lost due to fragmentation)
Generation 0: 32216 collections, 0 parallel, 0.29s, 0.38s
elapsed
Generation 1: 1 collections, 0 parallel, 0.00s, 0.00s
elapsed
INIT time 0.00s ( 0.00s elapsed)
MUT time 14.89s ( 15.12s elapsed)
GC time 0.29s ( 0.38s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 15.18s ( 15.50s elapsed)
%GC time 1.9% (2.4% elapsed)
Alloc rate 1,134,094,110 bytes per MUT second
Productivity 98.1% of total user, 96.1% of total elapsed
./a.out +RTS -s 15.18s user 0.11s system 98% cpu 15.503 total
Lowered to size = 100000 (bigger causes stack overflow in first main):
> main = let a = [1..size]
> l = length a + sum a
> in print $! l
5000150000
22,045,352 bytes allocated in the heap
18,781,768 bytes copied during GC
6,316,904 bytes maximum residency (4 sample(s))
3,141,912 bytes maximum slop
17 MB total memory in use (0 MB lost due to fragmentation)
Generation 0: 23 collections, 0 parallel, 0.05s, 0.05s
elapsed
Generation 1: 4 collections, 0 parallel, 0.03s, 0.04s
elapsed
INIT time 0.00s ( 0.00s elapsed)
MUT time 0.02s ( 0.03s elapsed)
GC time 0.08s ( 0.09s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 0.10s ( 0.12s elapsed)
%GC time 78.4% (75.8% elapsed)
Alloc rate 1,002,334,818 bytes per MUT second
Productivity 20.6% of total user, 17.2% of total elapsed
./a.out +RTS -s 0.10s user 0.02s system 96% cpu 0.129 total
> main = print $! length [1..size] + sum [1..size]
5000150000
30,077,024 bytes allocated in the heap
17,482,888 bytes copied during GC
5,602,600 bytes maximum residency (4 sample(s))
3,144,312 bytes maximum slop
15 MB total memory in use (0 MB lost due to fragmentation)
Generation 0: 38 collections, 0 parallel, 0.04s, 0.05s
elapsed
Generation 1: 4 collections, 0 parallel, 0.03s, 0.03s
elapsed
INIT time 0.00s ( 0.00s elapsed)
MUT time 0.02s ( 0.03s elapsed)
GC time 0.07s ( 0.08s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 0.09s ( 0.11s elapsed)
%GC time 72.0% (70.0% elapsed)
Alloc rate 1,156,986,613 bytes per MUT second
Productivity 26.9% of total user, 22.9% of total elapsed
./a.out +RTS -s 0.09s user 0.02s system 97% cpu 0.116 total
> main = print $! uncurry (+) (cFoldl' lengthFold (+) (0, 0) [1..size])
5000150000
17,128,128 bytes allocated in the heap
10,608 bytes copied during GC
2,072 bytes maximum residency (1 sample(s))
28,024 bytes maximum slop
1 MB total memory in use (0 MB lost due to fragmentation)
Generation 0: 32 collections, 0 parallel, 0.00s, 0.00s
elapsed
Generation 1: 1 collections, 0 parallel, 0.00s, 0.00s
elapsed
INIT time 0.00s ( 0.00s elapsed)
MUT time 0.02s ( 0.02s elapsed)
GC time 0.00s ( 0.00s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 0.02s ( 0.02s elapsed)
%GC time 5.3% (3.9% elapsed)
Alloc rate 951,721,286 bytes per MUT second
Productivity 94.7% of total user, 90.2% of total elapsed
./a.out +RTS -s 0.02s user 0.00s system 96% cpu 0.024 total
It seems that the best, at least for large inputs.
-----------------------------------------------------------------------
On the other hand it seems to form an arrow[1].
First the result of test:
5000000150000000
12,800,063,440 bytes allocated in the heap
2,545,048 bytes copied during GC
1,968 bytes maximum residency (1 sample(s))
28,216 bytes maximum slop
1 MB total memory in use (0 MB lost due to fragmentation)
Generation 0: 24414 collections, 0 parallel, 0.24s, 0.29s
elapsed
Generation 1: 1 collections, 0 parallel, 0.00s, 0.00s
elapsed
INIT time 0.00s ( 0.00s elapsed)
MUT time 7.18s ( 7.35s elapsed)
GC time 0.24s ( 0.29s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 7.42s ( 7.64s elapsed)
%GC time 3.3% (3.8% elapsed)
Alloc rate 1,782,759,994 bytes per MUT second
Productivity 96.7% of total user, 93.9% of total elapsed
./a.out +RTS -s 7.42s user 0.09s system 98% cpu 7.648 total
(Yes - lower then the code above - result reproducable).
Code:
> {-# LANGUAGE BangPatterns #-}
> import Control.Arrow
> import Control.Category
> import Data.List
> import Prelude hiding (id, (.))
>
> newtype FoldlArrow a b c = FoldlArrow (a -> b -> c)
>
> instance Category (FoldlArrow a) where
> id = FoldlArrow $ \a !b -> b
> (FoldlArrow f) . (FoldlArrow g) =
> FoldlArrow $ \a !b -> let !c = g a b
> in f a c
>
> instance Arrow (FoldlArrow a) where
> arr f = FoldlArrow $ const f
> first (FoldlArrow f) = FoldlArrow $ \a (!b, !c) -> (f a b, c)
> second (FoldlArrow f) = FoldlArrow $ \a (!b, !c) -> (b, f a c)
> (FoldlArrow f) *** (FoldlArrow g) =
> FoldlArrow $ \a (!b, !c) -> (f a b, g a c)
> (FoldlArrow f) &&& (FoldlArrow g) =
> FoldlArrow $ \a !b -> (f a b, g a b)
>
> instance ArrowChoice (FoldlArrow a) where
> left (FoldlArrow f) = FoldlArrow left'
> where left' a (Left !l) = (Left $! f a l)
> left' a (Right !r) = (Right r)
> right (FoldlArrow f) = FoldlArrow right'
> where right' a (Left !l) = (Left l)
> right' a (Right !r) =
> (Right $! f a r)
> (FoldlArrow f) +++ (FoldlArrow g) =
> FoldlArrow choice
> where choice a (Left !l) = (Left $! f a l)
> choice a (Right !r) = (Right $! g a r)
> (FoldlArrow f) ||| (FoldlArrow g) =
> FoldlArrow choice
> where choice a (Left !l) = f a l
> choice a (Right !r) = g a r
>
> instance ArrowApply (FoldlArrow a) where
> app = FoldlArrow $ \a (FoldlArrow !f, !b) -> f a b
>
> doFoldl :: FoldlArrow a b b -> b -> [a] -> b
> doFoldl (FoldlArrow f) = foldl' (flip f)
>
> element :: FoldlArrow a b a
> element = FoldlArrow const
>
> lengthA :: FoldlArrow a Int Int
> lengthA = arr (+1)
>
> sumA :: Num a => FoldlArrow a a a
> sumA = arr (uncurry (+)) . (element &&& id)
>
> size = 100000000
>
> main =
> print $! uncurry (+) $ doFoldl (lengthA *** sumA) (0, 0) [1..size]
On the other hand if I use arrow syntax:
> myArr :: Num a => FoldlArrow a (a, a) (a, a)
> myArr = proc (l, s) -> do e <- element -< ()
> returnA -< (l + 1, s + e)
It starts consuming memory as well. Somewhere is lazy passing of value
but I cannot find where
Regards
PS. As it is probably out of scope and topic of beginners mailing list
I'm CC'ing cafe (possibly beginners should be dropped).
[1] It can be extended to work on other arrows as well - not only (->).
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