[Haskell-cafe] Lists concatenation being O(n)
Daniel Fischer
daniel.is.fischer at googlemail.com
Fri Oct 14 17:47:11 CEST 2011
On Friday 14 October 2011, 16:55:14, Bas van Dijk wrote:
> On 13 October 2011 20:53, Albert Y. C. Lai <trebla at vex.net> wrote:
> > The number of new cons cells created in due course is Θ(length xs).
>
> I was actually surprised by this because I expected: length(xs++ys) to
> fuse into one efficient loop which doesn't create cons cells at all.
>
> Unfortunately, I was mistaken since length is defined recursively.
>
> length :: [a] -> Int
> length l = len l 0#
> where
> len :: [a] -> Int# -> Int
> len [] a# = I# a#
> len (_:xs) a# = len xs (a# +# 1#)
>
> However, if we would define it as:
>
> length = foldl' (l _ -> l+1) 0
>
> And implemented foldl' using foldr as described here:
>
> http://www.haskell.org/pipermail/libraries/2011-October/016895.html
>
> then fuse = length(xs++ys) where for example xs = replicate 1000000 1
> and ys = replicate 5000 (1::Int) would compile to the following
> totally fused core:
>
> fuse :: Int
> fuse = case $wxs 1000000 0 of ww_srS {
> __DEFAULT -> I# ww_srS
> }
>
> $wxs :: Int# -> Int# -> Int#
> $wxs = \ (w_srL :: Int#) (ww_srO :: Int#) ->
> case <=# w_srL 1 of _ {
> False -> $wxs (-# w_srL 1) (+# ww_srO 1);
> True -> $wxs1_rs8 5000 (+# ww_srO 1)
> }
>
> $wxs1_rs8 :: Int# -> Int# -> Int#
> $wxs1_rs8 =
> \ (w_srA :: Int#) (ww_srD :: Int#) ->
> case <=# w_srA 1 of _ {
> False -> $wxs1_rs8 (-# w_srA 1) (+# ww_srD 1);
> True -> +# ww_srD 1
> }
Yes, that's wonderful, but it's not so wonderful for types more complicated
than Int.
Integer is evil enough: With
fuse = length ([1 .. 50000000] ++ [0 .. 60000000])
Prelude Fuse> fuse
Heap exhausted;
Current maximum heap size is 1258291200 bytes (1200 MB);
use `+RTS -M<size>' to increase it.
The current length has no problems:
Prelude> length ([1 .. 50000000] ++ [0 .. 60000000])
110000001
(2.55 secs, 11609850632 bytes)
Before foldl('), sum, length can be implemented in terms of foldr to get
fusion, a lot has to be done still.
Currently you'd get an improvement in some cases for a catastrophic
behaviour in many others.
Cheers,
Daniel
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