Don Stewart dons at galois.com
Tue May 13 16:26:07 EDT 2008

```dons:
> jeff.polakow:
> >    Hello,
> >
> >    > For example, the natural and naive way to write Andrew's "mean" function
> >    > doesn't involve tuples at all: simply tail recurse with two accumulator
> >    > parameters, and compute the mean at the end.  GHC's strictness analyser
> >    > does the right thing with this, so there's no need for seq, \$!, or the
> >    > like.  It's about 3 lines of code.
> >    >
> >    Is this the code you mean?
> >
> >        meanNat = go 0 0 where
> >            go s n [] = s / n
> >            go s n (x:xs) = go (s+x) (n+1) xs
> >    If so, bang patterns are still required bang patterns in ghc-6.8.2 to run
> >    in constant memory:
> >
> >        meanNat = go 0 0 where
> >            go s n [] = s / n
> >            go !s !n (x:xs) = go (s+x) (n+1) xs
> >
> >    Is there some other way to write it so that ghc will essentially insert
> >    the bangs for me?
>
> Yes, give a type annotation, constraining 'n' to Int.
>
>     meanNat :: [Double] -> Double
>     meanNat = go 0 0
>       where
>        go :: Double -> Int -> [Double] -> Double
>        go s n []     = s / fromIntegral n
>        go s n (x:xs) = go (s+x) (n+1) xs
>
> And you get this loop:
>
>     M.\$wgo :: Double#
>               -> Int#
>               -> [Double]
>               -> Double#
>
>     M.\$wgo =
>       \ (ww_smN :: Double#)
>         (ww1_smR :: Int#)
>         (w_smT :: [Double]) ->
>         case w_smT of wild_B1 {
>           [] -> /## ww_smN (int2Double# ww1_smR);
>           : x_a9k xs_a9l ->
>             case x_a9k of wild1_am7 { D# y_am9 ->
>             M.\$wgo (+## ww_smN y_am9) (+# ww1_smR 1) xs_a9l
>             }
>         }
>

Note this is pretty much identical to the code you get with a foldl' (though
without the unboxed pair return):

import Data.List
import Text.Printf
import Data.Array.Vector

mean :: [Double] -> Double
mean arr = b / fromIntegral a
where
k (n :*: s) a = (n+1 :*: s+a)
(a :*: b) = foldl' k (0 :*: 0) arr :: (Int :*: Double)

main = printf "%f\n" . mean \$ [1 .. 1e9]

Note I'm using strict pairs for the accumulator, instead of banging lazy
pairs.

\$s\$wlgo :: [Double]
-> Double#
-> Int#
-> (# Int, Double #)

\$s\$wlgo =
\ (xs1_aMQ :: [Double])
(sc_sYK :: Double#)
(sc1_sYL :: Int#) ->
case xs1_aMQ of wild_aML {
[] -> (# I# sc1_sYL, D# sc_sYK #);
: x_aMP xs11_XMX ->
case x_aMP of wild1_aOg { D# y_aOi ->
\$s\$wlgo xs11_XMX (+## sc_sYK y_aOi) (+# sc1_sYL 1)
}
}

-- Don
```