efficient parallel foldMap for lists/sequences

[Sebastian Fischer]

Hello Parallel Haskellers,

(x-post from haskell-cafe)

in parallel programs it is a common pattern to accumulate a list of

results in parallel using an associative operator. This can be seen as

a simple form of the map-reduce pattern where each element of the list

is mapped into a monoid before combining the results using `mconcat`.

This pattern can be abstracted by the `foldMap` function of the

`Foldable` class and we can give a simple parallel implementation

using `par` and `pseq`:

~~~

import Data.Monoid

import Control.Parallel

foldMap :: Monoid m => (a -> m) -> [a] -> m

foldMap f []  = mempty

foldMap f [x] = f x

foldMap f xs  =

 let (ys,zs) = splitAt (length xs `div` 2) xs

     ys'     = foldMap f ys

     zs'     = foldMap f zs

  in zs' `par` (ys' `pseq` (ys' `mappend` zs'))

~~~

How can this pattern be implemented in Haskell efficiently?

I plan to investigate the following options and am interested in previous work.

1. Data.Sequence (from containers)

As finger trees are already balanced they look like a good candidate

for parallel consumption. However, the current implementation of the

`Foldable` instance is sequential. I wonder what would be the overhead

and how it could be reduced if it is is too large. I think, I would

first go for an implementation outside of `Foldable` and later

consider the overhead of overloading.

2. Data.Array.Repa (from repa)

provides a `map` and (sequential) `fold` functions. I think that the

main advantage of repa is fusion of successive traversals which is not

necessary for the pattern in question. Hence, I'm not sure whether

it's a good candidate for the job. Also I don't know how to implement

the pattern using repa. Can it be done using `slice` or should it be

done by changing repa itself?

3. Data.Monoid.Reducer (from monoids)

`foldMapReduce` looks promising. I wonder whether it could be used for

parallel reduction and how efficient it would be.

Which approach do you think is most promising? What other options are there?

Best,

Sebastian

[Johannes Waldmann]

Sebastian Fischer <federigo.pescatore@...> writes:

> foldMap :: Monoid m => (a -> m) -> [a] -> m
> foldMap f []  = mempty
> foldMap f [x] = f x
> foldMap f xs  =
>  let (ys,zs) = splitAt (length xs `div` 2) xs
>      ys'     = foldMap f ys
>      zs'     = foldMap f zs
>   in zs' `par` (ys' `pseq` (ys' `mappend` zs'))
> ~~~
>
> How can this pattern be implemented in Haskell efficiently?

0. use actual lists: does not really work: length and splitAt are expensive.
(Note: it does work, sort of, in cases like mergesort,
when you foldMap the "sort" part only. It seems the overhead
is small compared to the work that "merge" does.)

> 1. Data.Sequence (from containers)
> As finger trees are already balanced they look like a good candidate
> for parallel consumption. However, the current implementation of the
> `Foldable` instance is sequential.

Indeed. But you have Data.Sequence.splitAt (in log time),
so you can take the above code. When I tried this, I found the problem
is elsewhere: You generally want to avoid splitting and sparking (par)
deep down the tree (once you exhausted the actual number
of capabilities (= cores)). Then you want to use a sequential fold -
and I found Data.Sequence.foldl (rather, the Foldable instance)
quite expensive. You could instead use toList, but that's expensive as
well (should it be?)

So what I'm using now is Data.Vector(.Unboxed), and this looks good.
But cf. http://article.gmane.org/gmane.comp.lang.haskell.cafe/90211

[Christopher Brown]

Hi Johannes

foldMap :: Monoid m => (a -> m) -> [a] -> m

foldMap f []  = mempty

foldMap f [x] = f x

foldMap f xs  =

 let (ys,zs) = splitAt (length xs `div` 2) xs

     ys'     = foldMap f ys

     zs'     = foldMap f zs

  in zs' `par` (ys' `pseq` (ys' `mappend` zs'))

~~~

How can this pattern be implemented in Haskell efficiently?

This looks like a classic divide & conquer pattern to me. What you need to do is

to 

a) only spark of computations when the granularity is high enough to make it worth while

b) only spark of computations that are evaluated to normal forms. Otherwise, Haskell will only apply WHNF evaluation to the lists, which won't be very useful for parallelisation

I would use a version using the new strategies:

foldMap :: Monoid m => (a -> m) -> [a] -> m

foldMap f []  = mempty

foldMap f [x] = f x

foldMap f xs  =

 let (ys,zs) = splitAt (length xs `div` 2) xs

     ys'     = foldMap f ys

     zs'     = foldMap f zs

           (ys'', zs'') = runEval $ do ys'' <- ((rabs ys) `dot` rdeepseq) ys'

                                                       zs'' <- ((rabs zs) `dot` rdeepseq) zs'

               return (ys'', zs'')

           rabs xs | length xs > THRESHOLD = rpar

                         | otherwise                             = rseq

           in ys'' `mappend` zs''

You will have to define THRESHOLD to be a value that gives you good granularity: you may need to experiment with this.

I hope this gives you some insight. 

Kind regards,

Chris

----------

Dr Chris Brown, Postdoctoral Research Fellow, School of Computer Science, University of St Andrews

T: +44 1334 461633  F: +44 1334 463278  W: http://www.cs.st-andrews.ac.uk/~chrisb

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[Johannes Waldmann]

> a) only spark of computations when the granularity is high enough to make it
worth while
> b) only spark of computations that are evaluated to normal forms.

sure, that's what I do:

http://www.imn.htwk-leipzig.de/~waldmann/ss11/skpp/code/kw24/mps-vector.hs

I tried this with Data.List, and Data.Sequence,
but Data.Vector.Unboxed really makes it fly.

I found this post very helpful:
http://article.gmane.org/gmane.comp.lang.haskell.cafe/90211

[Sebastian Fischer]

Hi Johannes and Chris,

thanks! The version with unboxed vectors looks like a good baseline to
benchmarks other solutions.

>> a) only spark of computations when the granularity is high enough to make it
> worth while
>> b) only spark of computations that are evaluated to normal forms.
>
> sure, that's what I do:

Not exactly. Your code sparks of computations as long as there are
capabilities. You will use two sparks for a vector of length two.

The threshold approach can create more sparks than there are
capabilities which is good if the amount of work for each spark
fluctuates and unnecessary if all sparks require the same amount of
work. It creates less sparks for small inputs but that may be
negligible as small inputs can be processed fast anyway..

Sebastian