Re: [Haskell-cafe] Naive matrix multiplication with Accelerate

3 Dec 2012

      Hi Clark,

The trick is that most accelerate operations work over multidimensional arrays, so you can still get around the fact that we are limited to flat data-parallelism only.

Here is matrix multiplication in Accelerate, lifted from the first Repa paper [1].

import Data.Array.Accelerate as A

type Matrix a = Array DIM2 a

matMul :: (IsNum e, Elt e) => Acc (Matrix e) -> Acc (Matrix e) -> Acc (Matrix e)
matMul arr brr
  = A.fold (+) 0
  $ A.zipWith (*) arrRepl brrRepl
  where
    Z :. rowsA :. _     = unlift (shape arr)    :: Z :. Exp Int :. Exp Int
    Z :. _     :. colsB = unlift (shape brr)    :: Z :. Exp Int :. Exp Int

    arrRepl             = A.replicate (lift $ Z :. All   :. colsB :. All) arr
    brrRepl             = A.replicate (lift $ Z :. rowsA :. All   :. All) (A.transpose brr)

If you use github sources rather than the hackage package, those intermediate replicates will get fused away.

Cheers,
-Trev

 [1] http://www.cse.unsw.edu.au/~chak/papers/KCLPL10.html

On 03/12/2012, at 5:07 PM, Clark Gaebel  wrote:
...
Hello cafe,
I've recently started learning about cuda and hetrogenous programming, and have been using accelerate [1] to help me out. Right now, I'm running into trouble in that I can't call parallel code from sequential code. Turns out GPUs aren't exactly like Repa =P.
Here's what I have so far:
import qualified Data.Array.Accelerate as A
import Data.Array.Accelerate ( (:.)(..)
                             , Acc
                             , Vector
                             , Scalar
                             , Elt
                             , fold
                             , slice
                             , constant
                             , Array
                             , Z(..), DIM1, DIM2
                             , fromList
                             , All(..)
                             , generate
                             , lift, unlift
                             , shape
                             )
import Data.Array.Accelerate.Interpreter ( run )
dotP :: (Num a, Elt a) => Acc (Vector a) -> Acc (Vector a) -> Acc (Scalar a)
dotP xs ys = fold (+) 0 $ A.zipWith (*) xs ys
type Matrix a = Array DIM2 a
getRow :: Elt a => Int -> Acc (Matrix a) -> Acc (Vector a)
getRow n mat = slice mat . constant $ Z :. n :. All
-- Naive matrix multiplication:
--
-- index (i, j) is equal to the ith row of 'a' `dot` the jth row of 'b'
matMul :: A.Acc (Matrix Double) -> A.Acc (Matrix Double) -> A.Acc (Matrix Double)
matMul a b' = A.generate (constant $ Z :. nrows :. ncols) $
                \ix ->
                  let (Z :. i :. j) = unlift ix
                   in getRow i a `dotP` getRow j b
    where
        b = A.transpose b' -- I assume row indexing is faster than column indexing...
        (Z :. nrows :.   _  ) = unlift $ shape a
        (Z :.   _   :. ncols) = unlift $ shape b
This, of course, gives me errors right now because I'm calling getRow and dotP from within the generation function, which expects Exp[ression]s, not Acc[elerated computation]s.
So maybe I need to replace that line with an inner for loop? Is there an easy way to do that with Accelerate?
Thanks for your help,
  - Clark
[1] http://hackage.haskell.org/package/accelerate
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe

Re: [Haskell-cafe] Naive matrix multiplication with Accelerate

Trevor L. McDonell