Z. Hu, H. Iwasaki, and M. Takeichi, "An Accumulative Parallel Skeleton for All", In Proceedings of the 11th European Symposium on Programming, Grenoble, France, April 2002, pages 83--97.  Home/Search   Document Details and Download   Summary   Related Articles   Check

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Z. Hu, H. Iwasaki, and M. Takeichi, "An Accumulative Parallel Skeleton for All", In Proceedings of the 11th European Symposium on Programming, Grenoble, France, April 2002, pages 83--97.

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Hu, Z., Iwasaki, H., Takeichi, M.: An accumulative parallel skeleton for all. In: 11st European Symposium on Programming (ESOP 2002), Grenoble, France, Springer Verlag, LNCS 2305 (2002) 83--97

....(q x) z = x# y in (# (p z) g e # ) Therefore, recursive function accumulate abstracts a good combination of parallel primitives. On one hand, recursive functions defined in the form of accumulate can be decomposed into the form using skeletons. On the other hand, as discussed in [HIT02] compositions of primitive skeletons can be fused into accumulate. B.2 Segmented Di#usion Theorem Our theorem concerning nested skeletons states that mapping the function accumulate to every sublist can be turned into a form applying another accumulate to the flattened representation of the ....

....programs eliminating this nesting. F(f#) let f # = fusion(f) in if f # is not an accumulate then f# else let acc # = segmened di#usion(f # g = di#usion(acc # ) in g The algorithm can be read as follows. Given the program f#, first tries to apply the fusion transformation [HIT02] GWL99] to merge compositions of skeletons into a single one. If this fusion fails, then the result f # will not be in the form of accumulate, and will not change the program and returns the initial one as result. Otherwise, it applies the segmented di#usion theorem to flatten f # into ....

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Z. Hu, H. Iwasaki, and M. Takeichi. An accumulative parallel skeleton for all. In 11th European Symposium on Programming (ESOP 2002), pages 83--97, Grenoble, France, April 2002. Springer Verlag, LNCS 2305.

....e) e] id; 2 Note that in the above theorem, is used to represent a don t care value with consistent type. Powerful and general, accumulate can be used to solve many problems in a rather straightforward way, that is not more dicult than solving the problems in sequential setting [HIT01]. Consider a simple example computing a polynomial value, a case study in [SG99] and an exercise in [Ble90] poly [a 1 ; a 2 ; aN ] x = a 1 x a 1 x 2 aN x N : It can be easily de ned by the following recursive de nition with an accumulating parameter storing x i ....

.... e ) 4) f ) e ) g ) 5) 1 = e1 ) 2 = e2 ) Recall the lines of sight problem in Section 3 where we obtain the following compositional program for Pass 2 (b) after expansion of ass and as: mas = maximum= angle ps) We can fuse it into a single one [HIT01]. 6 Dealing with Nested Skeletons Our new skeleton accumulate can deal with nested data structures very well, especially irregular ones whose elements may have quite di erent sizes. To be concrete, given a list of lists, we are considering ecient implementation of a computation which maps some ....

Z. Hu, H. Iwasaki, and M. Takeichi. An accumulative parallel skeleton for all. Technical Report METR 01-05, University of Tokyo, September 2001. Available from http://www.ipl.t.u-tokyo.ac.jp/ ~ hu/pub/metr01-05.ps.gz.

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Z. Hu, H. Iwasaki, and M. Takeichi. Caculating accumulations. New Generation Computing, 17(2):153-173, 1999. An Accumulative Parallel Skeleton for All 17

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