Implementing O(N) N-Body Algorithms Efficiently in Data-Parallel Languages

The optimization techniques for hierarchical O(N) N{body algorithms described here focus on managing the data distribution and the data references, both between the memories of diierent nodes, and within the memory hierarchy of each node. We show how the techniques can be expressed in data{parallel languages, such as High Performance Fortran (HPF) and Connection Machine Fortran (CMF). The eeectiveness of our techniques is demonstrated on an implementation of Anderson's hierarchical O(N) N{body method for the Connection Machine system CM{5/5E. Of the total execution time, communication accounts for about 10{20% of the total time, with the average eeciency for arithmetic operations being about 40% and the total eeciency (including communication) being about 35%. For the CM{5E, a performance in excess of 60 MMop/s per node (peak 160 MMop/s per node) has been measured.