Implementing O(n) N{body Algorithms Eeciently in Data Parallel Languages (high Performance Fortran) Implementing O(n) N{body Algorithms Eeciently in Data Parallel Languages (high Performance Fortran)

O(N) algorithms for N{body simulations enable the simulation of particle systems with up to 100 million particles on current Massively Parallel Processors (MPPs). Our optimization techniques mainly focus on minimizing the data movement through careful management of 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 languages with an array syntax, such as Connection Machine Fortran (CMF). All CMF constructs used, with one exception, are included in High Performance Fortran. 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.