Conclusions and the future

  We have demonstrated that disk can be used for dynamic storage in an ``out-of-core'' implementation of an astrophysical treecode. An 80 million body model can run on a cluster of 16 PC-class systems. Simulating such a model over the age of the Universe will take a couple of months, but one should recall that the computer is extremely economical, costing under $60000. One can use cost-effective processors, modest amounts of DRAM, and much larger amounts of disk to address N-body problems that had heretofore been accessible only on the largest of parallel supercomputers. On the other hand, one can now imagine integrating extraordinarily large systems (billions of particles) on large MPPs with independently addressable disks.

Finally, we observe that memory hierarchies are getting deeper, with the gap between processor clock rates and memory latency continuing to widen. Out-of-core methods are designed to tolerate the extreme latencies of disk systems, but they may also be adapted to make effective use of caches and memory hierarchies in more traditional systems. Some approaches to the next generation of ``petaflop'' computers [5] will display latencies (measured in clocks ticks) as large as those we observe today in disk systems, so we might expect that optimal algorithms on those systems will be closely related to the out-of-core algorithms of today.