All-To-All Broadcast and Applications On the Connection Machine

An all{to{all broadcast algorithm that exploits concurrent communication on all channels of the Connection Machine system CM{200 binary cube network is described. Issues in integrating a physical all{to{all broadcast between processing nodes into a language environment using a global address space is dicussed. Timings for the physical broadcast between nodes, and the virtual broadcast are given for the Connection Machine system CM{200. The peak data transfer rate for the physical broadcast on a CM{200 is 5.9 Gbytes/sec, and the peak rate for the virtual broadcast is 31 Gbytes/sec. Array reshaping is an eeective performance optimization technique. An example is given where reshaping improved performance by a factor of seven by reducing the amount of local data motion. We also show how to exploit symmetry for computation of an interaction matrix using the all{to{all broadcast function. Further optimizations are suggested for N-body type calculations. Using the all{to{all broadcast function, a peak rate of 9.3 GGops/s has been achieved for the N-body computations in 32-bit precision on a 2,048 node Connection Machine system CM{200.