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

Abstract

An all-to-all broadcast algorithm that exploits concur rent communication on all channels of the Connection Machine system CM-200 binary cube network is de scribed. Issues in integrating a physical all-to-all broad cast between processing nodes into a language envi ronment using a global address space are discussed. Timings for the physical broadcast between nodes and for the virtual broadcast are given. The peak data transfer rate for the physical broadcast on a CM-200 is 5.9 gigabytes/sec, and the peak rate for the virtual broadcast is 31 gigabytes/sec. Array reshaping is an effective performance optimization technique. An ex ample is given where reshaping improved perfor mance by a factor of 7 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 GFLOPS/ sec has been achieved for the N-body computations in 32-bit precision on a 2,048 node Connection Machine system CM-200.