Efficient complex matrix multiplication on the Synergistic Processing Element of the Cell processor

In order to implement a complete Fast Multipole Method on the Cell processor, we need an efficient complex matrix multiplication on each Synergistic Processing Element (SPE) of the Cell processor. Since the last IBM SDK does not provide such routine, we build our own one in single precision with C programming. We show that the complex matrix multiplication requires a specific computation scheme for the micro-kernel running on the SPE, and that a 32×32 tile is appropriate for close to peak performance computation as well as for communication overlapping. Our micro-kernel delivers 23.74 Gflop/s, which is 92.7% of the SPE peak performance, and we obtain up to 23.65 Gflop/s for one complete complex matrix product on one SPE, and up to 378.36 Gflop/s for 16 products on 16 SPEs.