TIMINGS ON THE SEP CONNECTION MACHINE

The 3-D PSPI and Split-step were implamented on the SEP Connection Machine. The SEP CM-2 has 8K serial bit processors, with 64 Kbytes of local memory in each processor. For every 32 serial bit processors there is a Floating Point Unit (FPU) responsible for all the arithmetic operation. The full machine has a total of 256 FPUs, which can be considered the processing nodes of the parallel computer. Both programs ran on the full 8K machine (256 FPU).

The PSPI kernel took 133 seconds to run on a 64x64x256 data model to produce a 64x64x64 depth migration model. The total CM-2 time was 238.4 seconds. The kernel time corresponds to a rate of 177.08 Mflop/s (Mflop = million floating point operations). The Split-step kernel, running on the same data set, takes 108.7 seconds corresponding to a 124.7 Mflop/s rate.

In comparison, on the Convex, the total run time for the PSPI algorithm is 7966.1 seconds single CPU time, or 2:12:46 (2 hours, 12 minutes and 46 seconds), which with a load average of 3 or 4 the normal load average at SEP during report time, translates into more than 6 hours of waiting for the results. The ratio between the total time on the Convex and the total time on the Connection Machine for the PSPI algorithm is around 33 to 1. The Split-step algorithm runs for 1877.1 seconds single CPU time on the Convex, or 31 minutes and 17 seconds. The ratio between the total time on the Convex and the total time on the Connection Machine for the Split-step algorithm is 14 to 1.

Theoretically, the run-time ratio between the PSPI algorithm and the Split-step algorithm should approach 1.5 as PSPI executes three Fourier transforms in the inner loop while Split-step executes only two. The run-time ratio on the Connection Machine approaches this theoretical limit ratio, while on the Convex I have a peculiar ratio of 4.25 between the PSPI and Split-step algorithms.