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In order to validate our formulas for comparing speedup on different
architectures, we have used empirical performance data from
section 7.1 and developed performance comparisons for
complex variate LU factorization on the SP1 and SP2. We have extended
the number of processors beyond the number actually utilized to
collect the empirical data from the SPP architectures. Our
implementations on the SP1 and SP2 used the Message Passing Interface
(MPI), because it is being developed as a communications standard for
multi-processors with strong emphasis on optimizing message-passing
performance. The IBM SP2 has a 30
second latency and 30
megabyte-per-second bandwidth in present configurations [16].
In figure
, we present actual and predicted
speedup values for the complex LU factorization algorithm with the
EPRI6K power systems network for
- empirical speedup data from the CM-5 implementation using buffered communications,
- empirical speedup data from the SP1 implementation using MPI,
- empirical speedup data from the SP2 implementation using MPI,
- predicted speedup for the SP1 (
processor speedup),
- predicted speedup for the SP2 (
processor speedup),
In this figure, we plot predicted values for both the SP1 and the SP2,
where the single processor performance of the SP1 is 6.6 times the
single processor performance of the Thinking Machines CM-5 and the SP2
is 50% faster than the SP1. When comparing the actual data to the
predicted data, it may be possible that this simplistic technique has
some difficulties in vertical displacement. While the slope of the
curve splines for the predicted data and the curve splines for the
empirical data are similar for the SP2, the predicted curve appears to
underestimate the speedup by a nearly constant amount. These
predictions have been made using a very simple model, and should only
be interpreted as in indication of possible future performance.
Better estimates are possible by carefully simulating the algorithms
using models with more variables and greater detail.
Figure: Performance Validation for Parallel Complex LU Factorization
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David P. Koester
Sun Oct 22 17:27:14 EDT 1995