The Problem with the Linpack Benchmark 1.0 Matrix Generator

The Problem with the Linpack Benchmark 1.0 Matrix Generator
[v1] Thu Jun 12, 2008.
[v2] Thu Sep 18, 2008 (this version).
Jack Dongarra
Department of Electrical Engineering and Computer Science, University of Tennessee
Oak Ridge National Laboratory
University of Manchester
Julien Langou
Department of Mathematical and Statistical Sciences, University of Colorado Denver
Abstract:
We characterize the matrix sizes for which the Linpack Benchmark 1.0 matrix generator constructs
a matrix with identical columns.
1 Introduction
Since 1993, twice a year, a list of the sites operating the 500 most powerful computer systems is released by
the TOP500 project [10]. A single number is used to rank computer systems based on the results obtained
on the High Performance Linpack Benchmark (HPL Benchmark).
The HPL Benchmark consists of solving a dense linear system in double precision, 64–bit floating point
arithmetic, using Gaussian elimination with partial pivoting. The ground rules for running the benchmark
state that the supplied matrix generator, which uses a pseudo–random number generator, must be used in
running the HPL benchmark. The supplied matrix generator can be found in High Performance Linpack
1.0 (HPL–1.0) [9] which is an implementation of the HPL Benchmark. In a HPL benchmark program,
the correctness of the computed solution is established and the performance is reported in floating point
operations per sec (flops/sec). It is this number that is used to rank computer systems ...