The Problem with the Linpack Benchmark Matrix Generator

The Problem with the Linpack Benchmark Matrix Generator
June 28, 2008
Jack Dongarra
Department of Electrical Engineering and Computer Science, University of Tennessee
Oak Ridge National Laboatory
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 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 [3]. A single number is used to rank computer systems based on the results obtained on
the High Performance Linpack (HPL) Benchmark.
The High Performance Computing Linpack 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 HPL [2] which is an implementation of the High Performance Computing Linpack Benchmark.
In the 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 across the world in the TOP500 list ...