A note on scaling the Linpack benchmark

Abstract

Dimensional analysis yields a new scaling formula for the Linpack benchmark. The computational power r ( p 0 , q 0 ) on a set of processors decomposed into a ( p 0 , q 0 ) grid determines the computational power r ( p , q ) on a set of processors decomposed into a ( p , q ) grid by the formula r ( p , q ) = ( p / p 0 ) α ( q / q 0 ) β r ( p 0 , q 0 ) . The two scaling parameters α and β measure interprocessor communication overhead required by the algorithm. A machine that scales perfectly corresponds to α = β = 1 ; a machine that scales not at all corresponds to α = β = 0 . We have determined the two scaling parameters by imposing a fixed-time constraint on the problem size such that the execution time remains constant as the number of processors changes. Results for a collection of machines confirm that the formula suggested by dimensional analysis is correct. Machines with the same values for these parameters are self-similar. They scale the same way even though the details of their specific hardware and software may be quite different.