summa

This repository benchmarks the performance of the Scalable Universal Matrix Multiplication Algorithm, or SUMMA (R van de Geijn & J Watts, 1995). It builds on my earlier benchmarks for collective communication operations, which may be found here (repository, report).

This repository forms part of my final project for my master's degree at the University of Oklahoma. The report may be found here.

The implementation of SUMMA itself is the same for each benchmark (see summa.c), but differs in the implementation of the broadcast collective operation that SUMMA uses.

void summa(...)
{
    for (each block within my row/column of processors)
    {
        BROADCAST(ith block of A within my row of processors)
        BROADCAST(ith block of B within my column of processors)
        my block of C += MATRIX_MULTIPLY(ith block of A and B)
    }
}

Note in the above pseudocode, MATRIX_MULTIPLY refers to naïve (schoolbook) matrix multiplication.

I am benchmarking the performance of SUMMA when using:

• A minimum spanning tree broadcast, optimised for short vectors ('short')
• A minimum spanning tree scatter, followed by a bucket allgather, optimised for long vectors ('long')
• OpenMPI's built-in MPI_Bcast function ('builtin')

I test these against matrices of variable sizes, from 1024 by 1024 to 8192 by 8192. These are run 30 times each on different physical processor architectures: while in every case the processes are arranged in a 64 by 64 grid, those logical processors are distributed across 2, 4, and 8 compute nodes.

The computing for this project was performed at the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma.