HPL-MxP solves a dense linear system of equations by using a low-precision LU factorization followed by iterative refinement. Similar to HPL, its more famous cousin, HPL-MxP uses a processor grid for load balancing across MPI ranks. The matrix of size N is tiled into blocks of size B which are cyclically distributed across a processor grid with P rows and Q columns. P is an explicit input argument while Q is deduced from P and the total number of MPI ranks, i.e. Q = n/P. HPL-MxP requires that P is a multiple of the number of MPI ranks n, and that matrix size N is a multiple of block size B.
NOTE
formally known as HPL-AI (Accelerator Introspection)
HPL-MxP reports the apparent FLOPS associated with the direct solve of a dense linear system.
FLOPS = (2/3N^3 + 3/2N^2)/runtime
In reality, the number of FLOPS is somewhat higher as additional operations take place in the iterative refinement steps required to bring the accuracy of the solution to double precision. HPL-MxP also reports the residual at the end of the refinement steps to allow the user to verify that double precision accuracy has been obtained.
In general, HPL-MxP performance will increase with matrix size and the benchmark is typically scaled so that the global matrix fills most of the available GPU memory. Optimal parameters depend on the system. Examples of parameters on AMD Instinct GPUs:
- 1 GPU:
mpirun_rochplmxp -P 1 -Q 1 -N 81920 --NB 2560 - 2 GPUs:
mpirun_rochplmxp -P 2 -Q 1 -N 122880 --NB 2560 - 4 GPUs:
mpirun_rochplmxp -P 2 -Q 2 -N 168960 --NB 2560 - 8 GPUs:
mpirun_rochplmxp -P 4 -Q 2 -N 235520 --NB 2560
- 1 GPU:
mpirun_rochplmxp -P 1 -Q 1 -N 125440 --NB 2560 - 2 GPUs:
mpirun_rochplmxp -P 2 -Q 1 -N 179200 --NB 2560 - 4 GPUs:
mpirun_rochplmxp -P 2 -Q 2 -N 250880 --NB 2560 - 8 GPUs:
mpirun_rochplmxp -P 4 -Q 2 -N 358400 --NB 2560
For a complete list of hpl-mxp arguments, see rocHPL-MxP GitHub Repo
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