BLAS/LAPACK Benchmarks

Test Setup

Algorithms

The following H-matrix arithmetics are tested:

H-mm-eager	eager H matrix multiplication
H-mm-accu	H matrix multiplication using accumulators
H-lu-eager	eager H-LU factorization
H-lu-accu	H-LU factorization using accumulators
UniH-mm	Uniform-H matrix multiplication
UniH-lu	Uniform-H LU factorization

Applications

The following applications are used for testing:

• laplace : Laplace SLP

  • command line: --app laplaceslp --adm std --cluster h --ntile 64 --grid sphere2-6 -e 1e-6

  • problem size: 65536

  • truncation accuracy: 1e-6

BLAS/LAPACK Libraries

OpenBLAS

• version: 0.3.20

• compilation options: make TARGET=<...> USE_THREAD=0 USE_LOCKING=1 NO_LAPACK=1 with targets ZEN and SKYLAKEX

• with Reference-LAPACK v3.10.0

BLIS

• version: 0.8.1

• compilation options: ./configure --disable-threading --enable-mixed-dt --enable-sup-handling <...> with targets zen2 and skx

• with Reference-LAPACK v3.10.0

Intel MKL

• version: 2020.0

• on AMD Epyc with MKL_DEBUG_CPU_TYPE=5 to enable the AVX2 code path

• LAPACK also via Intel MKL

Results

Each benchmark is run 10 times and the best runtime is used.

Laplace

	AMD Epyc 7702 (Rome)			Intel Xeon 8360Y (IceLake)
Algorithm	OpenBLAS	BLIS	Intel MKL	OpenBLAS	BLIS	Intel MKL
H-mm-accu	144.0s	167.9s	127.3s	160.4s	288.9s	152.7s
UniH-mm	173.1s	169.5s	147.1s	161.7s	304.0s	154.3s
H-lu-eager	111.6s	145.2s	106.0s	136.5s	211.4s	128.6s
H-lu-accu	60.84s	70.14s	53.91s	73.94s	111.4s	68.80s
UniH-lu	86.23s	90.23s	75.95s	95.31s	141.0s	90.50s