zstang / matmul

Benchmarking matrix multiplication implementations

This repo evaluates different matrix multiplication implementations given two large square matrices (2000-by-2000 in the following example):

Implementation	Long description
Naive	Most obvious implementation
Transposed	Transposing the second matrix for cache efficiency
sdot w/o hints	Replacing the inner loop with BLAS sdot()
sdot with hints	sdot() with a bit unrolled loop
SSE sdot	vectorized sdot() with explicit SSE instructions
SSE+tiling sdot	SSE sdot() with loop tiling
OpenBLAS sdot	sdot() provided by OpenBLAS
OpenBLAS sgemm	sgemm() provided by OpenBLAS

To compile the evaluation program:

make CBLAS=/path/to/cblas/prefix

or omit the CBLAS setting you don't have it. After compilation, use

./matmul -h

to see the available options. Here is the result on my machines:

Implementation	-a	Linux,-n2000	Linux,-n4000	Linux/icc,-n4000	Mac,-n2000
Naive	0	7.53 sec	188.85 sec	173.76 sec	77.45 sec
Transposed	1	6.66 sec	55.48 sec	21.04 sec	9.73 sec
sdot w/o hints	4	6.66 sec	55.04 sec	21.35 sec	9.70 sec
sdot with hints	3	2.41 sec	29.47 sec	21.69 sec	2.92 sec
SSE sdot	2	1.36 sec	21.79 sec	22.18 sec	2.92 sec
SSE+tiling sdot	7	1.11 sec	10.84 sec	10.97 sec	1.90 sec
OpenBLAS sdot	5	2.69 sec	28.87 sec		5.61 sec
OpenBLAS sgemm	6	0.63 sec	4.91 sec		0.86 sec
uBLAS		7.43 sec	165.74 sec
Eigen		0.61 sec	4.76 sec	5.01 sec	0.85 sec

The machine configurations are as follows:

Machine	CPU	OS	Compiler
Linux	2.6 GHz Xeon E5-2697	CentOS 6	gcc-4.4.7/icc-15.0.3
Mac	1.7 GHz Intel Core i5-2557M	OS X 10.9.5	clang-600.0.57/LLVM-3.5svn

On both machines, OpenBLAS-0.2.18 is compiled with the following options (no AVX or multithreading):

TARGET=CORE2
BINARY=64
USE_THREAD=0
NO_SHARED=1
ONLY_CBLAS=1
NO_LAPACK=1
NO_LAPACKE=1