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Speed up float 5x5 matrix * vector multiplication with SSE

Asked 2011-07-07T22:04:27.080
13

I need to run a matrix-vector multiplication 240000 times per second. The matrix is 5x5 and is always the same, whereas the vector changes at each iteration. The data type is float. I was thinking of using some SSE (or similar) instructions.

  1. I am concerned that the number of arithmetic operations is too small compared to the number of memory operations involved. Do you think I can get some tangible (e.g. > 20%) improvement?

  2. Do I need the Intel compiler to do it?

  3. Can you point out some references?

c++ vectorization matrix-multiplication sse simd
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2 Answers

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This should be easy, especially when you're on Core 2 or later: You neeed 5* _mm_dp_ps , one _mm_mul_ps, two _mm_add_ps, one ordinary multiplication, plus some shuffles, loads and stores (and if the matrix is fixed, You can keep most of it in SSE registers, if you don't need them for anything else).

As for memory bandwidth: we're talking about 2,4 megabytes of vectors, when memory bandwidths are in single-digit gigabytes per second.

answered 2011-07-07T23:38:14.283
0

I would recommend having a look at an optimised BLAS library, such as the Intel MKL or the AMD ACML. Based on your description I would assume that you'd be after the SGEMV level 2 matrix-vector routine, to do y = A*x style operations.

If you really want to implement something yourself, using the (available) SSE..SSE4 and AVX instruction sets can offer significant performance improvements in some cases, although this is exactly what a good BLAS library will be doing. You also need to think alot about cache friendly data access patterns.

I don't know if this is applicable in your case, but can you operate on "chunks" of vectors at a time?? So rather than repeatedly doing an y = A*x style operation can you operate on blocks of [y1 y2 ... yn] = A * [x1 x2 ... xn]. If so, this means that you could use an optimised matrix-matrix routine, such as SGEMM. Due to the data access patterns this may be significantly more efficient than repeated calls to SGEMV. If it were me, I would try to go down this path...

Hope this helps.

answered 2011-07-07T22:41:55.243

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