1 / 7

Thijs Cornelissen (Wuppertal)

Track fitting and v ectorization. Thijs Cornelissen (Wuppertal). Updates in GlobalChi2Fitter. Rewritten calculation of jacobians Fewer temporary matrices calculated Matrix multiplication now uses SSE instructions, factor two faster (w/doubles)

tansy
Download Presentation

Thijs Cornelissen (Wuppertal)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Track fitting and vectorization ThijsCornelissen (Wuppertal)

  2. Updates in GlobalChi2Fitter • Rewritten calculation of jacobians • Fewer temporary matrices calculated • Matrix multiplication now uses SSE instructions, factor two faster (w/doubles) • Reorganized internal storage of matrices in fitter, mainly to make them properly aligned in memory (crucial for vector instructions) • In covariance matrix, inserted empty column between perigee and scatter entries, to make total number of entries even • Jacobians stored as a 5x4 matrix (by default they are 5x5, which is very bad for vectorization) • Optimized calculation of track errors at each measurement • Also taking advantage of SSE instructions • After these optimizations, main bottleneck is newing/deleting of Tracking EDM objects

  3. Matrix multiplication: scalar • Simple 4x4 matrix multiplication routine • With gcc 4.7.2, auto-vectorization makes this routine 30% slower!! • Gcc 4.8.1 shows small (~10%) improvement, still nowhere near theoretical speed-up (factor 4)

  4. Matrix multiplication: vectorized • Vectorized 4x4 matrix multiplication routine, calculates four dot products in parallel • Tested to be four times faster than scalar version • Runs in development version of fitter, gives correct results

  5. Profiling runIteration() devval new • Large reduction in derivative calculation thanks to matrix optimizations

  6. Profiling calculateTrackErrors() devval new • Overall factor 2 improvement after all optimizations (not just vectorization) • Performance of errors2() function does not look optimal yet, still investigating additional techniques like loop unrolling, blocking, …

  7. SSE and portability • Intel MIC and ARM processors don’t support SSE, code would crash immediately • Can implement runtime check at initialization using the assembler instruction ‘cpuid’, as explained here • Could then use result from cpuid to set function pointer to scalar or vectorized functions • In the end, using a higher level library like Eigen would be more elegant • But performance will have to match the low level code

More Related