Team : ALSOC
→ Temporary Research engineer
: Lionel LACASSAGNE Co-supervision
: Benjamen Couturier (CERN)
Tracking haute fréquence pour architectures SIMD : optimisation de la reconstruction LHCb
During this thesis, we studied linear algebra systems with small matrices (typically from 2x2 to 5x5) used within the LHCb experiment (and also in other domains like computer vision). Linear algebra libraries like Eigen, Magma or the MKL are not optimized for such small matrices.
We used and combined many well-known transforms helping SIMD and some unusual transforms like the fast reciprocal square root computation. We wrote a code generator in order to simplify the use of such transforms and to have a portable code.
We tested these optimizations and analyzed their impact on the speed of simple algorithm. Batch processing in SoA is crucial to process fast these small matrices. We also analyzed how the accuracy of the results depends on the precision of the data.
We implemented these transforms in order to speed-up the Cholesky factorization of small matrices (up to 12x12). The processing speed is capped if the fast reciprocal square root computation is not used. We got a speed up between x10 and x33 using F32.
Finally, we studied and sped up the Kalman filter in its general form. Our 4x4 F32 implementation is x90 faster. The Kalman filter used within LHCb has been sped up by x2.2 compared to the current SIMD version and by at least x2.3 compared to filters used other high energy physics experiments.
: 02/13/2019 - 14h00 - Site Jussieu 25-26/105Jury members
Albert COHEN Google [Rapporteur]
Daniel MENARD IETR (Université de Rennes) [Rapporteur]
Lionel LACASSAGNE LIP6 (Sorbonne Université)
Emmanuel CHAILLOUX LIP6 (Sorbonne Université)
Michèle GOUIFFÈS LIMSI (Université Paris-Sud)
Bertrand LE GAL IMS (Université de Bordeaux)