Small SIMD Matrices for CERN High Throughput Computing

Florian Lemaitre (1, 2) , Benjamin Couturier (2) , Lionel Lacassagne (1)

1 ALSOC - Architecture et Logiciels pour Systèmes Embarqués sur Puce
2 CERN - European Organization for Nuclear Research

System tracking is an old problem and has been heavily optimized throughout the past. However, in High Energy Physics, many small systems are tracked in real-time using Kalman filtering and no implementation satisfying those constraints currently exists. In this paper, we present a code generator used to speed up Cholesky Factorization and Kalman Filter for small matrices. The generator is easy to use and produces portable and heavily optimized code. We focus on current SIMD architectures (SSE, AVX, AVX512, Neon, SVE, Altivec and VSX). Our Cholesky factorization outperforms any existing libraries: from x3 to x10 faster than MKL. The Kalman Filter is also faster than existing implementations, and achieves 4e9 iter/s on a 2x24C Intel Xeon.

Mots clés: SIMD; AVX512; SVE; multithread; code generation; metaprogramming; small matrix; Kalman filter; linear algebra

Domaines: Architectures Matérielles [cs.AR]; Algorithme et structure de données [cs.DS]; Performance et fiabilité [cs.PF]; Arithmétique des ordinateurs; Calcul parallèle, distribué et partagé [cs.DC]; Génie logiciel [cs.SE]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Florian Lemaitre, Benjamin Couturier, Lionel Lacassagne. Small SIMD Matrices for CERN High Throughput Computing. WPMVP 2018 Workshop on Programming Models for SIMD/Vector Processing, Feb 2018, Vienna, Austria. ⟨10.1145/3178433.3178434⟩. ⟨hal-01760260⟩