Small SIMD Matrices for CERN High Throughput Computing

Abstract

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 ×3 to ×10 faster than MKL. The Kalman Filter is also faster than existing implementations, and achieves 4 • 10 9 iter/s on a 2×24C Intel Xeon.

Event and data persistency models for the LHCb Real Time Analysis System

“…The key elements in the process included having flexible data structures that can be grown and shrunk at run time using dynamic memory allocation, but also the possibility of traversing decay trees for the analysis of multi-staged particle decays. In order to reach a high computational speed, the model needed to allow easy vectorisation [10][11][12][13]. At the same time, the new model had to be compatible with the old event model also during the development phase to not break the workflow of the full reconstruction sequence and for quality assurance.…”

Flynn’s Reconciliation

“…DSLs can either generate high-level code in a more general language or directly go to an IR level such as LLVM-IR. For batched Cholesky factorization and Kalman filters, Lemaitre et al [34] propose a template system. Rodrigues et al [44] specify a small DSL for static tensor multiplications-even parallelizing error correction in 5G base stations [14] warrants a DSL.…”