Arm’s Pierre Blanchard will give a guest lecture on “Accuracy and Performance of libm Functions”. The presentation is part of the classes Rechnerstrukturen and High Performance Computing taught at Friedrich Schiller University Jena. Pierre’s virtual lecture is on Thursday, 1st of July 2021. Time is 02:15 - 03:45PM (GMT+2). Students outside of the specific classes are cordially invited to attend and may obtain access information by writing an e-mail to alex.breuer@uni-jena.de.

Abstract: Arm IP can now be found at the cutting edge of HPC, running scientific computing workloads that stress all aspects of the system and software stack. The increasing need for optimised elementary math routines expressed by leading actors in the HPC community, such as the US National Labs, has driven the design and productisation of libamath; a library delivering the best available performance on AArch64. While most commonly used routines have been extensively optimised and made publicly available in Arm Optimized Routines (AOR), efforts are made towards upstreaming optimisations and development of new routines (available in the productised version) into AOR. This lecture describes the main stages involved in designing efficient implementations of elementary math functions in floating-point arithmetic, while thoroughly controlling their accuracy and performance. We also show how vector units can be used to leverage performance. In particular, we point out some of the issues exposed by vectorising such routines and we explain how to overcome them on both Neon and SVE enabled micro-architectures. Examples of routines will be given throughout the presentation to illustrate our approach, including: trigonometric functions; exponentials; as well as more exotic routines such as error functions.

About the Speaker: After completing a masters in computational mechanics at the Ecole Normale Supérieure de Cachan, Pierre defended his Ph.D. thesis in applied mathematics and scientific computing at the University of Bordeaux. In 2017 he moved to Manchester (UK) to work as a postdoctoral research assistant at the Maths Department of the University of Manchester under the supervision of Nick Higham and Jack Dongarra. Pierre’s research has ranged from hierarchical matrix algorithms for High Performance Computing (HPC) to fast algorithms for standard and randomised numerical linear algebra, as well as mixed-precision floating point arithmetic. He joined the Arm Performance Libraries team in Manchester two years ago as a software engineer to work on the optimisation of elementary math functions on AArch64.