First steps towards more numerical reproducibility

International audienceQuestions whether numerical simulation is reproducible or not have been reported in several sensitive applications. Numerical reproducibility failure mainly comes from the finite precision of computer arithmetic. Results of floating-point computation depends on the computer arithmetic precision and on the order of arithmetic operations. Massive parallel HPC which merges, for instance, many-core CPU and GPU, clearly modifies these two parameters even from run to run on a given computing platform. How to trust such computed results? This paper presents how three classic approaches in computer arithmetic may provide some first steps towards more numerical reproducibility

L’écosystème buccal chez le patient âgé

La bouche est une cavité naturelle complexe qui forme le segment initial du tube digestif. Elle est un acteur essentiel des fonctions vitales que sont la nutrition, le langage et la communication. L’ensemble de la bouche (dents, parodonte, muqueuses, langue) est constamment hydraté et lubrifié par la salive. À tout âge, un équilibre s’établit entre la prolifération bactérienne, le flux salivaire et la réponse tissulaire : c’est l’écosystème buccal. La régulation de cet écosystème participe à la protection du complexe buccal contre les pathologies inflammatoires et infectieuses courantes (caries, gingivites, parodontopathies,candidoses). Chez les patients âgés, la modification du flux salivaire, l’apparition de pathologies spécifiques (caries radiculaires, absence de dents, parodontopathies. . .), les conditions locales (présence de prothèses amovibles), le développement de pathologies générales telles que le diabète, l’hypertension, la baisse des défenses immunitaires, la négligence de l’hygiène quotidienne sont autant d’éléments qui vont déséquilibrer l’écosystème buccal, favoriser la formation du biofilm (plaque bactérienne) et fragiliser les tissus bucco-dentaires. Le maintien de cet écosystème est essentiel pour le patient âgé : il lui permet de s’alimenter dans de bonnes conditions et ainsi prévenir les risques de dénutrition. Les auteurs décrivent la physiopathologie buccale (flore buccale, sécrétion salivaire) et les stratégies à adopter pour préserver l’équilibre buccal chez le patient âgé

Investigating mixed-precision for AGATA pulse-shape analysis

The AGATA project aims at building a 4π gamma-ray spectrometer consisting of 180 germanium crystals, each crystal being divided into 36 segments. Each gamma ray produces an electrical signal within several neighbouring segments, which is compared with a data base of reference signals, enabling to locate the interaction. This step is called Pulse-Shape Analysis (PSA). In the execution chain leading to the PSA, we observe successive data conversions: the original 14-bit integers given by the electronics are finally converted to 32-bit floats. This made us wonder about the real numerical accuracy of the results, and investigate the use of shorter floats, with the hope to speedup the computation, and also reduce a major cache-miss problem. In this article, we first describe the numerical validation of the PSA code, thanks to the CADNA library. After the code being properly instrumented, CADNA performs each computation three times with a random rounding mode. This allows, for each operation, to evaluate the number of exact significant digits using a Student test with 95% confidence threshold. In a second step, we report our successes and challenges while refactoring the code so to mix different numerical formats, using high precision only when necessary, and taking benefit of hardware speedup elsewhere

Numerical validation in quadruple precision using stochastic arithmetic

International audienceDiscrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floating-point variables, i.e. having 113-bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113-bit mantissa length variables. This new version of CADNA has been sucessfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision

White Paper from Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing

In numerical computations, precision of floating-point computations is a key factor to determine the performance (speed and energy-efficiency) as well as the reliability (accuracy and reproducibility). However, precision generally plays a contrary role for both. Therefore, the ultimate concept for maximizing both at the same time is the minimal-precision computing through precision-tuning, which adjusts the optimal precision for each operation and data. Several studies have been already conducted for it so far (e.g. Precimoniuos and Verrou), but the scope of those studies is limited to the precision-tuning alone. Hence, we aim to propose a broader concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. In 2019, we have started the Minimal-Precision Computing project to propose a more broad concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. Specifically, our system combines (1) a precision-tuning method based on Discrete Stochastic Arithmetic (DSA), (2) arbitrary-precision arithmetic libraries, (3) fast and accurate numerical libraries, and (4) Field-Programmable Gate Array (FPGA) with High-Level Synthesis (HLS). In this white paper, we aim to provide an overview of various technologies related to minimal- and mixed-precision, to outline the future direction of the project, as well as to discuss current challenges together with our project members and guest speakers at the LSPANC 2020 workshop; https://www.r-ccs.riken.jp/labs/lpnctrt/lspanc2020jan/

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at root s=7 and 8 TeV

70 pages plus author lists + cover page (104 pages total), 32 figures, 22 tables, submitted to JHEP. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HIGG-2015-07/ and at http://cms-results.web.cern.ch/cms-results/public-results/publications/HIG-15-002/Combined ATLAS and CMS measurements of the Higgs boson production and decay rates, as well as constraints on its couplings to vector bosons and fermions, are presented. The combination is based on the analysis of five production processes, namely gluon fusion, vector boson fusion, and associated production with a $W$ or a $Z$ boson or a pair of top quarks, and of the six decay modes $H \to ZZ, WW$, $\gamma\gamma, \tau\tau, bb$, and $\mu\mu$. All results are reported assuming a value of 125.09 GeV for the Higgs boson mass, the result of the combined measurement by the ATLAS and CMS experiments. The analysis uses the CERN LHC proton--proton collision data recorded by the ATLAS and CMS experiments in 2011 and 2012, corresponding to integrated luminosities per experiment of approximately 5 fb$^{-1}$ at $\sqrt{s}=7$ TeV and 20 fb$^{-1}$ at $\sqrt{s} = 8$ TeV. The Higgs boson production and decay rates measured by the two experiments are combined within the context of three generic parameterisations: two based on cross sections and branching fractions, and one on ratios of coupling modifiers. Several interpretations of the measurements with more model-dependent parameterisations are also given. The combined signal yield relative to the Standard Model prediction is measured to be 1.09 $\pm$ 0.11. The combined measurements lead to observed significances for the vector boson fusion production process and for the $H \to \tau\tau$ decay of $5.4$ and $5.5$ standard deviations, respectively. The data are consistent with the Standard Model predictions for all parameterisations considered.Peer reviewe