Julien Leduc

Parallelization of maximum likelihood fits with OpenMP and CUDA

Data analyses based on maximum likelihood fits are commonly used in the high energy physics community for fitting statistical models to data samples. This technique requires the numerical minimization of the negative log-likelihood function. MINUIT is the most common package used for this purpose in the high energy physics community. The main algorithm in this package, MIGRAD, searches the minimum by using the gradient information. The procedure requires several evaluations of the function, depending on the number of free parameters and their initial values. The whole procedure can be very CPU-time consuming in case of complex functions, with several free parameters, many independent variables and large data samples. Therefore, it becomes particularly important to speed-up the evaluation of the negative log-likelihood function. In this paper we present an algorithm and its implementation which benefits from data vectorization and parallelization (based on OpenMP) and which was also ported to Graphics Processing Units using CUDA.

Evaluation of Likelihood Functions for Data Analysis on Graphics Processing Units

Data analysis techniques based on likelihood function calculation play a crucial role in many High Energy Physics measurements. Depending on the complexity of the models used in the analyses, with several free parameters, many independent variables, large data samples, and complex functions, the calculation of the likelihood functions can require a long CPU execution time. In the past, the continuous gain in performance for each single CPU core kept pace with the increase on the complexity of the analyses, maintaining reasonable the execution time of the sequential software applications. Nowadays, the performance for single cores is not increasing as in the past, while the complexity of the analyses has grown significantly in the Large Hadron Collider era. In this context a breakthrough is represented by the increase of the number of computational cores per computational node. This allows to speed up the execution of the applications, redesigning them with parallelization paradigms. The likelihood function evaluation can be parallelized using data and task parallelism, which are suitable for CPUs and GPUs (Graphics Processing Units), respectively. In this paper we show how the likelihood function evaluation has been parallelized on GPUs. We describe the implemented algorithm and we give some performance results when running typical models used in High Energy Physics measurements. In our implementation we achieve a good scaling with respect to the number of events of the data samples.

Evaluation of likelihood functions on CPU and GPU devices

We describe parallel implementations of an algorithm used to evaluate the likelihood function used in data analysis. The implementations run, respectively, on CPU and GPU, and both devices cooperatively (hybrid). CPU and GPU implementations are based on OpenMP and OpenCL, respectively. The hybrid implementation allows the application to run also on multi-GPU systems (not necessarily of the same type). The hybrid case uses a scheduler so that the workload needed for the evaluation of function is split and balanced in corresponding sub-workloads to be executed in parallel on each device, i. e. CPU-GPU or multi-CPUs. We present the results of the scalability when running on CPU. Then we show the comparison of the performance of the GPU implementation on different hardware systems from different vendors, and the performance when running in the hybrid case. The tests are based on likelihood functions from real data analysis carried out in the high energy physics community.

How to harness the performance potential of current multi-core processors

Leakage currents have put a stop to the semiconductor industrys ability to increase processor frequency in order to enhance the performance of new microprocessors. Instead, we observe a slew of changes inside the micro-architecture with an aim of enhancing the performance. Several of these changes, however, do not translate into automatic speed improvements for the software. This paper discusses the increased complexity of modern microprocessors by separating out into dimensions each feature that impacts performance and mentions briefly ways of improving software, in particular that of the High Energy Physics community, to take full advantage.

Evaluating the scalability of HEP software and multi-core hardware

As researchers have reached the practical limits of processor performance improvements by frequency scaling, it is clear that the future of computing lies in the effective utilization of parallel and multi-core architectures. Since this significant change in computing is well underway, it is vital for HEP programmers to understand the scalability of their software on modern hardware and the opportunities for potential improvements. This work aims to quantify the benefit of new mainstream architectures to the HEP community through practical benchmarking on recent hardware solutions, including the usage of parallelized HEP applications.

Many-core experience with HEP software at CERN openlab

The continued progression of Moores law has led to many-core platforms becoming easily accessible commodity equipment. New opportunities that arose from this change have also brought new challenges: harnessing the raw potential of computation of such a platform is not always a straightforward task. This paper describes practical experience coming out of the work with many-core systems at CERN openlab and the observed differences with respect to their predecessors. We provide the latest results for a set of parallelized HEP benchmarks running on several classes of many-core platforms.

The breaking point of modern processor and platform technology

This work is an overview of state of the art processors used in High Energy Physics, their architecture and an extensive outline of the forthcoming technologies. Silicon process science and hardware design are making constant and rapid progress, and a solid grasp of these developments is imperative to the understanding of their possible future applications, which might include software strategy, optimizations, computing center operations and hardware acquisitions. In particular, the current issue of software and platform scalability is becoming more and more noticeable, and will develop in the near future with the growing core count of single chips and the approach of certain x86 architectural limits. Other topics brought forward include the hard, physical limits of innovation, the applicability of tried and tested computing formulas to modern technologies, as well as an analysis of viable alternate choices for continued development.