Efficient Parallel Random Sampling : Vectorized, Cache-Efficient, and Online

We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and leads to a parallel algorithm running in expected time $\mathcal{O}(n/p+\log p)$ on $p$ processors, i.e., scales to massively parallel machines even for moderate values of $n$. The amount of communication between the processors is very small (at most $\mathcal{O}(\log p)$) and independent of the sample size. We also discuss modifications needed for load balancing, online sampling, sampling with replacement, Bernoulli sampling, and vectorization on SIMD units or GPUs

Analysis of hybrid parallelization strategies: simulation of Anderson localization and Kalman Filter for LHCb triggers

This thesis presents two experiences of hybrid programming applied to condensed matter and high energy physics. The two projects differ in various aspects, but both of them aim to analyse the benefits of using accelerated hardware to speedup the calculations in current science-research scenarios. The first project enables massively parallelism in a simulation of the Anderson localisation phenomenon in a disordered quantum system. The code represents a Hamiltonian in momentum space, then it executes a diagonalization of the corresponding matrix using linear algebra libraries, and finally it analyses the energy-levels spacing statistics averaged over several realisations of the disorder. The implementation combines different parallelization approaches in an hybrid scheme. The averaging over the ensemble of disorder realisations exploits massively parallelism with a master-slave configuration based on both multi-threading and message passing interface (MPI). This framework is designed and implemented to easily interface similar application commonly adopted in scientific research, for example in Monte Carlo simulations. The diagonalization uses multi-core and GPU hardware interfacing with MAGMA, PLASMA or MKL libraries. The access to the libraries is modular to guarantee portability, maintainability and the extension in a near future. The second project is the development of a Kalman Filter, including the porting on GPU architectures and autovectorization for online LHCb triggers. The developed codes provide information about the viability and advantages for the application of GPU technologies in the first triggering step for Large Hadron Collider beauty experiment (LHCb). The optimisation introduced on both codes for CPU and GPU delivered a relevant speedup on the Kalman Filter. The two GPU versions in CUDA R and OpenCLTM have similar performances and are adequate to be considered in the upgrade and in the corresponding implementations of the Gaudi framework. In both projects we implement optimisation techniques in the CPU code. This report presents extensive benchmark analyses of the correctness and of the performances for both projects

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

Parallel Algorithms for Summing Floating-Point Numbers

The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point operations, this problem becomes very challenging. Moreover, all existing solutions rely on sequential algorithms which cannot scale to the huge datasets that need to be processed. In this paper, we provide several efficient parallel algorithms for summing n floating point numbers, so as to produce a faithfully rounded floating-point representation of the sum. We present algorithms in PRAM, external-memory, and MapReduce models, and we also provide an experimental analysis of our MapReduce algorithms, due to their simplicity and practical efficiency.Comment: Conference version appears in SPAA 201