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Register a new userAn analytic performance model for overlapping execution of memory-bound loop kernels on multicore CPUs
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Added by
Georg Hager
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Complex applications running on multicore processors show a rich performance phenomenology. The growing number of cores per ccNUMA domain complicates performance analysis of memory-bound code since system noise, load imbalance, or task-based programming models can lead to thread desynchronization. Hence, the simplifying assumption that all cores execute the same loop can not be upheld. Motivated by observations on plain and modifi
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Energy is now a first-class design constraint along with performance in all computing settings. Energy predictive modelling based on performance monitoring counts (PMCs) is the leading method used for prediction of energy consumption during an application execution. We use a model-theoretic approach to formulate the assumed properties of existing models in a mathematical form. We extend the formalism by adding properties, heretofore unconsidered, that account for a limited form of energy conservation law. The extended formalism defines our theory of energy of computing. By applying the basic practical implications of the theory, we improve the prediction accuracy of state-of-the-art energy models from 31% to 18%. We also demonstrate that use of state-of-the-art measurement tools for energy optimisation may lead to significant losses of energy (ranging from 56% to 65% for applications used in experiments) since they do not take into account the energy conservation properties.
Energy proportionality is the key design goal followed by architects of modern multicore CPUs. One of its implications is that optimization of an application for performance will also optimize it for energy. In this work, we show that energy proportionality does not hold true for multicore CPUs. This finding creates the opportunity for bi-objective optimization of applications for performance and energy. We propose and study the first application-level method for bi-objective optimization of multithreaded data-parallel applications for performance and energy. The method uses two decision variables, the number of identical multithreaded kernels (threadgroups) executing the application and the number of threads in each threadgroup, with the workload always partitioned equally between the threadgroups. We experimentally demonstrate the efficiency of the method using four highly optimized multithreaded data-parallel applications, 2D fast Fourier transform based on FFTW and Intel MKL, and dense matrix-matrix multiplication using OpenBLAS and Intel MKL. Four modern multicore CPUs are used in the experiments. The experiments show that optimization for performance alone results in the increase in dynamic energy consumption by up to 89% and optimization for dynamic energy alone degrades the performance by up to 49%. By solving the bi-objective optimization problem, the method determines up to 11 globally Pareto-optimal solutions. Finally, we propose a qualitative dynamic energy model employing performance monitoring counters as parameters, which we use to explain the discovered energy nonproportionality and the Pareto-optimal solutions determined by our method. The model shows that the energy nonproportionality in our case is due to the activity of the data translation lookaside buffer (dTLB), which is disproportionately energy expensive.
In addition to hardware wall-time restrictions commonly seen in high-performance computing systems, it is likely that future systems will also be constrained by energy budgets. In the present work, finite difference algorithms of varying computational and memory intensity are evaluated with respect to both energy efficiency and runtime on an Intel Ivy Bridge CPU node, an Intel Xeon Phi Knights Landing processor, and an NVIDIA Tesla K40c GPU. The conventional way of storing the discretised derivatives to global arrays for solution advancement is found to be inefficient in terms of energy consumption and runtime. In contrast, a class of algorithms in which the discretised derivatives are evaluated on-the-fly or stored as thread-/process-local variables (yielding high compute intensity) is optimal both with respect to energy consumption and runtime. On all three hardware architectures considered, a speed-up of ~2 and an energy saving of ~2 are observed for the high compute intensive algorithms compared to the memory intensive algorithm. The energy consumption is found to be proportional to runtime, irrespective of the power consumed and the GPU has an energy saving of ~5 compared to the same algorithm on a CPU node.
In the present paper we consider numerical methods to solve the discrete Schrodinger equation with a time dependent Hamiltonian (motivated by problems encountered in the study of spin systems). We will consider both short-range interactions, which lead to evolution equations involving sparse matrices, and long-range interactions, which lead to dense matrices. Both of these settings show very different computational characteristics. We use Magnus integrators for time integration and employ a framework based on Leja interpolation to compute the resulting action of the matrix exponential. We consider both traditional Magnus integrators (which are extensively used for these types of problems in the literature) as well as the recently developed commutator-free Magnus integrators and implement them on modern CPU and GPU (graphics processing unit) based systems. We find that GPUs can yield a significant speed-up (up to a factor of $10$ in the dense case) for these types of problems. In the sparse case GPUs are only advantageous for large problem sizes and the achieved speed-ups are more modest. In most cases the commutator-free variant is superior but especially on the GPU this advantage is rather small. In fact, none of the advantage of commutator-free methods on GPUs (and on multi-core CPUs) is due to the elimination of commutators. This has important consequences for the design of more efficient numerical methods.
In this paper, we use multithreaded fast Fourier transforms provided in three highly optimized packages, FFTW-2.1.5, FFTW-3.3.7, and Intel MKL FFT, to present a novel model-based parallel computing technique as a very effective and portable method for optimization of scientific multithreaded routines for performance, especially in the current multicore era where the processors have abundant number of cores. We propose two optimization methods, PFFT-FPM and PFFT-FPM-PAD, based on this technique. They compute 2D-DFT of a complex signal matrix of size NxN using p abstract processors. Both algorithms take as inputs, discrete 3D functions of performance against problem size of the processors and output the transformed signal matrix. Based on our experiments on a modern Intel Haswell multicore server consisting of 36 physical cores, the average and maximum speedups observed for PFFT-FPM using FFTW-3.3.7 are 1.9x and 6.8x respectively and the average and maximum speedups observed using Intel MKL FFT are 1.3x and 2x respectively. The average and maximum speedups observed for PFFT-FPM-PAD using FFTW-3.3.7 are 2x and 9.4x respectively and the average and maximum speedups observed using Intel MKL FFT are 1.4x and 5.9x respectively.
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