Design and implementation of multiple-precision BLAS Level 1 functions for graphics processing units

2020 ◽  
Vol 140 ◽  
pp. 25-36 ◽  
Author(s):  
Konstantin Isupov ◽  
Vladimir Knyazkov ◽  
Alexander Kuvaev
Keyword(s):  
Graphics Processing Units ◽  
Design And Implementation ◽  
Multiple Precision ◽  
Level 1 ◽  
Graphics Processing

scholarly journals TESLA GPUs versus MPI with OpenMP for the Forward Modeling of Gravity and Gravity Gradient of Large Prisms Ensemble

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Carlos Couder-Castañeda ◽  
Carlos Ortiz-Alemán ◽  
Mauricio Gabriel Orozco-del-Castillo ◽  
Mauricio Nava-Flores
Keyword(s):  
Parallel Computing ◽  
Graphics Processing Units ◽  
Forward Modeling ◽  
Gravity Gradient ◽  
Constant Density ◽  
Gravitational Fields ◽  
Design And Implementation ◽  
Cuda Technology ◽  
Performance Results ◽  
Graphics Processing

An implementation with the CUDA technology in a single and in several graphics processing units (GPUs) is presented for the calculation of the forward modeling of gravitational fields from a tridimensional volumetric ensemble composed by unitary prisms of constant density. We compared the performance results obtained with the GPUs against a previous version coded in OpenMP with MPI, and we analyzed the results on both platforms. Today, the use of GPUs represents a breakthrough in parallel computing, which has led to the development of several applications with various applications. Nevertheless, in some applications the decomposition of the tasks is not trivial, as can be appreciated in this paper. Unlike a trivial decomposition of the domain, we proposed to decompose the problem by sets of prisms and use different memory spaces per processing CUDA core, avoiding the performance decay as a result of the constant calls to kernels functions which would be needed in a parallelization by observations points. The design and implementation created are the main contributions of this work, because the parallelization scheme implemented is not trivial. The performance results obtained are comparable to those of a small processing cluster.

scholarly journals Multiple-Precision BLAS Library for Graphics Processing Units

2020 ◽  
Author(s):  
Konstantin Isupov ◽  
Vladimir Knyazkov
Keyword(s):  
Graphics Processing Units ◽  
Arithmetic Operation ◽  
Number System ◽  
Residue Number System ◽  
Floating Point ◽  
Data Types ◽  
Rounding Errors ◽  
Multiple Precision ◽  
Graphics Processing ◽  
Point Arithmetic

The binary32 and binary64 floating-point formats provide good performance on current hardware, but also introduce a rounding error in almost every arithmetic operation. Consequently, the accumulation of rounding errors in large computations can cause accuracy issues. One way to prevent these issues is to use multiple-precision floating-point arithmetic. This preprint, submitted to Russian Supercomputing Days 2020, presents a new library of basic linear algebra operations with multiple precision for graphics processing units. The library is written in CUDA C/C++ and uses the residue number system to represent multiple-precision significands of floating-point numbers. The supported data types, memory layout, and main features of the library are considered. Experimental results are presented showing the performance of the library.

scholarly journals Multiple-precision matrix-vector multiplication on graphics processing units

2020 ◽  
Vol 11 (3) ◽  
pp. 33-59 ◽  
Author(s):  
Константин Сергеевич Исупов ◽  
Владимир Сергеевич Князьков
Keyword(s):  
Graphics Processing Units ◽  
Precision Matrix ◽  
Matrix Vector Multiplication ◽  
Multiple Precision ◽  
Graphics Processing ◽  
Matrix Vector

Мы рассматриваем параллельную реализацию матрично/векторного умножения (GEMV, уровень 2 BLAS) для графических процессоров (GPU) с использованием арифметики многократной точности на основе системы остаточных классов. В нашей реализации GEMV покомпонентные операции с многоразрядными векторами и матрицами разбиваются на части, каждая из которых выполняется отдельным CUDA ядром. Это исключает ветвление логики исполнения и позволяет добиться более полного использования ресурсов GPU. Эффективная структура данных для хранения многоразрядных массивов обеспечивает объединение доступов параллельных потоков к глобальной памяти GPU в транзакции. Для предложенной реализации GEMV выполнен анализ ошибок округления и получены оценки точности. Представлены экспериментальные результаты, показывающие высокую эффективность разработанной реализации по сравнению с существующими программными пакетами многократной точности для GPU.

scholarly journals Multiple-precision matrix-vector multiplication on graphics processing units

2020 ◽  
Vol 11 (3) ◽  
pp. 61-84
Author(s):  
Konstantin Isupov ◽  
Vladimir Knyazkov
Keyword(s):  
Graphics Processing Units ◽  
High Efficiency ◽  
Parallel Implementation ◽  
Number System ◽  
Residue Number System ◽  
Global Memory ◽  
Matrix Vector Multiplication ◽  
Multiple Precision ◽  
Graphics Processing ◽  
Matrix Vector

We are considering a parallel implementation of matrix-vector multiplication (GEMV, Level 2 of the BLAS) for graphics processing units (GPUs) using multiple-precision arithmetic based on the residue number system. In our GEMV implementation, element-wise operations with multiple-precision vectors and matrices consist of several parts, each of which is calculated by a separate CUDA kernel. This feature eliminates branch divergence when performing sequential parts of multiple-precision operations and allows the full utilization of the GPU’s resources. An efficient data structure for storing arrays with multiple-precision entries provides a coalesced access pattern to the GPU global memory. We have performed a rounding error analysis and derived error bounds for the proposed GEMV implementation. Experimental results show the high efficiency of the proposed solution compared to existing high-precision packages deployed on GPU.

scholarly journals Multiple-Precision BLAS Library for Graphics Processing Units

2020 ◽  
Author(s):  
Konstantin Isupov ◽  
Vladimir Knyazkov
Keyword(s):  
Graphics Processing Units ◽  
Arithmetic Operation ◽  
Number System ◽  
Residue Number System ◽  
Floating Point ◽  
Data Types ◽  
Rounding Errors ◽  
Multiple Precision ◽  
Graphics Processing ◽  
Point Arithmetic

The binary32 and binary64 floating-point formats provide good performance on current hardware, but also introduce a rounding error in almost every arithmetic operation. Consequently, the accumulation of rounding errors in large computations can cause accuracy issues. One way to prevent these issues is to use multiple-precision floating-point arithmetic. This preprint, submitted to Russian Supercomputing Days 2020, presents a new library of basic linear algebra operations with multiple precision for graphics processing units. The library is written in CUDA C/C++ and uses the residue number system to represent multiple-precision significands of floating-point numbers. The supported data types, memory layout, and main features of the library are considered. Experimental results are presented showing the performance of the library.

scholarly journals K-means Clustering Algorithm: Efficient Implementation on Graphics Processing Units

2019 ◽  
Author(s):  
Kunjan Aggarwal ◽  
Mainak Chaudhuri
Keyword(s):  
Graphics Processing Units ◽  
Clustering Algorithm ◽  
Real Life ◽  
Number Of Clusters ◽  
Design And Implementation ◽  
Data Volume ◽  
Data Points ◽  
Life Phenomena ◽  
Graphics Processing ◽  
Analyze Data

Data analysis and classification play a big role in understanding various real life phenomena. Clustering helps analyze data with little or no prior knowledge about it. K-means clustering is a popular clustering algorithm with applications to computer vision, data mining, data visualization, etc.. Due to continuously increasing data volume, parallel computing is necessary to overcome the computational challenges involved in K-means clustering. We present the design and implementation of Kmeans clustering algorithm on widely available graphics processing units (GPUs), which have the required hardware architecture to meet these parallelism needs. We analyze the scalability of our proposed methods with increase in number and dimensionality of data points as well as the number of clusters. We also compare our results with current best available implementations on GPUs and a 24-way threaded parallel CPU implementation. We achieved a consistent speedup of 6.5x over the parallel CPU implementation.

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