Plasma

Dongarra, Jack; Gates, Mark; Haidar, Azzam; Kurzak, Jakub; Łuszczek, Piotr; Wu, Panruo; Yamazaki, Ichitaro; YarKhan, Asim; Abalenkovs, Maksims; Bagherpour, Negin; Hammarling, Sven; Šístek, Jakub; Stevens, David; Zounon, Mawussi; Relton, Samuel D.

doi:10.1145/3264491

Cited by 40 publications

(6 citation statements)

References 36 publications

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“…We now experiment with the state-of-the-art parallel numerical linear algebra library PLASMA [6]. PLASMA includes much of the functionality of the BLAS and LAPACK, but partitions matrices into t \times t blocks called tiles.…”

Section: Matrix Multiplicationmentioning

confidence: 99%

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A Class of Fast and Accurate Summation Algorithms

Blanchard¹,

Higham²,

Mary³

2020

SIAM J. Sci. Comput.

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The need to sum floating-point numbers is ubiquitous in scientific computing. Standard recursive summation of n summands, often implemented in a blocked form, has a backward error bound proportional to nu, where u is the unit roundoff. With the growing interest in low precision floating-point arithmetic and ever increasing n in applications, computed sums are more likely to have insufficient accuracy. We propose a class of summation algorithms called FABsum (for fast and accurate block summation"") that applies a fast summation algorithm (such as recursive summation) blockwise and then sums the partial sums using an accurate summation algorithm (such as compensated summation, or recursive summation in higher precision). We give a rounding error analysis to show that FABsum with a fixed block size b has a backward error bound (b + 1)u + O(u 2), which is independent of n to first order. Our computational experiments show that with a suitable choice of b (independent of n) FABsum can deliver substantially more accurate results than blocked recursive summation, with only a modest drop in performance. FABsum is especially attractive for low precisions, where it can provide correct digits for much larger n than recursive summation.

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Section: Matrix Multiplicationmentioning

confidence: 99%

“…In section 5.1 we experiment with summation using MATLAB R2018b. In section 5.2 we present performance and accuracy results with PLASMA [6], a state-ofthe-art numerical linear algebra library that we have modified by integrating FABsum.…”

mentioning

confidence: 99%

A Class of Fast and Accurate Summation Algorithms

Blanchard¹,

Higham²,

Mary³

2020

SIAM J. Sci. Comput.

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“…In our calculations a custom implementation of this algorithm inspired by the PLASMA library [39] was utilized with custom vectorization of quaddouble arithmetics based on Bailey's quad-double precision algorithms [40]. Incorporation of both the communication-avoiding variant of Aasen's factorization and vectorized quad-double arithmetics constitutes a very efficient implementation of dense matrix factorization -an essential component of the inverse iteration method with nonorthogonal bases.…”

Section: Methodsmentioning

confidence: 99%

Accurate Born-Oppenheimer potentials for excited $Σ^{+}$ states of the hydrogen molecule

Siłkowski,

Zientkiewicz,

Pachucki

2021

Preprint

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We report on highly accurate calculations of Born-Oppenheimer potentials for excited n Σ + states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to n = 7. A relative accuracy of 10 −10 (0.00002 cm −1 ) or better is achieved for all the internuclear distances and all the excited states under considerationan improvement with respect to the best results available in the literature by at least 6 orders of magnitude. Presented variational calculations rely on efficient evaluation of molecular integrals with the explicitly correlated exponential basis in arbitrary precision arithmetics.

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“…Paper [17] presents PLASMA-the Parallel Linear Algebra Software for Multicore Architectures-a version which is an OpenMP task based implementation adopting a tilebased approach to storage, along with algorithms that operate on tiles and use OpenMP for dynamic scheduling based on tasks with dependencies and priorities. Detailed assessment of the software performance is presented in the paper using three platforms with 2 × Intel Xeon CPU E5-2650 v3 CPUs at 2.3 GHz, Intel Xeon Phi 7250 and 2 × IBM POWER8 CPUs at 3.5 GHz, respectively, using gcc compared to MKL (for Intel) and ESSL (for IBM).…”

Section: Openmp Related Framework and Layers For Parallelizationmentioning

confidence: 99%

Assessment of OpenMP Master–Slave Implementations for Selected Irregular Parallel Applications

Czarnul

2021

Electronics

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The paper investigates various implementations of a master–slave paradigm using the popular OpenMP API and relative performance of the former using modern multi-core workstation CPUs. It is assumed that a master partitions available input into a batch of predefined number of data chunks which are then processed in parallel by a set of slaves and the procedure is repeated until all input data has been processed. The paper experimentally assesses performance of six implementations using OpenMP locks, the tasking construct, dynamically partitioned for loop, without and with overlapping merging results and data generation, using the gcc compiler. Two distinct parallel applications are tested, each using the six aforementioned implementations, on two systems representing desktop and worstation environments: one with Intel i7-7700 3.60GHz Kaby Lake CPU and eight logical processors and the other with two Intel Xeon E5-2620 v4 2.10GHz Broadwell CPUs and 32 logical processors. From the application point of view, irregular adaptive quadrature numerical integration, as well as finding a region of interest within an irregular image is tested. Various compute intensities are investigated through setting various computing accuracy per subrange and number of image passes, respectively. Results allow programmers to assess which solution and configuration settings such as the numbers of threads and thread affinities shall be preferred.

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Plasma

Cited by 40 publications

References 36 publications

A Class of Fast and Accurate Summation Algorithms

A Class of Fast and Accurate Summation Algorithms

Accurate Born-Oppenheimer potentials for excited $Σ^{+}$ states of the hydrogen molecule

Assessment of OpenMP Master–Slave Implementations for Selected Irregular Parallel Applications

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