scholarly journals Implementation and Performance Evaluation of an Extended Precision Floating-Point Arithmetic Library for High-Accuracy Semidefinite Programming

2017 ◽  
Author(s):  
Mioara Joldes ◽  
Jean-Michel Muller ◽  
Valentina Popescu
Keyword(s):  
Performance Evaluation ◽  
Semidefinite Programming ◽  
High Accuracy ◽  
Floating Point ◽  
Floating Point Arithmetic ◽  
And Performance ◽  
Point Arithmetic

scholarly journals Performance/accuracy trade-offs of floating-point arithmetic on NVidia GPUs : from a characterization to an auto-tuner

2017 ◽  
Author(s):  
◽  
Sruthikesh Surineni
Keyword(s):  
Floating Point ◽  
Processing Unit ◽  
Double Precision ◽  
Graphic Processing Units ◽  
Arithmetic Operations ◽  
Floating Point Arithmetic ◽  
Performance Accuracy ◽  
Trade Offs ◽  
And Performance ◽  
Point Arithmetic

Floating-point computations produce approximate results, possibly leading to inaccuracy and reproducibility problems. Existing work addresses two issues: first, the design of high precision floating-point representations, and second, the study of methods to support a trade-off between accuracy and performance of central processing unit (CPU) applications. However, a comprehensive study of trade-offs between accuracy and performance on modern graphic processing units (GPUs) is missing. This thesis covers the use of different floating-point precisions (i.e., single and double floating-point precision) in the IEEE 754 standard, the GNU Multiple Precision Arithmetic Library (GMP), and composite floating-point precision on a GPU using a variety of synthetic and real-world benchmark applications. First, we analyze the support for a single and double precision floating-point arithmetic on the considered GPU architectures, and we characterize the latencies of all floating-point instructions on GPU. Second, a study is presented on the performance/accuracy tradeoffs related to the use of different arithmetic precisions on addition, multiplication, division, and natural exponential function. Third, an analysis is given on the combined use of different arithmetic operations on three benchmark applications characterized by different instruction mixes and arithmetic intensities. As a result of this analysis, a novel auto tuner was designed in order to select the arithmetic precision of a GPU program leading to a better performance and accuracy tradeoff depending on the arithmetic operations and math functions used in the program and the degree of multithreading of the code.

scholarly journals Numerical algorithms for high-performance computational science

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190066 ◽  
Author(s):  
Jack Dongarra ◽  
Laura Grigori ◽  
Nicholas J. Higham
Keyword(s):  
High Performance ◽  
Numerical Algorithms ◽  
Computational Science ◽  
Floating Point ◽  
Important Criterion ◽  
Data Movement ◽  
Floating Point Arithmetic ◽  
High Performance Computers ◽  
Point Arithmetic ◽  
Speed And Accuracy

A number of features of today’s high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

Fast and robust mesh arrangements using floating-point arithmetic

2020 ◽  
Vol 39 (6) ◽  
pp. 1-16
Author(s):  
Gianmarco Cherchi ◽  
Marco Livesu ◽  
Riccardo Scateni ◽  
Marco Attene
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

Floating-point arithmetic with 84-bit numbers

1964 ◽  
Vol 7 (1) ◽  
pp. 10-13 ◽  
Author(s):  
Robert T. Gregory ◽  
James L. Raney
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic
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