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’.

Implementation of Embedded Floating Point Arithmetic Units on FPGA

2014 ◽  
Vol 550 ◽  
pp. 126-136
Author(s):  
N. Ramya Rani
Keyword(s):  
High Speed ◽  
High Performance ◽  
Floating Point ◽  
Double Precision ◽  
Embedded Computing ◽  
Floating Point Arithmetic ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Arithmetic Units ◽  
Point Arithmetic

:Floating point arithmetic plays a major role in scientific and embedded computing applications. But the performance of field programmable gate arrays (FPGAs) used for floating point applications is poor due to the complexity of floating point arithmetic. The implementation of floating point units on FPGAs consumes a large amount of resources and that leads to the development of embedded floating point units in FPGAs. Embedded applications like multimedia, communication and DSP algorithms use floating point arithmetic in processing graphics, Fourier transformation, coding, etc. In this paper, methodologies are presented for the implementation of embedded floating point units on FPGA. The work is focused with the aim of achieving high speed of computations and to reduce the power for evaluating expressions. An application that demands high performance floating point computation can achieve better speed and density by incorporating embedded floating point units. Additionally this paper describes a comparative study of the design of single precision and double precision pipelined floating point arithmetic units for evaluating expressions. The modules are designed using VHDL simulation in Xilinx software and implemented on VIRTEX and SPARTAN FPGAs.

Floating point arithmetic teaching for computational science

2003 ◽  
Vol 19 (8) ◽  
pp. 1321-1334 ◽  
Author(s):  
José-Jesús Fernández ◽  
Inmaculada Garcı́a ◽  
Ester M. Garzón
Keyword(s):  
Computational Science ◽  
Floating Point ◽  
Floating Point Arithmetic ◽  
Arithmetic Teaching ◽  
Point Arithmetic

High-Performance FPGA-Based CNN Accelerator With Block-Floating-Point Arithmetic

2019 ◽  
Vol 27 (8) ◽  
pp. 1874-1885 ◽  
Author(s):  
Xiaocong Lian ◽  
Zhenyu Liu ◽  
Zhourui Song ◽  
Jiwu Dai ◽  
Wei Zhou ◽  
...  
Keyword(s):  
High Performance ◽  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

scholarly journals Fuzzy Processing Implementation in Dedicated Digital Hardware

2010 ◽  
Vol 56 (4) ◽  
pp. 405-410 ◽  
Author(s):  
Przemysław Szecówka ◽  
Adam Musiał
Keyword(s):  
Fuzzy Sets ◽  
High Performance ◽  
Digital Circuit ◽  
Synchronous Machine ◽  
Floating Point ◽  
Weighted Sum ◽  
Sample Design ◽  
Floating Point Arithmetic ◽  
Digital Hardware ◽  
Point Arithmetic

Fuzzy Processing Implementation in Dedicated Digital HardwareThe paper presents a concept of digital circuit dedicated for fuzzy processing with numerical inputs and outputs. Partially concurrent and pipelined data flow provides high performance, with relatively low dependence on particular algorithm complexity. Sample design with triangular fuzzy sets, rule strength calculation (minimumapproach) and defuzzyfication by weighted sum of fuzzy sets centers was implemented in VHDL, verified and synthesized for FPGA. Floating point arithmetic was applied, including dvision performed by dedicated synchronous machine. All modules were prepared for easy reuse/redesign.

scholarly journals Generation of test matrices with specified eigenvalues using floating-point arithmetic

2021 ◽  
Author(s):  
Katsuhisa Ozaki ◽  
Takeshi Ogita
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Algorithms ◽  
Numerical Linear Algebra ◽  
Floating Point ◽  
Diagonal Form ◽  
Floating Point Arithmetic ◽  
Complex Eigenvalues ◽  
Test Matrices ◽  
Block Diagonal Form ◽  
Point Arithmetic

AbstractThis paper concerns test matrices for numerical linear algebra using an error-free transformation of floating-point arithmetic. For specified eigenvalues given by a user, we propose methods of generating a matrix whose eigenvalues are exactly known based on, for example, Schur or Jordan normal form and a block diagonal form. It is also possible to produce a real matrix with specified complex eigenvalues. Such test matrices with exactly known eigenvalues are useful for numerical algorithms in checking the accuracy of computed results. In particular, exact errors of eigenvalues can be monitored. To generate test matrices, we first propose an error-free transformation for the product of three matrices YSX. We approximate S by ${S^{\prime }}$ S ′ to compute ${YS^{\prime }X}$ Y S ′ X without a rounding error. Next, the error-free transformation is applied to the generation of test matrices with exactly known eigenvalues. Note that the exactly known eigenvalues of the constructed matrix may differ from the anticipated given eigenvalues. Finally, numerical examples are introduced in checking the accuracy of numerical computations for symmetric and unsymmetric eigenvalue problems.

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