Floating Point Operations in PipeRench CGRA

2012 ◽  
Vol 1 (6) ◽  
pp. 67-68
Author(s):  
M. Somasekhar M. Somasekhar ◽  
Keyword(s):  
Floating Point

CONVEYOR MODEL AND IMPLEMENTATION OF THE REAL NUMBERS ADDER ON FPGA

2020 ◽  
Vol 33 (109) ◽  
pp. 21-31
Author(s):  
І. Ya. Zeleneva ◽  
Т. V. Golub ◽  
T. S. Diachuk ◽  
А. Ye. Didenko
Keyword(s):  
Performance Improvement ◽  
Experimental Studies ◽  
Production Costs ◽  
Floating Point ◽  
Computing Device ◽  
Quartus Ii ◽  
Functional Blocks ◽  
Mental Testing ◽  
Processor Cores ◽  
Floating Point Numbers

The purpose of these studies is to develop an effective structure and internal functional blocks of a digital computing device – an adder, that performs addition and subtraction operations on floating- point numbers presented in IEEE Std 754TM-2008 format. To improve the characteristics of the adder, the circuit uses conveying, that is, division into levels, each of which performs a specific action on numbers. This allows you to perform addition / subtraction operations on several numbers at the same time, which increas- es the performance of calculations, and also makes the adder suitable for use in modern synchronous cir- cuits. Each block of the conveyor structure of the adder on FPGA is synthesized as a separate project of a digital functional unit, and thus, the overall task is divided into separate subtasks, which facilitates experi- mental testing and phased debugging of the entire device. Experimental studies were performed using EDA Quartus II. The developed circuit was modeled on FPGAs of the Stratix III and Cyclone III family. An ana- logue of the developed circuit was a functionally similar device from Altera. A comparative analysis is made and reasoned conclusions are drawn that the performance improvement is achieved due to the conveyor structure of the adder. Implementation of arithmetic over the floating-point numbers on programmable logic integrated cir- cuits, in particular on FPGA, has such advantages as flexibility of use and low production costs, and also provides the opportunity to solve problems for which there are no ready-made solutions in the form of stand- ard devices presented on the market. The developed adder has a wide scope, since most modern computing devices need to process floating-point numbers. The proposed conveyor model of the adder is quite simple to implement on the FPGA and can be an alternative to using built-in multipliers and processor cores in cases where the complex functionality of these devices is redundant for a specific task.

Encapsulation and the C++ class

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Program Design ◽  
Internal Representation ◽  
Floating Point ◽  
Complex Class ◽  
Numerical Examples ◽  
Important Notion ◽  
Standard Library

Built-in datatypes and C++ classes are introduced in this chapter, and discussed in relation to the important notion of encapsulation, which refers to the separation between the internal representation of the datatype and the operations to which it responds. Encapsulation later becomes an important consideration in the design of custom C++ classes that programmers develop themselves. It is illustrated with built-in floating-point datatypes float and double and with the complex class from the C++ standard library. While a sophisticated programmer is aware of the internal representation of data and its resulting limitations, encapsulation allows one to consider these as details and frees one to think at a higher level of program design. Some simple numerical examples are discussed in the text and in the exercises.

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’.

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