scholarly journals Rigorous Estimation of Floating-Point Round-Off Errors with Symbolic Taylor Expansions

2019 ◽  
Vol 41 (1) ◽  
pp. 1-39 ◽  
Author(s):  
Alexey Solovyev ◽  
Marek S. Baranowski ◽  
Ian Briggs ◽  
Charles Jacobsen ◽  
Zvonimir Rakamarić ◽  
...  
Keyword(s):  
Floating Point ◽  
Taylor Expansions

scholarly journals Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions

2015 ◽  
pp. 532-550 ◽  
Author(s):  
Alexey Solovyev ◽  
Charles Jacobsen ◽  
Zvonimir Rakamarić ◽  
Ganesh Gopalakrishnan
Keyword(s):  
Floating Point ◽  
Taylor Expansions

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.

Floating Point Operations in PipeRench CGRA

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

Export Citation Format

Share Document