Computer VLSI Arithmetic

Spring 2004

Prof. Vojin G. Oklobdzija

vojin.oklobdzija@epfl.edu (alternately vojin@acsel-lab.com )
Telephone: TBA
Office Hours: TBA, and by appointment via e-mail

 

Course Description:

This course addresses selected topics in design of arithmetic units for high-performance and low-power systems. In the area of fast VLSI Arithmetic this course will be investigating the relationship between the algorithms and technology, i.e. how efficiently do algorithms map into the specifics of the technology applied.  The knowledge of this relationship enables one to properly select and modify an algorithm so that it would result in the most efficient implementation. There is also a growing interest in low-power and ultra low-power devices and design metrics guiding design of arithmetic units will be addressed.

The course will cover basic arithmetic operations: addition, multiplication, division and square root and evaluation of function with the emphasis on the various ways to implement them in hardware.

 

Project:

The course provides an opportunity to carry a project of student choice. The project may require the use of CAD tools (Cadence, H-Spice, Synopsys) or writing of a simulator. It is possible to complete the project and implement it as an extension of this course (such a thesis project). The project is determined at the beginning of the course. The goal of this project is to provide a possible MSc or PhD thesis, a publication, or provide a valuable  research experience.
 

Useful Computer Arithmetic Hardware Simulator:

Courtesy of Prof. Alain Guyot, TIMA, Grenoble, FRANCE - please see the link bellow in this page.
 

This course is divided into seven sections of study. Outline is as follows:
 

I.             Introduction and Number Representation

II.           Basic Arithmetic Algorithms

III.         Implementation of Addition

IV.         Multiplication

V.           Division

VI.         Square Root

VII.    Evaluation of Functions

 


Prerequisite: BSEE or coursework / experience in logic and circuit design 
 

Text:

  1. V.G. Oklobdzija,  ”Class Notes and Handouts", April, 2001.

  2. Design of High-Performance Microprocessor Circuits ( chapter 10)
    edited by Anantha Chandrakasan, MIT, William Bowhill, Compaq Computer
    2001;Hardcover;2001;ISBN 0-7803-6001-X

  3. Milos Ercegovac, Tomas Lang, "Digital Arithmetic", Morgan Kaufman, 2004. (Link to Book Resources)

Recommended Additional Text

  1. K. Hwang, “Computer Arithmetic, Principles, Architecture, and Design”, New York, NY: John Wiley & Sons, 1979.

  2. B. Parhami, "Computer Arithmetic, Algorithms and Hardware Designs", Oxford University Press, 2000.

 

Useful Link  Op-Art

A very useful link showing simulation of various digital components. Courtesy of Prof. Alain Guyot, TIMA, Grenoble, FRANCE. Please use it and report any errors in English to me or Prof. Alain Guyot directly. From TIMA and

Entrer

Books on Computer Arithmetic

  1. Milos Ercegovac, Tomas Lang, "Digital Arithmetic", Morgan Kaufman, 2004.

  2. B. Parhami, "Computer Arithmetic, Algorithms and Hardware Designs", Oxford University Press, 2000.

  3. I. Koren Computer Arithmetic Algorithms Englewood Cliffs, NJ: Prentice-Hall, 1993.

  4. K. Hwang Computer Arithmetic, Principles, Architecture, and Design New York, NY: John Wiley & Sons, 1979.

  5.  A. R. Omondi Computer Arithmetic Systems: Algorithms, Architecture and Implementations New York, NY: Prentice-Hall, 1994.

  6. J. B. Gosling Design of Arithmetic Units for Digital Computers New York, NY: Springer-Verlag, 1980

  7. U. W. Kulisch and W. L. Miranker Computer Arithmetic in Theory and Practice New York, NY: Academic Press, 1981

  8. J. H. McClellan and C. M. Rader Number Theory in Digital Signal Processing Englewood Cliffs, NJ: Prentice-Hall, 1979

  9. R. K. Richards Arithmetic Operations in Digital Computers Princeton, NJ: D. Van Nostrand, 1955

  10. H. Schmid Decimal Computation Malabar, FL: Robert E. Krieger, 1983

  11. N. R. Scott Computer Number Systems and Arithmetic Englewood Cliffs, NJ: Prentice-Hall, 1985

  12. M. A. Soderstrand, W. K. Jenkins, G. A. Jullien, and F. J. Taylor Residue Arithmetic: Modern Applications in Digital Signal Processing New York, NY: IEEE Press, 1986

  13. E. E. Swartzlander Computer Arithmetic, Volumes I and II Los Alamitos, CA: IEEE Computer Society Press, 1990

  14. N. S. Szabo and R. I. Tanaka Residue Arithmetic and its Applications to Computer TechnologyNew York, NY: McGraw-Hill, 1967

  15. C. Ullrich Computer Arithmetic and Self-Validating Numerical Methods New York, NY: Academic Press, 1990

  16. P. J. L. Wallis Improving Floating-Point Programming New York, NY: John Wiley & Sons, 1990

  17. S. Waser and M. J. Flynn Introduction to Arithmetic for Digital System Designers New York, NY: Holt, Rinehart and Winston, 1982.

  18. J. J. F. Cavanagh, "Digital Computer Arithmetic", New York, NY: McGraw-Hill, 1984.

 

Computer Arithmetic Proceedings

  1. Proceedings of 16th Symposium on Computer Arithmetic J-C. Bajard, M. Schulte (Editors), Santiago de Compostela, Spain, June 15-18, 2003. IEEE Computer Society Press.

  2. Proceedings of 15th Symposium on Computer Arithmetic N. Burges, L. Ciminiera (Editors), Vail, Colorado, June 11-17, 2001. IEEE Computer Society Press.

  3. Proceedings of 14th Symposium on Computer Arithmetic I. Koren, P. Korenerup (Editors), Adelaide, Australia, April 14-16, 1999. IEEE Computer Society Press.

  4. Proceedings of 13th Symposium on Computer Arithmetic T. Lang, J.-M. Muller, and N. Takagi (Editors), Asilomar, California, July 6-9, 1997. IEEE Computer Society Press.

  5. Proceedings of 12th Symposium on Computer Arithmetic L S. Knowles and W. H. McAllister (Editors), Bath, England, July 19 - 21, 1995. IEEE Computer Society Press.

  6. Proceedings of 11th Symposium on Computer Arithmetic E. Swartzlander, Jr., M. J. Irwin, and G. Jullien (Editors), Windsor, Ontario, June 29 - July 2, 1993. IEEE Computer Society Press.

  7. Proceedings of 10th Symposium on Computer Arithmetic P. Kornerup and D. W. Matula (Editors),
    Grenoble, France, June 26 - 28, 1991. IEEE Computer Society Press.

  8. Proceedings of 9th Symposium on Computer Arithmetic M. D. Ercegovac and E. Swartzlander (Editors), Santa Monica, California, September 6 - 8, 1989. IEEE Computer Society Press.

  9. Proceedings of 8th Symposium on Computer Arithmetic M. J. Irwin and R. Stefanelli (Editors), Como, Italy, May 19 - 21, 1987. IEEE Computer Society Press.

  10. Proceedings of 7th Symposium on Computer Arithmetic Kai Hwang, Editor, University of Illinois, Urbana, Illinois, June4-6, 1985.

  11. Proceedings of 6th Symposium on Computer Arithmetic Aarhus, Denmark, June 20 - 22, 1983.

  12. Proceedings of 5th Symposium on Computer Arithmetic Ann Arbor, Michigan, May 18 - 19, 1981.

  13. Proceedings of 4th Symposium on Computer Arithmetic Santa Monica, California, October 25 - 27, 1978.

  14. Proceedings of 3th Symposium on Computer Arithmetic Dullas, Texas, 1975.

  15. Proceedings of 2nd Symposium on Computer Arithmetic Maryland, 1972

  16. Proceedings of 1st Symposium on Computer Arithmetic Minneapolis, Minnesota, 1969