The Computer Arithmetic course is about how to design an Arithmetic
Logic Unit (ALU) and a Floating Point Unit. The course deals with the
mathematical foundation as well as the hardware implementation.
Thursdays, 16-18, Room 207, Kitot Building.
Time to start thinking about projects. About 5 pairs of students may
do a project instead of the final exam. Students interested in doing
a project will have to be already halfway in completing the project by
the end of the semester. So it is about time to consider working on
it. I am open to suggestions, but am also providing a ``list'' of
- Timing analysis of the Seidel-Even FP-ADD algorithm. This
project requires access to a simulation tool with timing analysis.
One can also download some free simulators. Timing analysis
requires gate level description and should take into account not
only gate delays but also loads and fanouts. Wire delays are harder
to account for, unfortunately...
- Error analysis of iterative division algorithms. This topic
requires using using some multi-precision software such as
Mathematica, Maple, or simple bc. The goal is to design a software
tool that will analyze the precision of a (floating point) divider
(i.e. is the initial approximation good enough? are intermediate
multiplications precise enough? etc.).
- Hardware and software projects related to arithmetic
applications on smart cards. Topics can be related to implementing
cryptographic applications, arithmetic co-processors, etc.
- Recodings. There are three references for this topic. See also
references mentioned within these papers.
- Partial Compression and
by Daumas, Even, and Matula.
- Further reducing the redundancy of a
notation over a minimally redundant digit
by Daumas and Matula.
- An IEEE compliant floating-point adder that
conforms with the pipelined packet-forwarding
by Nielsen, Matula, Lyu, and Even, in IEEE Transactions on
Computers, Vol. 49, No. 1, pp. 33-47, January 2000.
- IEEE standard on floating point arithmetic.
- On the design of IEEE compliant floating
by Even and Paul, IEEE Transactions on Computers Volume: 49 Issue:
5 , May 2000.
- Arnon Warshavsky's IEEE floating point demo.
I needed to install some DLL files from here.
- The Decomposition Theorem for IEEE Floating
By S. M.
Müller and W.J. Paul.
- IEEE rounding (injection based rounding)
- Guy Even, Silvia M. Müller, and Peter-Michael Seidel,
A Dual Precision IEEE Floating-Point
Integration, The VLSI Journal, Volume 29, Issue 2, pp. 167-180,
- Floating Point Multiplication. A comparison
of three rounding algorithms for IEEE floating-point
by Even and Seidel, Page(s): 638 -650, IEEE Transactions on
Computers, Volume: 49 Issue: 7 , July 2000.
- Floating-Point Addition.
- On the Design of Fast IEEE Floating-Point
by Peter Seidel and Guy Even.
- Floating Point Division
- Floating Point Division and Square Root
Algorithms and Implementation in the AMDK7
S. Oberman - Advanced Micro Devices. Paper from 14th IEEE
Symposium on Computer Arithmetic Adelaide, Australia April 14 -
16, 1999. (click on the posrtscript version)
- A draft of a paper on an error analysis of
Goldschmidt's division algorithm by Even, Seidel, and Feguson.
- List of references.
- Class Notes written in the past two years by students taking the
course. Some of these class notes are pretty good - however, read
with a (big) grain of salt.