High Performance Arithmetic Units

A good optimization of the arithmetic blocks results in an improved datapath which directly leads to a better overall design. Such an optimization might be to improve the speed of operation, to lower the power consumption, to lower the cost of the circuit (usually related to the number of gates used or the area on the chip), or to improve any other desired factor. As the different possibilities for implementing the arithmetic operations are explored, we discover that the designer has a large array of techniques to use in order to fulfill the desired outcome. A skilled designer chooses the best technique for the problem at hand. We hope to help future designers make these informed choices by presenting different techniques and tools to measure the different factors for the options that they evaluate.

Related conferences

Journals that publish computer arithmetic articles

There are obviously journals from technical publishers

• IEEE Transactions on Computers
• IEEE Transactions on Circuits and Systems-I
• IEEE Transactions on VLSI
• IET Computers and Digital Techniques
• IET Circuits, Devices, and Systems
• Computers and Electrical Engineering
• The Computer Journal
• Integration, the VLSI Journal
• The Microelectronics Journal
• Journal of Signal Processing Systems
• The CSI Journal of Computer Science and Engineering

There are some online journals from the companies in the field

• IBM journals
• HP Technical Reports

Here are some other lists of journals

• Big list of journals and conferences
• ACM list of journals/transactions
• IEEE Journals, Transactions, and Magazines

Arithmetic disasters

• Bad numerical computing
• Numerical errors
• Software bugs

Some sub-fields with a few representative pages

Basic notions

Arithmetic in general, not just on computers

• What is arithmetic?
• Elementary arithmetic
• Binary system
• Computer arithmetic sub-fields

Number systems and redundant representations

How do we represent integers and manipulate them?

• Behrooz Parhami
• Israel Koren
• Peter Kornerup

Floating point units and the IEEE standard

What about fractions?

• David Matula
• William Kahan
• David Hough (revision of the standard)

Algorithms and implementations: Addition, Multiplication, and Division

How is arithmetic done in current and future hardware?

• Michael Flynn
• Vojin Oklobdzija
• Milos Ercegovac
• Sorin Cotofana

Elementary functions

These are the famous exp(x), sin(x), ...

• Jean-Michel Muller
• Elisardo Antelo

Decimal Arithmetic

Quite important for financial applications. Most people think in decimal anyway!

• Mike Cowlishaw
• Michael Schulte

Accurate arithmetic

Can we be "sure" of the results?

• Valerie Menissier-Morain
• Interval Computations community
• David Hough (validlab)
• Paul Zimmermann
• Institute for Reliable Computing
• C library for multiple-precision floating-point computations
• Arithmos : a reliable integrated computational environment
• GNU Multiple Precision Arithmetic Library

Formal proofs

• Marc Daumas

Applications

Graphics, signal processing, and cryptography.

• Why use floating point for graphics?
• Signal Arithmetic
• work on Galois field
• Finite field arithmetic and Galois fields

Classes on computer arithmetic

Many good classes cover different aspects

• My own class!
• Stanford, USA
• TIMA, France (with animated applets)
• George Mason University, USA
• UC Santa Barbara, USA
• University of Massachusetts, USA

Other topics

Bibliography, Tools, ...

• Floating Point bibliography
• Elementary functions computation bibliography
• Library of Arithmetic Units (VHDL)
• Fixed point arithmetic (in VHDL)
• Library for Integer and Modular Arithmetic (VHDL)
• Digital Computer Arithmetic Datapath Design Using Verilog HDL
• Arithmetic Module Generator
• A dedicated language for describing computer arithmetic algorithms
• Many good examples (with complete VHDL code) especially for finite-fields circuits