Advanced Computer Arithmetic

Aim

By the end of the class, the student should be able to analyze and design high performance arithmetic blocks for use in the data-path of large digital systems.

Recommended Texts

• Digital Arithmetic, Milos  D. Ercegovac and Tomas Lang; Morgan Kaufmann 2004, Library code: CSI 112.
• Advanced Computer Arithmetic Design, Michael J. Flynn and Stuart Oberman; Pub John Wiley 2001, Library code: CSI 111.
• Computer Arithmetic: Algorithms and Hardware Designs, Behrooz Parhami; Oxford University Press 2001
• Computer Arithmetic Algorithms, Israel Koren; Pub A K Peters 2002, Library code: CSI 114.
• Elementary Functions Algorithms and Implementation, Jean-Michel Muller; Birkhauser 2006, Library code: CSI 113.
• Synthesis of Arithmetic Circuits, Jean-Pierre Deschamps, Gery Bioul, and Gustavo Sutter; John Wiley 2006, Library code: LOG 26.
• Computer Arithmetic Systems, Amos Omondi, Library code: CAR 24.

Other text, lecture slide handouts, and notes are on the web.

Introduction

Arithmetic is the science of handling numbers and operating on them. This course is about the arithmetic done on computers. To fulfill its purpose, there is a need to describe the computer representations of the different numbers that humans use and the implementation of the basic mathematical operations such as addition, subtraction, multiplication and division. These operations can be implemented in software or in hardware. The focus of this class is to introduce the hardware aspects of computer arithmetic. The enhancements to improve the usual performance metrics (speed, area, and power) are discussed and the students are expected to use them in their projects. We will actually look at some of the designs used in commercial processors as well as the recent research in the field.

Assessment

Tentative schedule

Handouts

Book

A draft of the new/old book is available, please provide me with your comments.

Lecture notes

• Lecture 01 "What is Computer Arithmetic?"
• Lecture 02 "Introduction to Floating Point Numbers" , A draft of the standard , Useful wikipedia page
• Lecture 03 "Decimal and the `fine print' of the standard"
• Lecture 04 "Are there any limits?"
• Lecture 05 "Time bounds"
• Lecture 06 "1+1=10"
• Lecture 07 "Go forth and multiply"
• Lecture 08 "The big summation"
• Lecture 09 "Division"
• Lecture 10 "One fast unit for division and square root"
• Lecture 11 "Learning how to add two numbers" (A sample design)
• Midterm solution
• Lecture 12 "Recent adders" (Subnormal numbers) (Hexadecimal and binary) (Packet forwarding adder) (Comparative analysis) (Detailed design)
• Lecture 13 "(Re)Learning the multiplication" (FMA and wide divider)
• Invited lecture by Prof. David M. Harris on the generalization of Ling adders titled Jackson adders. (Also see his paper on the taxonomy of adders.)
• Lecture 14 "Tables and series: for many functions"
• Lecture 15 "Decimal Floating Point Units" (Decimal BID adder) (Decimal BID rounder) (Decimal Mul) (Decimal HW and energy)
• Lecture 16 "Elementary functions"
• Lecture 17 "Arithmetic: linking the past to the future" (Scaling, power, and the future) (Stream processor)