A New Book on Computer Arithmetic

[Amos Omondi]

ANNOUNCING A NEW BOOK ON COMPUTER ARITHMETIC
============================================


Title:	 	Computer Arithmetic Systems -- Algorithms, Architecture, 
		Implementation.  522 pages.  
Author:	 	Amos R. Omondi
Publisher:	Prentice-Hall International, UK
		(CAR Hoare series in Computer Science)
ISBN:		0-13-334301-4
Date:		1994


Short description of the book
============================

This book attempts to do for the 1990s what Flores's "Logic of Computer 
Arithmetic" did for the 1960s.  It covers much more than any other book 
currently available on the subject.  

Detailed description of the book
===============================

This book is primarily intended to be a text for postgraduate and advanced
undergraduate students in computer science,  computer engineering, and 
electrical engineering, and the chief concern has been to cater to the needs
of these groups.  Nevertheless, professionals engaged in the design and 
and implementation of digital computers will also find the book useful 
as a reference manual, as will prospective researchers in the field of 
computer arithmetic.  

Small selected parts of the book can be used as supplementary 
material in courses on computer architecture and implementation.  Larger 
parts, comprising about half the book, 
 can be used as the basis of an undergraduate course devoted entirely to 
computer arithmetic; a similar course at the postgraduate level can 
reasonably cover 
most, if not all, of the book.  
Whatever the use of the book, 
it is assumed that the reader has a reasonable background 
knowledge of digital logic design techniques, 
such as can be obtained from a good first course.  
For a few sections of the book,  
an acquaintance with  basic numerical analysis would be helpful but 
is not altogether indispensable.  

The book is divided into three major 
parts.  The first part consists of four chapters and is devoted  to 
algorithms and hardware for basic arithmetic 
operations in conventional fixed-point number systems.  
The second part consists of three chapters, 
the subject of which is various aspects of 
floating-point number systems  and 
algorithms and hardware for operations in these systems.    
The third part is a single chapter that 
deals with unconventional number representations and arithmetic. 
(The third part, because of  limitations 
of space, 
is intended to be no more than a brief introduction to the subjects 
discussed.)  
A number of case studies are included where appropriate. In reviewing
these case studies, especially the older ones, 
the reader should distinguish between some logical
design technique and an instance of the same; that is, architecture,
implementation,  and realization should be separated and the effects of
one on another recognized.

Part I: The first chapter is a brief introduction to the commonly used 
fixed-point number representations.  
The second, third, and fourth chapters deal with algorithms 
and hardware for addition and subtraction, multiplication, and division.  
Part II: 
The fifth chapter is mainly a discussion of various 
abstract features of floating-point number 
 systems and their concrete representation within a computer.
Basic error analysis is introduced in this chapter, and related topics, 
such as rounding, are also discussed.  The sixth
chapter deals with hardware structures for the implementation of the basic 
floating-point arithmetic operations, and 
the seventh covers the elementary functions:  
square root, 
sine, cosine, logarithms, exponential, and so forth.  
Part III: 
The  eighth chapter of the book 
deals with unconventional 
number systems and corresponding algorithms and hardware for the basic 
arithmetic 
operations. Three number systems are discussed there: 
redundant signed-digit, residue, and decimal.

There are three appendices.  The first is a brief 
introduction to pipelining, an important technique in the design of 
high-performance 
computers.  Pipelining is normally covered in depth in 
a course on computer architecture but is nevertheless 
of some importance 
here.  The second appendix is a discussion on the design of shifters, a
subject that gets short shrift in most textbooks and courses on digital logic 
design.   
The last appendix is a design library.  It  
consists of detailed descriptions of some commercial 
integrated-circuit modules and is 
to be used as the basis of various design exercises.  This appendix 
has been bound separately and can be obtained by writing to the publisher; 
alternatively, a suitable databook may be substituted.    


Table of contents
=================
(A detailed table of contents is available, in the form of a LaTeX "toc" file, 
 by e-mail.)

1. Fixed-point number systems
	1.1 Introduction
	1.2 Representing signed numbers
	1.3 Other fixed-point number systems
	1.4 Summary
	1.5 Bibliographic notes
	1.6 Exercises

2. Fixed-point addition and subtraction
	2.1 Algorithms
	2.2 Implementation 
	2.3 Subtraction
 	2.4 Case studies
	2.5 Bibliographic notes
	2.6 Exercises

3. Fixed-point multiplication 
	3.1 Basic algorithms
	3.2 Fast multiplication
	3.3 Evaluation of powers
	3.4 Implementation 
 	3.5 Case studies
	3.6 Bibliographic notes
	3.7 Exercises

4. Fixed-point division 
	4.1 Basic algorithms
	4.2 Fast division 
	4.3 Implementation 
 	4.4 Case studies
	4.5 Bibliographic notes
	4.6 Exercises

5. Floating-point arithmetic
	5.1 Introduction
	5.2 Normalization
	5.3 Basic arithmetic operations
	5.4 Overflow and underflow
	5.5 Representation format
	5.6 Error analysis
	5.7 Case studies
	5.8 Bibliographic notes
	5.9 Exercises

6. Basic floating-point operations: implementation
	6.1 Rounding
	6.2 Addition and subtraction 
	6.3 Multiplication and division
	6.4 Summary
	6.5 Bibliographic notes
	6.6 Exercises

7. Elementary functions
	7.1 Square root and related functions
	7.2 Trigonometric functions
	7.3 Exponential and logarithm functions
	7.4 Polynomial approximations
	7.5 Summary
	7.6 Case study
	7.7 Bibliographic notes
	7.8 Exercises
	
8. Unconventional number systems and arithmetic
	8.1 Residue number systems and arithmetic
	8.2 Decimal number systems and arithmetic
	8.3 Redundant signed-digit number systems and arithmetic
	8.4 Bibliographic notes
	8.5 Exercises


Bibliography

Appendix A: Pipelining

Appendix B: Design of shifters