The End of Error

Contents

Preface

Acknowledgments

How to read this book

Part 1A New Number Format: The Unum

Chapter 1 Overview

1.1 Fewer bits. Better answers

1.2 Why better arithmetic can save energy and power

Chapter 2 Building up to the unum format

2.1 A graphical view of bit strings: Value and closure plots

2.2 Negative numbers

2.3 Fixed point format

2.4 Floating point format, almost

2.5 What about infinity and NaN? Improving on IEEE rules

Chapter 3 The “original sin” of computer arithmetic

3.1 The acceptance of incorrect answers

3.2 “Almost infinite” and “beyond infinity”

3.3 No overflow, no underflow, and no rounding

3.4 Visualizing ubit-enabled numbers

Chapter 4 The complete unum format

4.1 Overcoming the tyranny of fixed storage size

4.2 The IEEE Standard ...