- Cover Page
- Half Title Page
- Title Page
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Part 1 A New Number Format: The Unum
- Chapter 1 Overview
- Chapter 2 Building up to the unum format
- Chapter 3 The “original sin” of computer arithmetic
- Chapter 4 The complete unum format
- 4.1 Overcoming the tyranny of fixed storage size
- 4.2 The IEEE Standard float formats
- 4.3 Unum format: Flexible range and precision
- 4.4 How can appending extra bits save storage?
- 4.5 Ludicrous precision? The vast range of unums
- 4.6 Changing environment settings within a computing task
- 4.7 The reference prototype
- 4.8 Special values in a flexible precision environment
- 4.9 Converting exact unums to real numbers
- 4.10 A complete exact unum set for a small utag
- 4.11 Inexact unums
- 4.12 A visualizer for unum strings
- Chapter 5 Hidden scratchpads and the three layers
- Chapter 6 Information per bit
- Chapter 7 Fixed-size unum storage
- Chapter 8 Comparison operations
- Chapter 9 Add/subtract, and the unbiased rounding myth
- Chapter 10 Multiplication and division
- Chapter 11 Powers
- 11.1 Square
- 11.2 Square root
- 11.3 Nested square roots and “ULP straddling”
- 11.4 Taxing the scratchpad: Integers to integer powers
- 11.5 A practice calculation of xy at low precision
- 11.6 Practical considerations and the actual working routine
- 11.7 Exp(x) and “The Table-Maker’s Dilemma”) and “The Table-Maker’s Dilemma”
- Chapter 12 Other important unary operations
- Chapter 13 Fused operations (single-use expressions)
- Chapter 14 Trial runs: Unums face challenge calculations
- Part 1 Summary
- Part 2 A New Way to Solve: The Ubox
- Chapter 15 The other kind of error
- 15.1 Sampling error
- 15.2 The deeply unsatisfying nature of classical error bounds
- 15.3 The ubox approach
- 15.4 Walking the line
- 15.5 A ubox connected-region example: Computing the unit circle area
- 15.6 A definition of answer quality and computing “speed”
- 15.7 Another Kahan booby trap: The “smooth surprise”
- Chapter 16 Avoiding interval arithmetic pitfalls
- Chapter 17 What does it mean to “solve” an equation?
- Chapter 18 Permission to guess
- Chapter 19 Pendulums done correctly
- Chapter 20 The two-body problem (and beyond)
- Chapter 21 Calculus considered evil: Discrete physics
- Chapter 22 The end of error
- Chapter 15 The other kind of error
- Glossary
- Appendix A: Glossary of unum functions
- A.1 Environment and bit-extraction functions
- A.2 Constructors
- A.3 Visualization functions
- A.4 Conversion functions
- A.5 Argument validity tests
- A.6 Helper functions for functions defined above
- A.7 Comparison operations
- A.8 Arithmetic operations
- A.9 Fused operations (single-use expressions)
- A.10 Some defined data values
- A.11 Auto-precision functions
- Appendix B: Glossary of ubox functions
- Appendix C: Algorithm listings for Part 1
- C.1 The set-the-environment function
- C.2 Type-checking functions
- C.3 The unum-to-float converter and supporting functions
- C.4 The u-layer to general interval conversions
- C.5 The real-to-unum or x" conversion function
- C.6 Unification functions and supporting functions
- C.7 The general interval to unum converter
- C.8 Comparison tests and ubound intersection
- C.9 Addition and subtraction functions
- C.10 Multiplication functions
- C.11 Division routines
- C.12 Automatic precision adjustment functions
- C.13 Fused operations (single-use expressions)
- C.14 Square and square root
- C.15 The power function xy and exp(x)
- C.16 Absolute value, logarithm, and trigonometry functions
- C.17 The unum Fast Fourier Transform
- Appendix D: Algorithm listings for Part 2
- For Further Reading
- Index
THE END of
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Unum Computing
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