- Copyright
- Foreword
- Preface
- Chapter 1. Introduction
- Chapter 2. Basics
- Manipulating Rightmost Bits
- Addition Combined with Logical Operations
- Inequalities among Logical and Arithmetic Expressions
- Absolute Value Function
- Sign Extension
- Shift Right Signed from Unsigned
- Sign Function
- Three-Valued Compare Function
- Transfer of Sign
- Decoding a "Zero Means 2**n" Field
- Comparison Predicates
- Overflow Detection
- Condition Code Result of Add, Subtract, and Multiply
- Rotate Shifts
- Double-Length Add/Subtract
- Double-Length Shifts
- Multibyte Add, Subtract, Absolute Value
- Doz, Max, Min
- Exchanging Registers
- Alternating among Two or More Values
- Chapter 3. Power-of-2 Boundaries
- Rounding Up/Down to a Multiple of a Known Power of 2
- Rounding Up/Down to the Next Power of 2
- Detecting a Power-of-2 Boundary Crossing
- Chapter 4. Arithmetic Bounds
- Checking Bounds of Integers
- Propagating Bounds through Add's and Subtract's
- Propagating Bounds through Logical Operations
- Chapter 5. Counting Bits
- Chapter 6. Searching Words
- Chapter 7. Rearranging Bits and Bytes
- Reversing Bits and Bytes
- Shuffling Bits
- Transposing a Bit Matrix
- Compress, or Generalized Extract
- General Permutations, Sheep and Goats Operation
- Rearrangements and Index Transformations
- Chapter 8. Multiplication
- Multiword Multiplication
- High-Order Half of 64-Bit Product
- High-Order Product Signed from/to Unsigned
- Multiplication by Constants
- Chapter 9. Integer Division
- Chapter 10. Integer Division by Constants
- Signed Division by a Known Power of 2
- Signed Remainder from Division by a Known Power of 2
- Signed Division and Remainder by Non-Powers of 2
- Signed Division by Divisors greater than or equal to 2
- Signed Division by Divisors less than or equal to -2
- Incorporation into a Compiler
- Miscellaneous Topics
- Unsigned Division
- Unsigned Division by Divisors greater than or equal to 1
- Incorporation into a Compiler (Unsigned)
- Miscellaneous Topics (Unsigned)
- Applicability to Modulus and Floor Division
- Similar Methods
- Sample Magic Numbers
- Exact Division by Constants
- Test for Zero Remainder after Division by a Constant
- Chapter 11. Some Elementary Functions
- Chapter 12. Unusual Bases for Number Systems
- Chapter 13. Gray Code
- Chapter 14. Hilbert's Curve
- A Recursive Algorithm for Generating the Hilbert Curve
- Coordinates from Distance along the Hilbert Curve
- Distance from Coordinates on the Hilbert Curve
- Incrementing the Coordinates on the Hilbert Curve
- Non-recursive Generating Algorithms
- Other Space-Filling Curves
- Applications
- Chapter 15. Floating-Point
- IEEE Format
- Comparing Floating-Point Numbers Using Integer Operations
- The Distribution of Leading Digits
- Table of Miscellaneous Values
- Chapter 16. Formulas for Primes
- Appendix A. Arithmetic Tables for a 4-Bit Machine
- Appendix B. Newton's Method
- Bibliography