Instruction Set and Execution Time Model.
Addition Combined with Logical Operations.
Inequalities among Logical and Arithmetic Expressions.
Shift Right Signed from Unsigned.
Transfer of Sign.
Decoding a “Zero Means 2**n” Field.
Condition Code Result of Add, Subtract, and Multiply.
Multibyte Add, Subtract, Absolute Value.
Doz, Max, Min.
Alternating among Two or More Values.
3. Power-of-2 Boundaries.
Rounding up/down to the Next Power of 2.
Detecting a Power-of-2 Boundary Crossing.
4. Arithmetic Bounds.
Propagating Bounds through Adds and Subtracts.
Propagating Bounds through Logical Operations.
5. Counting Bits.
Counting Leading Zeros.
Counting Trailing Zeros.
6. Searching Words.
Find First String of 1-bits of a Given Length.
7. Rearranging Bits and Bytes.
Transposing a Bit Matrix.
Compress, or Generalized Extract.
General Permutations, Sheep and Goats Operation.
Rearrangements and Index Transformations.
High-order Half of 64-bit Product.
High-order Product Signed from/to Unsigned.
Multiplication by Constants.
9. Integer Division.
Unsigned Short Division from Signed Division.
Unsigned Long Division.
10. Integer Division by Constants.
Signed Remainder from Division by a Known Power of 2.
Signed Division and Remainder by Non-powers of 2.
Signed Division by Divisors >= 2.
Signed Division by Divisors <= -2.
Incorporation into a compiler.
Unsigned Division by Divisors >= 1.
Incorporation into a Compiler (unsigned).
Miscellaneous Topics (unsigned).
Applicability to Nodulus and floor division.
Sample Magic Numbers.
Exact Division by constants.
Test for Zero Remainder after Division by a Bonstant.
11. Some Elementary Functions.
Integer Cube Root.
12. Unusual Bases for Number Systems.
Base -1 + i.
What is the Most Efficient Base?
13. Gray Code.
Incrementing a Gray Coded Integer.
Negabinary Gray Code.
Brief History and Applications.
14. Hilbert's 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.
Comparing Floating-point Numbers Using Integer Operations.
The Distribution of Leading Digits.
Table of Miscellaneous Values.
16. Formulas for Primes.
Formulas for Other Difficult Functions.
Appendix A. Arithmetic Tables for a Four-Bit Machine.
Appendix B. Newton's Method.