Preface.
1. Introduction.
Notation.
Instruction Set and Execution Time Model.
2. Basis.
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.
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.
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.
4. Arithmetic Bounds.
Checking Bounds of Integers.
Propagating Bounds through Adds and Subtracts.
Propagating Bounds through Logical Operations.
Signed Bounds.
5. Counting Bits.
Counting 1-bits.
Parity.
Counting Leading 0's.
Counting Trailing 0's.
6. Searching Words.
Find First 0-Byte.
Find First String of 1-Bits of a Given Length.
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.
8. Multiplication.
Multiword Multiplication.
High-Order Half of 64-Bit Product.
High-Order Product Signed from/to Unsigned.
Multiplication by Constants.
9. Integer Division.
Preliminaries.
Multiword Division.
Unsigned Short Division from Signed Division.
Unsigned Long Division.
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 >= 2.
Signed Division by Divisors #= -2.
Incorporation into a Compiler.
Miscellaneous Topics.
Unsigned Division.
Unsigned Division by Divisors >= 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.
11. Some Elementary Functions.
Integer Square Root.
Integer Cube Root.
Integer Exponentiation.
Integer Logarithm.
12. Unusual Bases for Number Systems.
Base -2.
Base -1 + i.
Other Bases.
What is the Most Efficient Base?
13. Gray Code.
Gray Code.
Incrementing a Gray Coded Integer.
Negabinary Gray Code.
Brief History and Applications.
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.
15. Floating-Point.
IEEE Format.
Comparing Floating-Point Numbers Using Integer Operations.
The Distribution of Leading Digits.
Table of Miscellaneous Values.
16. Formulas for Primes.
Introduction.
Willans's Formulas.
Wormell's Formula.
Formulas for Other Difficult Functions.
Appendix A. Arithmetic Tables for a 4-Bit Machine.
Appendix B. Newton's Method.
Bibliography.
Index. 0201914654T08282002
