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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