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| Foreword | |
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| Preface | |
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| Introduction | |
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| Notation | |
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| Instruction Set and Execution Time Model | |
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| Basics | |
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| Manipulating Rightmost Bits | |
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| Addition Combined with Logical Operations | |
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| Inequalities among Logical and Arithmetic Expressions | |
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| Absolute Value Function | |
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| Sign Extension | |
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| Shift Right Signed from Unsigned | |
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| Sign Function | |
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| Three-Valued Compare Function | |
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| Transfer of Sign | |
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| Decoding a "Zero Means 2**n" Field | |
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| Comparison Predicates | |
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| Overflow Detection | |
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| Condition Code Result of Add, Subtract, and Multiply | |
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| Rotate Shifts | |
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| Double-Length Add/Subtract | |
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| Double-Length Shifts | |
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| Multibyte Add, Subtract, Absolute Value | |
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| Doz, Max, Min | |
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| Exchanging Registers | |
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| Alternating among Two or More Values | |
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| Power-of-2 Boundaries | |
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| Rounding Up/Down to a Multiple of a Known Power of 2 | |
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| Rounding Up/Down to the Next Power of 2 | |
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| Detecting a Power-of-2 Boundary Crossing | |
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| Arithmetic Bounds | |
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| Checking Bounds of Integers | |
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| Propagating Bounds through Add's and Subtract's | |
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| Propagating Bounds through Logical Operations | |
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| Counting Bits | |
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| Counting 1-Bits | |
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| Parity | |
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| Counting Leading 0's | |
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| Counting Trailing 0's | |
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| Searching Words | |
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| Find First 0-Byte | |
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| Find First String of 1-Bits of a Given Length | |
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| Rearranging Bits and Bytes | |
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| Reversing Bits and Bytes | |
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| Shuffling Bits | |
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| Transposing a Bit Matrix | |
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| Compress, or Generalized Extract | |
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| General Permutations, Sheep and Goats Operation | |
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| Rearrangements and Index Transformations | |
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| Multiplication | |
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| Multiword Multiplication | |
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| High-Order Half of 64-Bit Product | |
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| High-Order Product Signed from/to Unsigned | |
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| Multiplication by Constants | |
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| Integer Division | |
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| Preliminaries | |
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| Multiword Division | |
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| Unsigned Short Division from Signed Division | |
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| Unsigned Long Division | |
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| Integer Division by Constants | |
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| Signed Division by a Known Power of 2 | |
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| Signed Remainder from Division by a Known Power of 2 | |
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| Signed Division and Remainder by Non-Powers of 2 | |
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| Signed Division by Divisors [greater than or equal] 2 | |
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| Signed Division by Divisors [less than or equal] -2 | |
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| Incorporation into a Compiler | |
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| Miscellaneous Topics | |
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| Unsigned Division | |
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| Unsigned Division by Divisors [greater than or equal] 1 | |
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| Incorporation into a Compiler (Unsigned) | |
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| Miscellaneous Topics (Unsigned) | |
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| Applicability to Modulus and Floor Division | |
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| Similar Methods | |
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| Sample Magic Numbers | |
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| Exact Division by Constants | |
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| Test for Zero Remainder after Division by a Constant | |
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| Some Elementary Functions | |
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| Integer Square Root | |
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| Integer Cube Root | |
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| Integer Exponentiation | |
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| Integer Logarithm | |
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| Unusual Bases for Number Systems | |
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| Base-2 | |
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| Base-1 + i | |
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| Other Bases | |
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| What Is the Most Efficient Base? | |
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| Gray Code | |
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| Gray Code | |
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| Incrementing a Gray-Coded Integer | |
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| Negabinary Gray Code | |
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| Brief History and Applications | |
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| Hilbert's Curve | |
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| A Recursive Algorithm for Generating the Hilbert Curve | |
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| Coordinates from Distance along the Hilbert Curve | |
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| Distance from Coordinates on the Hilbert Curve | |
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| Incrementing the Coordinates on the Hilbert Curve | |
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| Non-recursive Generating Algorithms | |
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| Other Space-Filling Curves | |
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| Applications | |
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| Floating-point | |
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| IEEE Format | |
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| Comparing Floating-Point Numbers Using Integer Operations | |
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| The Distribution of Leading Digits | |
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| Table of Miscellaneous Values | |
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| Formulas for Primes | |
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| Introduction | |
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| Willans's Formulas | |
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| Wormell's Formula | |
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| Formulas for Other Difficult Functions | |
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| Arithmetic Tables for a 4-Bit Machine | |
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| Newton's Method | |
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| Bibliography | |
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| Index | |