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near the beginning  \nJ􀁿org Arndt  \n[arndt@jjj. de](arndt@jjj. de)  \nDraft version 1 of 2008-January-19  \n1 The latest version and the accompanying software is online at [http://www.jjj.de/fxt/](http://www.jjj.de/fxt/) .  \nii  \n[fxtbook draft of 2008-January-19]  \nCONTENTS iii  \nContents  \nImportant remarks about this document xi  \nI Low level algorithms 1  \n1 Bit wizardry 3  \n1.1 Trivia ............................................... 3  \n1.2 Operations on individual bits .................................. 8  \n1.3 Operations on low bits or blocks of a word .......................... 9  \n1.4 Isolating blocks of bits and single bits ............................. 12  \n1.5 Computing the index of a single set bit ............................ 14  \n1.6 Operations on high bits or blocks of a word .......................... 16  \n1.7 Functions related to the base-2 logarithm ........................... 18  \n1.8 Counting bits and blocks of a word .............................. 19  \n1.9 Bit set lookup .......................................... 21  \n1.10 Avoiding branches ........................................ 22  \n1.11 Bit-wise rotation of a word ................................... 26  \n1.12 Functions related to bit-wise rotation * ............................ 27  \n1.13 Reversing the bits of a word .................................. 30  \n1.14 Bit-wise zip ............................................ 35  \n1.15 Gray code and parity ...................................... 36  \n1.16 Bit sequency ........................................... 42  \n1.17 Powers of the Gray code .................................... 43  \n1.18 Invertible transforms on words ................................. 45  \n1.19 Moves of the Hilbert curve ................................... 51  \n1.20 The Z-order ........................................... 53  \n1.21 Scanning for zero bytes ..................................... 54  \n1.22 2-adic inverse and square root ................................. 55  \n1.23 Radix 􀀀2 representation .................................... 56  \n1.24 A sparse signed binary representation ............................. 59  \n1.25 Generating bit combinations .................................. 61  \n1.26 Generating bit subsets of a given word ............................ 63  \n1.27 Binary words as subsets in lexicographic order ........................ 64  \n1.28 Minimal-change bit combinations ............................... 69  \n1.29 Fibonacci words ......................................... 71  \n1.30 Binary words and parentheses strings * ............................ 74  \n1.31 Error detection by hashing: the CRC ............................. 77  \n1.32 Permutations via primitives ................................... 81  \n1.33 CPU instructions often missed ................................. 84  \n2 Permutations 85  \n2.1 The revbin permutation ..................................... 85  \n[fxtbook draft of 2008-January-19]  \niv CONTENTS  \n2.2 The radix permutation ..................................... 89  \n2.3 In-place matrix transposition .................................. 89  \n2.4 Revbin permutation and matrix transposition * ....................... 91  \n2.5 The zip permutation ....................................... 93  \n2.6 The reversed zip permutation .................................. 95  \n2.7 The XOR permutation ..................................... 96  \n2.8 The Gray code permutation .................................. 97  \n2.9 The reversed Gray code permutation ............................. 101  \n2.10 Decomposing permutations * .................................. 102  \n2.11 General permutations and their operations .......................... 104  \n3 Sorting and searching 115  \n3.1 Sorting .............................................. 115  \n3.2 Binary search ........................................... 117  \n3.3 Index sorting ....................","cbCairvTjtvx5LPi","https://ap.wps.com/l/cbCairvTjtvx5LPi","pdf",2872892,938,"English","# Contents\n## Important remarks about this document\n## I Low level algorithms\n## 1 Bit wizardry\n## 2 Permutations\n## 3 Sorting and searching\n## 4 Data structures\n## II Combinatorial generation\n## 5 Conventions and considerations\n## 6 Combinations","[{\"question\":\"What topics are covered in the low-level part of the book draft?\",\"answer\":\"It covers detailed bit operations and techniques, including isolating bits, counting and indexing set bits, bit-wise rotation and reversal, Gray code and parity, and other word-based bit methods.\"},{\"question\":\"How does the document structure material after permutations?\",\"answer\":\"After the permutations section, it moves to sorting and searching methods, then to foundational data structures like stacks, queues, heaps, and finite-state machines.\"},{\"question\":\"What does the combinatorial generation section focus on?\",\"answer\":\"It provides conventions and considerations for representations and ordering, plus techniques for ranking/unranking and counting, followed by methods for generating combinations in lexicographic and minimal-change orders.\"}]","Algorithms for Programmers - Low Level Algorithms - 1 | PDF",1789975756,2364]