| 1 | ========================================
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| 2 | Generic Associative Array Implementation
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| 3 | ========================================
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| 4 |
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| 5 | Overview
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| 6 | ========
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| 7 |
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| 8 | This associative array implementation is an object container with the following
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| 9 | properties:
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| 10 |
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| 11 | 1. Objects are opaque pointers. The implementation does not care where they
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| 12 | point (if anywhere) or what they point to (if anything).
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| 13 |
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| 14 | .. note::
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| 15 |
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| 16 | Pointers to objects _must_ be zero in the least significant bit.
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| 17 |
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| 18 | 2. Objects do not need to contain linkage blocks for use by the array. This
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| 19 | permits an object to be located in multiple arrays simultaneously.
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| 20 | Rather, the array is made up of metadata blocks that point to objects.
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| 21 |
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| 22 | 3. Objects require index keys to locate them within the array.
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| 23 |
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| 24 | 4. Index keys must be unique. Inserting an object with the same key as one
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| 25 | already in the array will replace the old object.
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| 26 |
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| 27 | 5. Index keys can be of any length and can be of different lengths.
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| 28 |
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| 29 | 6. Index keys should encode the length early on, before any variation due to
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| 30 | length is seen.
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| 31 |
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| 32 | 7. Index keys can include a hash to scatter objects throughout the array.
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| 33 |
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| 34 | 8. The array can iterated over. The objects will not necessarily come out in
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| 35 | key order.
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| 36 |
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| 37 | 9. The array can be iterated over while it is being modified, provided the
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| 38 | RCU readlock is being held by the iterator. Note, however, under these
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| 39 | circumstances, some objects may be seen more than once. If this is a
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| 40 | problem, the iterator should lock against modification. Objects will not
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| 41 | be missed, however, unless deleted.
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| 42 |
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| 43 | 10. Objects in the array can be looked up by means of their index key.
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| 44 |
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| 45 | 11. Objects can be looked up while the array is being modified, provided the
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| 46 | RCU readlock is being held by the thread doing the look up.
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| 47 |
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| 48 | The implementation uses a tree of 16-pointer nodes internally that are indexed
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| 49 | on each level by nibbles from the index key in the same manner as in a radix
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| 50 | tree. To improve memory efficiency, shortcuts can be emplaced to skip over
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| 51 | what would otherwise be a series of single-occupancy nodes. Further, nodes
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| 52 | pack leaf object pointers into spare space in the node rather than making an
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| 53 | extra branch until as such time an object needs to be added to a full node.
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| 54 |
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| 55 |
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| 56 | The Public API
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| 57 | ==============
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| 58 |
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| 59 | The public API can be found in ``<linux/assoc_array.h>``. The associative
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| 60 | array is rooted on the following structure::
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| 61 |
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| 62 | struct assoc_array {
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| 63 | ...
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| 64 | };
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| 65 |
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| 66 | The code is selected by enabling ``CONFIG_ASSOCIATIVE_ARRAY`` with::
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| 67 |
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| 68 | ./script/config -e ASSOCIATIVE_ARRAY
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| 69 |
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| 70 |
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| 71 | Edit Script
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| 72 | -----------
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| 73 |
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| 74 | The insertion and deletion functions produce an 'edit script' that can later be
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| 75 | applied to effect the changes without risking ``ENOMEM``. This retains the
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| 76 | preallocated metadata blocks that will be installed in the internal tree and
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| 77 | keeps track of the metadata blocks that will be removed from the tree when the
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| 78 | script is applied.
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| 79 |
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| 80 | This is also used to keep track of dead blocks and dead objects after the
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| 81 | script has been applied so that they can be freed later. The freeing is done
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| 82 | after an RCU grace period has passed - thus allowing access functions to
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| 83 | proceed under the RCU read lock.
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| 84 |
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| 85 | The script appears as outside of the API as a pointer of the type::
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| 86 |
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| 87 | struct assoc_array_edit;
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| 88 |
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| 89 | There are two functions for dealing with the script:
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| 90 |
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| 91 | 1. Apply an edit script::
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| 92 |
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| 93 | void assoc_array_apply_edit(struct assoc_array_edit *edit);
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| 94 |
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| 95 | This will perform the edit functions, interpolating various write barriers
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| 96 | to permit accesses under the RCU read lock to continue. The edit script
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| 97 | will then be passed to ``call_rcu()`` to free it and any dead stuff it
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| 98 | points to.
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| 99 |
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| 100 | 2. Cancel an edit script::
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| 101 |
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| 102 | void assoc_array_cancel_edit(struct assoc_array_edit *edit);
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| 103 |
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| 104 | This frees the edit script and all preallocated memory immediately. If
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| 105 | this was for insertion, the new object is *not* released by this function,
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| 106 | but must rather be released by the caller.
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| 107 |
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| 108 | These functions are guaranteed not to fail.
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| 109 |
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| 110 |
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| 111 | Operations Table
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| 112 | ----------------
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| 113 |
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| 114 | Various functions take a table of operations::
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| 115 |
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| 116 | struct assoc_array_ops {
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| 117 | ...
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| 118 | };
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| 119 |
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| 120 | This points to a number of methods, all of which need to be provided:
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| 121 |
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| 122 | 1. Get a chunk of index key from caller data::
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| 123 |
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| 124 | unsigned long (*get_key_chunk)(const void *index_key, int level);
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| 125 |
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| 126 | This should return a chunk of caller-supplied index key starting at the
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| 127 | *bit* position given by the level argument. The level argument will be a
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| 128 | multiple of ``ASSOC_ARRAY_KEY_CHUNK_SIZE`` and the function should return
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| 129 | ``ASSOC_ARRAY_KEY_CHUNK_SIZE bits``. No error is possible.
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| 130 |
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| 131 |
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| 132 | 2. Get a chunk of an object's index key::
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| 133 |
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| 134 | unsigned long (*get_object_key_chunk)(const void *object, int level);
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| 135 |
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| 136 | As the previous function, but gets its data from an object in the array
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| 137 | rather than from a caller-supplied index key.
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| 138 |
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| 139 |
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| 140 | 3. See if this is the object we're looking for::
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| 141 |
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| 142 | bool (*compare_object)(const void *object, const void *index_key);
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| 143 |
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| 144 | Compare the object against an index key and return ``true`` if it matches
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| 145 | and ``false`` if it doesn't.
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| 146 |
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| 147 |
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| 148 | 4. Diff the index keys of two objects::
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| 149 |
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| 150 | int (*diff_objects)(const void *object, const void *index_key);
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| 151 |
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| 152 | Return the bit position at which the index key of the specified object
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| 153 | differs from the given index key or -1 if they are the same.
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| 154 |
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| 155 |
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| 156 | 5. Free an object::
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| 157 |
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| 158 | void (*free_object)(void *object);
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| 159 |
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| 160 | Free the specified object. Note that this may be called an RCU grace period
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| 161 | after ``assoc_array_apply_edit()`` was called, so ``synchronize_rcu()`` may
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| 162 | be necessary on module unloading.
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| 163 |
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| 164 |
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| 165 | Manipulation Functions
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| 166 | ----------------------
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| 167 |
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| 168 | There are a number of functions for manipulating an associative array:
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| 169 |
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| 170 | 1. Initialise an associative array::
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| 171 |
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| 172 | void assoc_array_init(struct assoc_array *array);
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| 173 |
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| 174 | This initialises the base structure for an associative array. It can't fail.
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| 175 |
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| 176 |
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| 177 | 2. Insert/replace an object in an associative array::
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| 178 |
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| 179 | struct assoc_array_edit *
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| 180 | assoc_array_insert(struct assoc_array *array,
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| 181 | const struct assoc_array_ops *ops,
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| 182 | const void *index_key,
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| 183 | void *object);
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| 184 |
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| 185 | This inserts the given object into the array. Note that the least
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| 186 | significant bit of the pointer must be zero as it's used to type-mark
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| 187 | pointers internally.
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| 188 |
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| 189 | If an object already exists for that key then it will be replaced with the
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| 190 | new object and the old one will be freed automatically.
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| 191 |
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| 192 | The ``index_key`` argument should hold index key information and is
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| 193 | passed to the methods in the ops table when they are called.
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| 194 |
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| 195 | This function makes no alteration to the array itself, but rather returns
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| 196 | an edit script that must be applied. ``-ENOMEM`` is returned in the case of
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| 197 | an out-of-memory error.
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| 198 |
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| 199 | The caller should lock exclusively against other modifiers of the array.
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| 200 |
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| 201 |
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| 202 | 3. Delete an object from an associative array::
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| 203 |
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| 204 | struct assoc_array_edit *
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| 205 | assoc_array_delete(struct assoc_array *array,
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| 206 | const struct assoc_array_ops *ops,
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| 207 | const void *index_key);
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| 208 |
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| 209 | This deletes an object that matches the specified data from the array.
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| 210 |
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| 211 | The ``index_key`` argument should hold index key information and is
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| 212 | passed to the methods in the ops table when they are called.
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| 213 |
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| 214 | This function makes no alteration to the array itself, but rather returns
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| 215 | an edit script that must be applied. ``-ENOMEM`` is returned in the case of
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| 216 | an out-of-memory error. ``NULL`` will be returned if the specified object
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| 217 | is not found within the array.
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| 218 |
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| 219 | The caller should lock exclusively against other modifiers of the array.
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| 220 |
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| 221 |
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| 222 | 4. Delete all objects from an associative array::
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| 223 |
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| 224 | struct assoc_array_edit *
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| 225 | assoc_array_clear(struct assoc_array *array,
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| 226 | const struct assoc_array_ops *ops);
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| 227 |
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| 228 | This deletes all the objects from an associative array and leaves it
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| 229 | completely empty.
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| 230 |
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| 231 | This function makes no alteration to the array itself, but rather returns
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| 232 | an edit script that must be applied. ``-ENOMEM`` is returned in the case of
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| 233 | an out-of-memory error.
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| 234 |
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| 235 | The caller should lock exclusively against other modifiers of the array.
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| 236 |
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| 237 |
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| 238 | 5. Destroy an associative array, deleting all objects::
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| 239 |
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| 240 | void assoc_array_destroy(struct assoc_array *array,
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| 241 | const struct assoc_array_ops *ops);
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| 242 |
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| 243 | This destroys the contents of the associative array and leaves it
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| 244 | completely empty. It is not permitted for another thread to be traversing
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| 245 | the array under the RCU read lock at the same time as this function is
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| 246 | destroying it as no RCU deferral is performed on memory release -
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| 247 | something that would require memory to be allocated.
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| 248 |
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| 249 | The caller should lock exclusively against other modifiers and accessors
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| 250 | of the array.
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| 251 |
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| 252 |
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| 253 | 6. Garbage collect an associative array::
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| 254 |
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| 255 | int assoc_array_gc(struct assoc_array *array,
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| 256 | const struct assoc_array_ops *ops,
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| 257 | bool (*iterator)(void *object, void *iterator_data),
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| 258 | void *iterator_data);
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| 259 |
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| 260 | This iterates over the objects in an associative array and passes each one
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| 261 | to ``iterator()``. If ``iterator()`` returns ``true``, the object is kept.
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| 262 | If it returns ``false``, the object will be freed. If the ``iterator()``
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| 263 | function returns ``true``, it must perform any appropriate refcount
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| 264 | incrementing on the object before returning.
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| 265 |
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| 266 | The internal tree will be packed down if possible as part of the iteration
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| 267 | to reduce the number of nodes in it.
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| 268 |
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| 269 | The ``iterator_data`` is passed directly to ``iterator()`` and is otherwise
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| 270 | ignored by the function.
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| 271 |
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| 272 | The function will return ``0`` if successful and ``-ENOMEM`` if there wasn't
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| 273 | enough memory.
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| 274 |
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| 275 | It is possible for other threads to iterate over or search the array under
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| 276 | the RCU read lock while this function is in progress. The caller should
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| 277 | lock exclusively against other modifiers of the array.
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| 278 |
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| 279 |
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| 280 | Access Functions
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| 281 | ----------------
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| 282 |
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| 283 | There are two functions for accessing an associative array:
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| 284 |
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| 285 | 1. Iterate over all the objects in an associative array::
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| 286 |
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| 287 | int assoc_array_iterate(const struct assoc_array *array,
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| 288 | int (*iterator)(const void *object,
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| 289 | void *iterator_data),
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| 290 | void *iterator_data);
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| 291 |
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| 292 | This passes each object in the array to the iterator callback function.
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| 293 | ``iterator_data`` is private data for that function.
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| 294 |
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| 295 | This may be used on an array at the same time as the array is being
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| 296 | modified, provided the RCU read lock is held. Under such circumstances,
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| 297 | it is possible for the iteration function to see some objects twice. If
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| 298 | this is a problem, then modification should be locked against. The
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| 299 | iteration algorithm should not, however, miss any objects.
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| 300 |
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| 301 | The function will return ``0`` if no objects were in the array or else it
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| 302 | will return the result of the last iterator function called. Iteration
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| 303 | stops immediately if any call to the iteration function results in a
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| 304 | non-zero return.
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| 305 |
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| 306 |
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| 307 | 2. Find an object in an associative array::
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| 308 |
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| 309 | void *assoc_array_find(const struct assoc_array *array,
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| 310 | const struct assoc_array_ops *ops,
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| 311 | const void *index_key);
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| 312 |
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| 313 | This walks through the array's internal tree directly to the object
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| 314 | specified by the index key.
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| 315 |
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| 316 | This may be used on an array at the same time as the array is being
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| 317 | modified, provided the RCU read lock is held.
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| 318 |
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| 319 | The function will return the object if found (and set ``*_type`` to the
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| 320 | object type) or will return ``NULL`` if the object was not found.
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| 321 |
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| 322 |
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| 323 | Index Key Form
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| 324 | --------------
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| 325 |
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| 326 | The index key can be of any form, but since the algorithms aren't told how long
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| 327 | the key is, it is strongly recommended that the index key includes its length
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| 328 | very early on before any variation due to the length would have an effect on
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| 329 | comparisons.
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| 330 |
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| 331 | This will cause leaves with different length keys to scatter away from each
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| 332 | other - and those with the same length keys to cluster together.
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| 333 |
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| 334 | It is also recommended that the index key begin with a hash of the rest of the
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| 335 | key to maximise scattering throughout keyspace.
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| 336 |
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| 337 | The better the scattering, the wider and lower the internal tree will be.
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| 338 |
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| 339 | Poor scattering isn't too much of a problem as there are shortcuts and nodes
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| 340 | can contain mixtures of leaves and metadata pointers.
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| 341 |
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| 342 | The index key is read in chunks of machine word. Each chunk is subdivided into
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| 343 | one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and
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| 344 | on a 64-bit CPU, 16 levels. Unless the scattering is really poor, it is
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| 345 | unlikely that more than one word of any particular index key will have to be
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| 346 | used.
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| 347 |
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| 348 |
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| 349 | Internal Workings
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| 350 | =================
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| 351 |
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| 352 | The associative array data structure has an internal tree. This tree is
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| 353 | constructed of two types of metadata blocks: nodes and shortcuts.
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| 354 |
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| 355 | A node is an array of slots. Each slot can contain one of four things:
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| 356 |
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| 357 | * A NULL pointer, indicating that the slot is empty.
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| 358 | * A pointer to an object (a leaf).
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| 359 | * A pointer to a node at the next level.
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| 360 | * A pointer to a shortcut.
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| 361 |
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| 362 |
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| 363 | Basic Internal Tree Layout
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| 364 | --------------------------
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| 365 |
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| 366 | Ignoring shortcuts for the moment, the nodes form a multilevel tree. The index
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| 367 | key space is strictly subdivided by the nodes in the tree and nodes occur on
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| 368 | fixed levels. For example::
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| 369 |
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| 370 | Level: 0 1 2 3
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| 371 | =============== =============== =============== ===============
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| 372 | NODE D
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| 373 | NODE B NODE C +------>+---+
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| 374 | +------>+---+ +------>+---+ | | 0 |
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| 375 | NODE A | | 0 | | | 0 | | +---+
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| 376 | +---+ | +---+ | +---+ | : :
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| 377 | | 0 | | : : | : : | +---+
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| 378 | +---+ | +---+ | +---+ | | f |
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| 379 | | 1 |---+ | 3 |---+ | 7 |---+ +---+
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| 380 | +---+ +---+ +---+
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| 381 | : : : : | 8 |---+
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| 382 | +---+ +---+ +---+ | NODE E
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| 383 | | e |---+ | f | : : +------>+---+
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| 384 | +---+ | +---+ +---+ | 0 |
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| 385 | | f | | | f | +---+
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| 386 | +---+ | +---+ : :
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| 387 | | NODE F +---+
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| 388 | +------>+---+ | f |
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| 389 | | 0 | NODE G +---+
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| 390 | +---+ +------>+---+
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| 391 | : : | | 0 |
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| 392 | +---+ | +---+
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| 393 | | 6 |---+ : :
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| 394 | +---+ +---+
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| 395 | : : | f |
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| 396 | +---+ +---+
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| 397 | | f |
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| 398 | +---+
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| 399 |
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| 400 | In the above example, there are 7 nodes (A-G), each with 16 slots (0-f).
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| 401 | Assuming no other meta data nodes in the tree, the key space is divided
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| 402 | thusly:
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| 403 |
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| 404 | =========== ====
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| 405 | KEY PREFIX NODE
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| 406 | =========== ====
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| 407 | 137* D
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| 408 | 138* E
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| 409 | 13[0-69-f]* C
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| 410 | 1[0-24-f]* B
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| 411 | e6* G
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| 412 | e[0-57-f]* F
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| 413 | [02-df]* A
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| 414 | =========== ====
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| 415 |
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| 416 | So, for instance, keys with the following example index keys will be found in
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| 417 | the appropriate nodes:
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| 418 |
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| 419 | =============== ======= ====
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| 420 | INDEX KEY PREFIX NODE
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| 421 | =============== ======= ====
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| 422 | 13694892892489 13 C
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| 423 | 13795289025897 137 D
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| 424 | 13889dde88793 138 E
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| 425 | 138bbb89003093 138 E
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| 426 | 1394879524789 12 C
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| 427 | 1458952489 1 B
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| 428 | 9431809de993ba \- A
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| 429 | b4542910809cd \- A
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| 430 | e5284310def98 e F
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| 431 | e68428974237 e6 G
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| 432 | e7fffcbd443 e F
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| 433 | f3842239082 \- A
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| 434 | =============== ======= ====
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| 435 |
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| 436 | To save memory, if a node can hold all the leaves in its portion of keyspace,
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| 437 | then the node will have all those leaves in it and will not have any metadata
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| 438 | pointers - even if some of those leaves would like to be in the same slot.
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| 439 |
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| 440 | A node can contain a heterogeneous mix of leaves and metadata pointers.
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| 441 | Metadata pointers must be in the slots that match their subdivisions of key
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| 442 | space. The leaves can be in any slot not occupied by a metadata pointer. It
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| 443 | is guaranteed that none of the leaves in a node will match a slot occupied by a
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| 444 | metadata pointer. If the metadata pointer is there, any leaf whose key matches
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| 445 | the metadata key prefix must be in the subtree that the metadata pointer points
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| 446 | to.
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| 447 |
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| 448 | In the above example list of index keys, node A will contain:
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| 449 |
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| 450 | ==== =============== ==================
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| 451 | SLOT CONTENT INDEX KEY (PREFIX)
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| 452 | ==== =============== ==================
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| 453 | 1 PTR TO NODE B 1*
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| 454 | any LEAF 9431809de993ba
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| 455 | any LEAF b4542910809cd
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| 456 | e PTR TO NODE F e*
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| 457 | any LEAF f3842239082
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| 458 | ==== =============== ==================
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| 459 |
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| 460 | and node B:
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| 461 |
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| 462 | ==== =============== ==================
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| 463 | SLOT CONTENT INDEX KEY (PREFIX)
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| 464 | ==== =============== ==================
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| 465 | 3 PTR TO NODE C 13*
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| 466 | any LEAF 1458952489
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| 467 | ==== =============== ==================
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| 468 |
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| 469 |
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| 470 | Shortcuts
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| 471 | ---------
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| 472 |
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| 473 | Shortcuts are metadata records that jump over a piece of keyspace. A shortcut
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| 474 | is a replacement for a series of single-occupancy nodes ascending through the
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| 475 | levels. Shortcuts exist to save memory and to speed up traversal.
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| 476 |
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| 477 | It is possible for the root of the tree to be a shortcut - say, for example,
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| 478 | the tree contains at least 17 nodes all with key prefix ``1111``. The
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| 479 | insertion algorithm will insert a shortcut to skip over the ``1111`` keyspace
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| 480 | in a single bound and get to the fourth level where these actually become
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| 481 | different.
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| 482 |
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| 483 |
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| 484 | Splitting And Collapsing Nodes
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| 485 | ------------------------------
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| 486 |
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| 487 | Each node has a maximum capacity of 16 leaves and metadata pointers. If the
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| 488 | insertion algorithm finds that it is trying to insert a 17th object into a
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| 489 | node, that node will be split such that at least two leaves that have a common
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| 490 | key segment at that level end up in a separate node rooted on that slot for
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| 491 | that common key segment.
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| 492 |
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| 493 | If the leaves in a full node and the leaf that is being inserted are
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| 494 | sufficiently similar, then a shortcut will be inserted into the tree.
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| 495 |
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| 496 | When the number of objects in the subtree rooted at a node falls to 16 or
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| 497 | fewer, then the subtree will be collapsed down to a single node - and this will
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| 498 | ripple towards the root if possible.
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| 499 |
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| 500 |
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| 501 | Non-Recursive Iteration
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| 502 | -----------------------
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| 503 |
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| 504 | Each node and shortcut contains a back pointer to its parent and the number of
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| 505 | slot in that parent that points to it. None-recursive iteration uses these to
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| 506 | proceed rootwards through the tree, going to the parent node, slot N + 1 to
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| 507 | make sure progress is made without the need for a stack.
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| 508 |
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| 509 | The backpointers, however, make simultaneous alteration and iteration tricky.
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| 510 |
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| 511 |
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| 512 | Simultaneous Alteration And Iteration
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| 513 | -------------------------------------
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| 514 |
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| 515 | There are a number of cases to consider:
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| 516 |
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| 517 | 1. Simple insert/replace. This involves simply replacing a NULL or old
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| 518 | matching leaf pointer with the pointer to the new leaf after a barrier.
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| 519 | The metadata blocks don't change otherwise. An old leaf won't be freed
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| 520 | until after the RCU grace period.
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| 521 |
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| 522 | 2. Simple delete. This involves just clearing an old matching leaf. The
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| 523 | metadata blocks don't change otherwise. The old leaf won't be freed until
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| 524 | after the RCU grace period.
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| 525 |
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| 526 | 3. Insertion replacing part of a subtree that we haven't yet entered. This
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| 527 | may involve replacement of part of that subtree - but that won't affect
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| 528 | the iteration as we won't have reached the pointer to it yet and the
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| 529 | ancestry blocks are not replaced (the layout of those does not change).
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| 530 |
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| 531 | 4. Insertion replacing nodes that we're actively processing. This isn't a
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| 532 | problem as we've passed the anchoring pointer and won't switch onto the
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| 533 | new layout until we follow the back pointers - at which point we've
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| 534 | already examined the leaves in the replaced node (we iterate over all the
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| 535 | leaves in a node before following any of its metadata pointers).
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| 536 |
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| 537 | We might, however, re-see some leaves that have been split out into a new
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| 538 | branch that's in a slot further along than we were at.
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| 539 |
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| 540 | 5. Insertion replacing nodes that we're processing a dependent branch of.
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| 541 | This won't affect us until we follow the back pointers. Similar to (4).
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| 542 |
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| 543 | 6. Deletion collapsing a branch under us. This doesn't affect us because the
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| 544 | back pointers will get us back to the parent of the new node before we
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| 545 | could see the new node. The entire collapsed subtree is thrown away
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| 546 | unchanged - and will still be rooted on the same slot, so we shouldn't
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| 547 | process it a second time as we'll go back to slot + 1.
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| 548 |
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| 549 | .. note::
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| 550 |
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| 551 | Under some circumstances, we need to simultaneously change the parent
|
| 552 | pointer and the parent slot pointer on a node (say, for example, we
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| 553 | inserted another node before it and moved it up a level). We cannot do
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| 554 | this without locking against a read - so we have to replace that node too.
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| 555 |
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| 556 | However, when we're changing a shortcut into a node this isn't a problem
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| 557 | as shortcuts only have one slot and so the parent slot number isn't used
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| 558 | when traversing backwards over one. This means that it's okay to change
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| 559 | the slot number first - provided suitable barriers are used to make sure
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| 560 | the parent slot number is read after the back pointer.
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| 561 |
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| 562 | Obsolete blocks and leaves are freed up after an RCU grace period has passed,
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| 563 | so as long as anyone doing walking or iteration holds the RCU read lock, the
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| 564 | old superstructure should not go away on them.
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