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554 lines
21 KiB
554 lines
21 KiB
======================================== |
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Generic Associative Array Implementation |
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======================================== |
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Overview |
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======== |
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This associative array implementation is an object container with the following |
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properties: |
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1. Objects are opaque pointers. The implementation does not care where they |
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point (if anywhere) or what they point to (if anything). |
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.. note:: |
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Pointers to objects _must_ be zero in the least significant bit. |
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2. Objects do not need to contain linkage blocks for use by the array. This |
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permits an object to be located in multiple arrays simultaneously. |
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Rather, the array is made up of metadata blocks that point to objects. |
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3. Objects require index keys to locate them within the array. |
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4. Index keys must be unique. Inserting an object with the same key as one |
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already in the array will replace the old object. |
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5. Index keys can be of any length and can be of different lengths. |
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6. Index keys should encode the length early on, before any variation due to |
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length is seen. |
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7. Index keys can include a hash to scatter objects throughout the array. |
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8. The array can iterated over. The objects will not necessarily come out in |
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key order. |
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9. The array can be iterated over while it is being modified, provided the |
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RCU readlock is being held by the iterator. Note, however, under these |
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circumstances, some objects may be seen more than once. If this is a |
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problem, the iterator should lock against modification. Objects will not |
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be missed, however, unless deleted. |
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10. Objects in the array can be looked up by means of their index key. |
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11. Objects can be looked up while the array is being modified, provided the |
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RCU readlock is being held by the thread doing the look up. |
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The implementation uses a tree of 16-pointer nodes internally that are indexed |
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on each level by nibbles from the index key in the same manner as in a radix |
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tree. To improve memory efficiency, shortcuts can be emplaced to skip over |
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what would otherwise be a series of single-occupancy nodes. Further, nodes |
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pack leaf object pointers into spare space in the node rather than making an |
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extra branch until as such time an object needs to be added to a full node. |
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The Public API |
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============== |
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The public API can be found in ``<linux/assoc_array.h>``. The associative |
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array is rooted on the following structure:: |
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struct assoc_array { |
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... |
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}; |
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The code is selected by enabling ``CONFIG_ASSOCIATIVE_ARRAY`` with:: |
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./script/config -e ASSOCIATIVE_ARRAY |
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Edit Script |
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----------- |
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The insertion and deletion functions produce an 'edit script' that can later be |
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applied to effect the changes without risking ``ENOMEM``. This retains the |
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preallocated metadata blocks that will be installed in the internal tree and |
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keeps track of the metadata blocks that will be removed from the tree when the |
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script is applied. |
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This is also used to keep track of dead blocks and dead objects after the |
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script has been applied so that they can be freed later. The freeing is done |
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after an RCU grace period has passed - thus allowing access functions to |
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proceed under the RCU read lock. |
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The script appears as outside of the API as a pointer of the type:: |
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struct assoc_array_edit; |
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There are two functions for dealing with the script: |
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1. Apply an edit script:: |
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void assoc_array_apply_edit(struct assoc_array_edit *edit); |
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This will perform the edit functions, interpolating various write barriers |
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to permit accesses under the RCU read lock to continue. The edit script |
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will then be passed to ``call_rcu()`` to free it and any dead stuff it points |
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to. |
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2. Cancel an edit script:: |
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void assoc_array_cancel_edit(struct assoc_array_edit *edit); |
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This frees the edit script and all preallocated memory immediately. If |
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this was for insertion, the new object is _not_ released by this function, |
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but must rather be released by the caller. |
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These functions are guaranteed not to fail. |
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Operations Table |
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---------------- |
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Various functions take a table of operations:: |
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struct assoc_array_ops { |
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... |
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}; |
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This points to a number of methods, all of which need to be provided: |
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1. Get a chunk of index key from caller data:: |
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unsigned long (*get_key_chunk)(const void *index_key, int level); |
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This should return a chunk of caller-supplied index key starting at the |
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*bit* position given by the level argument. The level argument will be a |
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multiple of ``ASSOC_ARRAY_KEY_CHUNK_SIZE`` and the function should return |
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``ASSOC_ARRAY_KEY_CHUNK_SIZE bits``. No error is possible. |
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2. Get a chunk of an object's index key:: |
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unsigned long (*get_object_key_chunk)(const void *object, int level); |
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As the previous function, but gets its data from an object in the array |
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rather than from a caller-supplied index key. |
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3. See if this is the object we're looking for:: |
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bool (*compare_object)(const void *object, const void *index_key); |
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Compare the object against an index key and return ``true`` if it matches and |
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``false`` if it doesn't. |
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4. Diff the index keys of two objects:: |
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int (*diff_objects)(const void *object, const void *index_key); |
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Return the bit position at which the index key of the specified object |
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differs from the given index key or -1 if they are the same. |
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5. Free an object:: |
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void (*free_object)(void *object); |
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Free the specified object. Note that this may be called an RCU grace period |
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after ``assoc_array_apply_edit()`` was called, so ``synchronize_rcu()`` may be |
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necessary on module unloading. |
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Manipulation Functions |
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---------------------- |
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There are a number of functions for manipulating an associative array: |
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1. Initialise an associative array:: |
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void assoc_array_init(struct assoc_array *array); |
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This initialises the base structure for an associative array. It can't fail. |
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2. Insert/replace an object in an associative array:: |
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struct assoc_array_edit * |
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assoc_array_insert(struct assoc_array *array, |
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const struct assoc_array_ops *ops, |
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const void *index_key, |
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void *object); |
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This inserts the given object into the array. Note that the least |
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significant bit of the pointer must be zero as it's used to type-mark |
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pointers internally. |
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If an object already exists for that key then it will be replaced with the |
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new object and the old one will be freed automatically. |
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The ``index_key`` argument should hold index key information and is |
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passed to the methods in the ops table when they are called. |
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This function makes no alteration to the array itself, but rather returns |
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an edit script that must be applied. ``-ENOMEM`` is returned in the case of |
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an out-of-memory error. |
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The caller should lock exclusively against other modifiers of the array. |
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3. Delete an object from an associative array:: |
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struct assoc_array_edit * |
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assoc_array_delete(struct assoc_array *array, |
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const struct assoc_array_ops *ops, |
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const void *index_key); |
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This deletes an object that matches the specified data from the array. |
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The ``index_key`` argument should hold index key information and is |
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passed to the methods in the ops table when they are called. |
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This function makes no alteration to the array itself, but rather returns |
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an edit script that must be applied. ``-ENOMEM`` is returned in the case of |
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an out-of-memory error. ``NULL`` will be returned if the specified object is |
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not found within the array. |
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The caller should lock exclusively against other modifiers of the array. |
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4. Delete all objects from an associative array:: |
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struct assoc_array_edit * |
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assoc_array_clear(struct assoc_array *array, |
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const struct assoc_array_ops *ops); |
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This deletes all the objects from an associative array and leaves it |
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completely empty. |
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This function makes no alteration to the array itself, but rather returns |
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an edit script that must be applied. ``-ENOMEM`` is returned in the case of |
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an out-of-memory error. |
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The caller should lock exclusively against other modifiers of the array. |
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5. Destroy an associative array, deleting all objects:: |
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void assoc_array_destroy(struct assoc_array *array, |
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const struct assoc_array_ops *ops); |
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This destroys the contents of the associative array and leaves it |
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completely empty. It is not permitted for another thread to be traversing |
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the array under the RCU read lock at the same time as this function is |
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destroying it as no RCU deferral is performed on memory release - |
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something that would require memory to be allocated. |
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The caller should lock exclusively against other modifiers and accessors |
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of the array. |
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6. Garbage collect an associative array:: |
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int assoc_array_gc(struct assoc_array *array, |
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const struct assoc_array_ops *ops, |
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bool (*iterator)(void *object, void *iterator_data), |
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void *iterator_data); |
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This iterates over the objects in an associative array and passes each one to |
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``iterator()``. If ``iterator()`` returns ``true``, the object is kept. If it |
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returns ``false``, the object will be freed. If the ``iterator()`` function |
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returns ``true``, it must perform any appropriate refcount incrementing on the |
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object before returning. |
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The internal tree will be packed down if possible as part of the iteration |
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to reduce the number of nodes in it. |
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The ``iterator_data`` is passed directly to ``iterator()`` and is otherwise |
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ignored by the function. |
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The function will return ``0`` if successful and ``-ENOMEM`` if there wasn't |
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enough memory. |
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It is possible for other threads to iterate over or search the array under |
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the RCU read lock while this function is in progress. The caller should |
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lock exclusively against other modifiers of the array. |
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Access Functions |
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---------------- |
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There are two functions for accessing an associative array: |
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1. Iterate over all the objects in an associative array:: |
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int assoc_array_iterate(const struct assoc_array *array, |
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int (*iterator)(const void *object, |
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void *iterator_data), |
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void *iterator_data); |
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This passes each object in the array to the iterator callback function. |
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``iterator_data`` is private data for that function. |
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This may be used on an array at the same time as the array is being |
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modified, provided the RCU read lock is held. Under such circumstances, |
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it is possible for the iteration function to see some objects twice. If |
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this is a problem, then modification should be locked against. The |
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iteration algorithm should not, however, miss any objects. |
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The function will return ``0`` if no objects were in the array or else it will |
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return the result of the last iterator function called. Iteration stops |
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immediately if any call to the iteration function results in a non-zero |
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return. |
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2. Find an object in an associative array:: |
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void *assoc_array_find(const struct assoc_array *array, |
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const struct assoc_array_ops *ops, |
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const void *index_key); |
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This walks through the array's internal tree directly to the object |
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specified by the index key.. |
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This may be used on an array at the same time as the array is being |
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modified, provided the RCU read lock is held. |
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The function will return the object if found (and set ``*_type`` to the object |
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type) or will return ``NULL`` if the object was not found. |
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Index Key Form |
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-------------- |
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The index key can be of any form, but since the algorithms aren't told how long |
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the key is, it is strongly recommended that the index key includes its length |
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very early on before any variation due to the length would have an effect on |
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comparisons. |
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This will cause leaves with different length keys to scatter away from each |
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other - and those with the same length keys to cluster together. |
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It is also recommended that the index key begin with a hash of the rest of the |
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key to maximise scattering throughout keyspace. |
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The better the scattering, the wider and lower the internal tree will be. |
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Poor scattering isn't too much of a problem as there are shortcuts and nodes |
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can contain mixtures of leaves and metadata pointers. |
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The index key is read in chunks of machine word. Each chunk is subdivided into |
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one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and |
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on a 64-bit CPU, 16 levels. Unless the scattering is really poor, it is |
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unlikely that more than one word of any particular index key will have to be |
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used. |
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Internal Workings |
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================= |
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The associative array data structure has an internal tree. This tree is |
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constructed of two types of metadata blocks: nodes and shortcuts. |
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A node is an array of slots. Each slot can contain one of four things: |
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* A NULL pointer, indicating that the slot is empty. |
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* A pointer to an object (a leaf). |
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* A pointer to a node at the next level. |
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* A pointer to a shortcut. |
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Basic Internal Tree Layout |
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-------------------------- |
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Ignoring shortcuts for the moment, the nodes form a multilevel tree. The index |
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key space is strictly subdivided by the nodes in the tree and nodes occur on |
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fixed levels. For example:: |
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Level: 0 1 2 3 |
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=============== =============== =============== =============== |
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NODE D |
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NODE B NODE C +------>+---+ |
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+------>+---+ +------>+---+ | | 0 | |
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NODE A | | 0 | | | 0 | | +---+ |
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+---+ | +---+ | +---+ | : : |
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| 0 | | : : | : : | +---+ |
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+---+ | +---+ | +---+ | | f | |
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| 1 |---+ | 3 |---+ | 7 |---+ +---+ |
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+---+ +---+ +---+ |
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: : : : | 8 |---+ |
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+---+ +---+ +---+ | NODE E |
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| e |---+ | f | : : +------>+---+ |
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+---+ | +---+ +---+ | 0 | |
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| f | | | f | +---+ |
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+---+ | +---+ : : |
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| NODE F +---+ |
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+------>+---+ | f | |
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| 0 | NODE G +---+ |
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+---+ +------>+---+ |
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: : | | 0 | |
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+---+ | +---+ |
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| 6 |---+ : : |
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+---+ +---+ |
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: : | f | |
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+---+ +---+ |
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| f | |
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+---+ |
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In the above example, there are 7 nodes (A-G), each with 16 slots (0-f). |
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Assuming no other meta data nodes in the tree, the key space is divided |
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thusly:: |
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KEY PREFIX NODE |
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========== ==== |
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137* D |
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138* E |
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13[0-69-f]* C |
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1[0-24-f]* B |
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e6* G |
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e[0-57-f]* F |
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[02-df]* A |
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So, for instance, keys with the following example index keys will be found in |
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the appropriate nodes:: |
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INDEX KEY PREFIX NODE |
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=============== ======= ==== |
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13694892892489 13 C |
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13795289025897 137 D |
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13889dde88793 138 E |
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138bbb89003093 138 E |
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1394879524789 12 C |
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1458952489 1 B |
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9431809de993ba - A |
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b4542910809cd - A |
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e5284310def98 e F |
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e68428974237 e6 G |
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e7fffcbd443 e F |
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f3842239082 - A |
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To save memory, if a node can hold all the leaves in its portion of keyspace, |
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then the node will have all those leaves in it and will not have any metadata |
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pointers - even if some of those leaves would like to be in the same slot. |
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A node can contain a heterogeneous mix of leaves and metadata pointers. |
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Metadata pointers must be in the slots that match their subdivisions of key |
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space. The leaves can be in any slot not occupied by a metadata pointer. It |
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is guaranteed that none of the leaves in a node will match a slot occupied by a |
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metadata pointer. If the metadata pointer is there, any leaf whose key matches |
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the metadata key prefix must be in the subtree that the metadata pointer points |
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to. |
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In the above example list of index keys, node A will contain:: |
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SLOT CONTENT INDEX KEY (PREFIX) |
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==== =============== ================== |
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1 PTR TO NODE B 1* |
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any LEAF 9431809de993ba |
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any LEAF b4542910809cd |
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e PTR TO NODE F e* |
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any LEAF f3842239082 |
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and node B:: |
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3 PTR TO NODE C 13* |
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any LEAF 1458952489 |
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Shortcuts |
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--------- |
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Shortcuts are metadata records that jump over a piece of keyspace. A shortcut |
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is a replacement for a series of single-occupancy nodes ascending through the |
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levels. Shortcuts exist to save memory and to speed up traversal. |
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It is possible for the root of the tree to be a shortcut - say, for example, |
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the tree contains at least 17 nodes all with key prefix ``1111``. The |
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insertion algorithm will insert a shortcut to skip over the ``1111`` keyspace |
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in a single bound and get to the fourth level where these actually become |
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different. |
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Splitting And Collapsing Nodes |
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------------------------------ |
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Each node has a maximum capacity of 16 leaves and metadata pointers. If the |
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insertion algorithm finds that it is trying to insert a 17th object into a |
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node, that node will be split such that at least two leaves that have a common |
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key segment at that level end up in a separate node rooted on that slot for |
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that common key segment. |
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If the leaves in a full node and the leaf that is being inserted are |
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sufficiently similar, then a shortcut will be inserted into the tree. |
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When the number of objects in the subtree rooted at a node falls to 16 or |
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fewer, then the subtree will be collapsed down to a single node - and this will |
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ripple towards the root if possible. |
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Non-Recursive Iteration |
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----------------------- |
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Each node and shortcut contains a back pointer to its parent and the number of |
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slot in that parent that points to it. None-recursive iteration uses these to |
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proceed rootwards through the tree, going to the parent node, slot N + 1 to |
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make sure progress is made without the need for a stack. |
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The backpointers, however, make simultaneous alteration and iteration tricky. |
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Simultaneous Alteration And Iteration |
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------------------------------------- |
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There are a number of cases to consider: |
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1. Simple insert/replace. This involves simply replacing a NULL or old |
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matching leaf pointer with the pointer to the new leaf after a barrier. |
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The metadata blocks don't change otherwise. An old leaf won't be freed |
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until after the RCU grace period. |
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2. Simple delete. This involves just clearing an old matching leaf. The |
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metadata blocks don't change otherwise. The old leaf won't be freed until |
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after the RCU grace period. |
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3. Insertion replacing part of a subtree that we haven't yet entered. This |
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may involve replacement of part of that subtree - but that won't affect |
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the iteration as we won't have reached the pointer to it yet and the |
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ancestry blocks are not replaced (the layout of those does not change). |
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4. Insertion replacing nodes that we're actively processing. This isn't a |
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problem as we've passed the anchoring pointer and won't switch onto the |
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new layout until we follow the back pointers - at which point we've |
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already examined the leaves in the replaced node (we iterate over all the |
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leaves in a node before following any of its metadata pointers). |
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We might, however, re-see some leaves that have been split out into a new |
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branch that's in a slot further along than we were at. |
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5. Insertion replacing nodes that we're processing a dependent branch of. |
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This won't affect us until we follow the back pointers. Similar to (4). |
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6. Deletion collapsing a branch under us. This doesn't affect us because the |
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back pointers will get us back to the parent of the new node before we |
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could see the new node. The entire collapsed subtree is thrown away |
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unchanged - and will still be rooted on the same slot, so we shouldn't |
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process it a second time as we'll go back to slot + 1. |
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.. note:: |
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Under some circumstances, we need to simultaneously change the parent |
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pointer and the parent slot pointer on a node (say, for example, we |
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inserted another node before it and moved it up a level). We cannot do |
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this without locking against a read - so we have to replace that node too. |
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However, when we're changing a shortcut into a node this isn't a problem |
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as shortcuts only have one slot and so the parent slot number isn't used |
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when traversing backwards over one. This means that it's okay to change |
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the slot number first - provided suitable barriers are used to make sure |
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the parent slot number is read after the back pointer. |
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Obsolete blocks and leaves are freed up after an RCU grace period has passed, |
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so as long as anyone doing walking or iteration holds the RCU read lock, the |
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old superstructure should not go away on them.
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