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801 lines
19 KiB
801 lines
19 KiB
// SPDX-License-Identifier: GPL-2.0-only |
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/* |
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* lib/btree.c - Simple In-memory B+Tree |
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* |
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* Copyright (c) 2007-2008 Joern Engel <[email protected]> |
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* Bits and pieces stolen from Peter Zijlstra's code, which is |
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* Copyright 2007, Red Hat Inc. Peter Zijlstra |
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* |
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* see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch |
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* |
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* A relatively simple B+Tree implementation. I have written it as a learning |
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* exercise to understand how B+Trees work. Turned out to be useful as well. |
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* |
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* B+Trees can be used similar to Linux radix trees (which don't have anything |
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* in common with textbook radix trees, beware). Prerequisite for them working |
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* well is that access to a random tree node is much faster than a large number |
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* of operations within each node. |
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* |
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* Disks have fulfilled the prerequisite for a long time. More recently DRAM |
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* has gained similar properties, as memory access times, when measured in cpu |
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* cycles, have increased. Cacheline sizes have increased as well, which also |
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* helps B+Trees. |
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* |
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* Compared to radix trees, B+Trees are more efficient when dealing with a |
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* sparsely populated address space. Between 25% and 50% of the memory is |
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* occupied with valid pointers. When densely populated, radix trees contain |
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* ~98% pointers - hard to beat. Very sparse radix trees contain only ~2% |
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* pointers. |
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* |
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* This particular implementation stores pointers identified by a long value. |
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* Storing NULL pointers is illegal, lookup will return NULL when no entry |
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* was found. |
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* |
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* A tricks was used that is not commonly found in textbooks. The lowest |
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* values are to the right, not to the left. All used slots within a node |
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* are on the left, all unused slots contain NUL values. Most operations |
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* simply loop once over all slots and terminate on the first NUL. |
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*/ |
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|
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#include <linux/btree.h> |
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#include <linux/cache.h> |
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#include <linux/kernel.h> |
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#include <linux/slab.h> |
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#include <linux/module.h> |
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#define MAX(a, b) ((a) > (b) ? (a) : (b)) |
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#define NODESIZE MAX(L1_CACHE_BYTES, 128) |
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|
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struct btree_geo { |
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int keylen; |
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int no_pairs; |
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int no_longs; |
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}; |
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struct btree_geo btree_geo32 = { |
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.keylen = 1, |
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.no_pairs = NODESIZE / sizeof(long) / 2, |
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.no_longs = NODESIZE / sizeof(long) / 2, |
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}; |
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EXPORT_SYMBOL_GPL(btree_geo32); |
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|
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#define LONG_PER_U64 (64 / BITS_PER_LONG) |
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struct btree_geo btree_geo64 = { |
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.keylen = LONG_PER_U64, |
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.no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64), |
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.no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)), |
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}; |
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EXPORT_SYMBOL_GPL(btree_geo64); |
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struct btree_geo btree_geo128 = { |
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.keylen = 2 * LONG_PER_U64, |
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.no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64), |
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.no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)), |
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}; |
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EXPORT_SYMBOL_GPL(btree_geo128); |
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#define MAX_KEYLEN (2 * LONG_PER_U64) |
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static struct kmem_cache *btree_cachep; |
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|
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void *btree_alloc(gfp_t gfp_mask, void *pool_data) |
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{ |
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return kmem_cache_alloc(btree_cachep, gfp_mask); |
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} |
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EXPORT_SYMBOL_GPL(btree_alloc); |
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void btree_free(void *element, void *pool_data) |
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{ |
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kmem_cache_free(btree_cachep, element); |
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} |
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EXPORT_SYMBOL_GPL(btree_free); |
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static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp) |
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{ |
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unsigned long *node; |
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node = mempool_alloc(head->mempool, gfp); |
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if (likely(node)) |
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memset(node, 0, NODESIZE); |
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return node; |
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} |
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static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n) |
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{ |
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size_t i; |
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for (i = 0; i < n; i++) { |
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if (l1[i] < l2[i]) |
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return -1; |
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if (l1[i] > l2[i]) |
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return 1; |
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} |
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return 0; |
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} |
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static unsigned long *longcpy(unsigned long *dest, const unsigned long *src, |
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size_t n) |
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{ |
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size_t i; |
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for (i = 0; i < n; i++) |
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dest[i] = src[i]; |
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return dest; |
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} |
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static unsigned long *longset(unsigned long *s, unsigned long c, size_t n) |
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{ |
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size_t i; |
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for (i = 0; i < n; i++) |
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s[i] = c; |
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return s; |
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} |
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static void dec_key(struct btree_geo *geo, unsigned long *key) |
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{ |
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unsigned long val; |
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int i; |
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for (i = geo->keylen - 1; i >= 0; i--) { |
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val = key[i]; |
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key[i] = val - 1; |
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if (val) |
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break; |
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} |
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} |
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static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n) |
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{ |
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return &node[n * geo->keylen]; |
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} |
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static void *bval(struct btree_geo *geo, unsigned long *node, int n) |
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{ |
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return (void *)node[geo->no_longs + n]; |
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} |
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static void setkey(struct btree_geo *geo, unsigned long *node, int n, |
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unsigned long *key) |
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{ |
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longcpy(bkey(geo, node, n), key, geo->keylen); |
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} |
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static void setval(struct btree_geo *geo, unsigned long *node, int n, |
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void *val) |
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{ |
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node[geo->no_longs + n] = (unsigned long) val; |
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} |
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static void clearpair(struct btree_geo *geo, unsigned long *node, int n) |
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{ |
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longset(bkey(geo, node, n), 0, geo->keylen); |
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node[geo->no_longs + n] = 0; |
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} |
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static inline void __btree_init(struct btree_head *head) |
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{ |
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head->node = NULL; |
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head->height = 0; |
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} |
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void btree_init_mempool(struct btree_head *head, mempool_t *mempool) |
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{ |
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__btree_init(head); |
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head->mempool = mempool; |
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} |
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EXPORT_SYMBOL_GPL(btree_init_mempool); |
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int btree_init(struct btree_head *head) |
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{ |
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__btree_init(head); |
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head->mempool = mempool_create(0, btree_alloc, btree_free, NULL); |
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if (!head->mempool) |
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return -ENOMEM; |
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return 0; |
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} |
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EXPORT_SYMBOL_GPL(btree_init); |
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void btree_destroy(struct btree_head *head) |
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{ |
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mempool_free(head->node, head->mempool); |
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mempool_destroy(head->mempool); |
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head->mempool = NULL; |
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} |
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EXPORT_SYMBOL_GPL(btree_destroy); |
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void *btree_last(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key) |
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{ |
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int height = head->height; |
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unsigned long *node = head->node; |
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if (height == 0) |
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return NULL; |
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for ( ; height > 1; height--) |
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node = bval(geo, node, 0); |
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longcpy(key, bkey(geo, node, 0), geo->keylen); |
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return bval(geo, node, 0); |
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} |
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EXPORT_SYMBOL_GPL(btree_last); |
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static int keycmp(struct btree_geo *geo, unsigned long *node, int pos, |
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unsigned long *key) |
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{ |
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return longcmp(bkey(geo, node, pos), key, geo->keylen); |
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} |
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static int keyzero(struct btree_geo *geo, unsigned long *key) |
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{ |
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int i; |
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for (i = 0; i < geo->keylen; i++) |
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if (key[i]) |
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return 0; |
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return 1; |
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} |
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void *btree_lookup(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key) |
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{ |
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int i, height = head->height; |
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unsigned long *node = head->node; |
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if (height == 0) |
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return NULL; |
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for ( ; height > 1; height--) { |
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for (i = 0; i < geo->no_pairs; i++) |
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if (keycmp(geo, node, i, key) <= 0) |
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break; |
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if (i == geo->no_pairs) |
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return NULL; |
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node = bval(geo, node, i); |
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if (!node) |
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return NULL; |
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} |
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if (!node) |
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return NULL; |
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for (i = 0; i < geo->no_pairs; i++) |
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if (keycmp(geo, node, i, key) == 0) |
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return bval(geo, node, i); |
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return NULL; |
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} |
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EXPORT_SYMBOL_GPL(btree_lookup); |
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int btree_update(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key, void *val) |
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{ |
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int i, height = head->height; |
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unsigned long *node = head->node; |
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if (height == 0) |
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return -ENOENT; |
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for ( ; height > 1; height--) { |
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for (i = 0; i < geo->no_pairs; i++) |
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if (keycmp(geo, node, i, key) <= 0) |
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break; |
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if (i == geo->no_pairs) |
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return -ENOENT; |
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node = bval(geo, node, i); |
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if (!node) |
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return -ENOENT; |
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} |
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if (!node) |
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return -ENOENT; |
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for (i = 0; i < geo->no_pairs; i++) |
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if (keycmp(geo, node, i, key) == 0) { |
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setval(geo, node, i, val); |
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return 0; |
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} |
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return -ENOENT; |
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} |
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EXPORT_SYMBOL_GPL(btree_update); |
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/* |
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* Usually this function is quite similar to normal lookup. But the key of |
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* a parent node may be smaller than the smallest key of all its siblings. |
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* In such a case we cannot just return NULL, as we have only proven that no |
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* key smaller than __key, but larger than this parent key exists. |
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* So we set __key to the parent key and retry. We have to use the smallest |
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* such parent key, which is the last parent key we encountered. |
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*/ |
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void *btree_get_prev(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *__key) |
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{ |
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int i, height; |
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unsigned long *node, *oldnode; |
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unsigned long *retry_key = NULL, key[MAX_KEYLEN]; |
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if (keyzero(geo, __key)) |
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return NULL; |
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if (head->height == 0) |
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return NULL; |
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longcpy(key, __key, geo->keylen); |
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retry: |
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dec_key(geo, key); |
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node = head->node; |
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for (height = head->height ; height > 1; height--) { |
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for (i = 0; i < geo->no_pairs; i++) |
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if (keycmp(geo, node, i, key) <= 0) |
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break; |
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if (i == geo->no_pairs) |
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goto miss; |
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oldnode = node; |
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node = bval(geo, node, i); |
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if (!node) |
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goto miss; |
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retry_key = bkey(geo, oldnode, i); |
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} |
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if (!node) |
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goto miss; |
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for (i = 0; i < geo->no_pairs; i++) { |
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if (keycmp(geo, node, i, key) <= 0) { |
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if (bval(geo, node, i)) { |
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longcpy(__key, bkey(geo, node, i), geo->keylen); |
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return bval(geo, node, i); |
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} else |
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goto miss; |
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} |
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} |
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miss: |
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if (retry_key) { |
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longcpy(key, retry_key, geo->keylen); |
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retry_key = NULL; |
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goto retry; |
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} |
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return NULL; |
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} |
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EXPORT_SYMBOL_GPL(btree_get_prev); |
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static int getpos(struct btree_geo *geo, unsigned long *node, |
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unsigned long *key) |
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{ |
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int i; |
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for (i = 0; i < geo->no_pairs; i++) { |
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if (keycmp(geo, node, i, key) <= 0) |
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break; |
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} |
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return i; |
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} |
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static int getfill(struct btree_geo *geo, unsigned long *node, int start) |
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{ |
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int i; |
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for (i = start; i < geo->no_pairs; i++) |
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if (!bval(geo, node, i)) |
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break; |
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return i; |
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} |
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|
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/* |
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* locate the correct leaf node in the btree |
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*/ |
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static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key, int level) |
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{ |
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unsigned long *node = head->node; |
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int i, height; |
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for (height = head->height; height > level; height--) { |
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for (i = 0; i < geo->no_pairs; i++) |
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if (keycmp(geo, node, i, key) <= 0) |
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break; |
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if ((i == geo->no_pairs) || !bval(geo, node, i)) { |
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/* right-most key is too large, update it */ |
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/* FIXME: If the right-most key on higher levels is |
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* always zero, this wouldn't be necessary. */ |
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i--; |
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setkey(geo, node, i, key); |
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} |
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BUG_ON(i < 0); |
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node = bval(geo, node, i); |
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} |
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BUG_ON(!node); |
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return node; |
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} |
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static int btree_grow(struct btree_head *head, struct btree_geo *geo, |
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gfp_t gfp) |
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{ |
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unsigned long *node; |
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int fill; |
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node = btree_node_alloc(head, gfp); |
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if (!node) |
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return -ENOMEM; |
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if (head->node) { |
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fill = getfill(geo, head->node, 0); |
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setkey(geo, node, 0, bkey(geo, head->node, fill - 1)); |
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setval(geo, node, 0, head->node); |
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} |
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head->node = node; |
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head->height++; |
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return 0; |
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} |
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static void btree_shrink(struct btree_head *head, struct btree_geo *geo) |
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{ |
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unsigned long *node; |
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int fill; |
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if (head->height <= 1) |
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return; |
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node = head->node; |
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fill = getfill(geo, node, 0); |
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BUG_ON(fill > 1); |
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head->node = bval(geo, node, 0); |
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head->height--; |
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mempool_free(node, head->mempool); |
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} |
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static int btree_insert_level(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key, void *val, int level, |
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gfp_t gfp) |
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{ |
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unsigned long *node; |
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int i, pos, fill, err; |
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BUG_ON(!val); |
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if (head->height < level) { |
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err = btree_grow(head, geo, gfp); |
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if (err) |
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return err; |
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} |
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retry: |
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node = find_level(head, geo, key, level); |
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pos = getpos(geo, node, key); |
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fill = getfill(geo, node, pos); |
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/* two identical keys are not allowed */ |
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BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0); |
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|
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if (fill == geo->no_pairs) { |
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/* need to split node */ |
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unsigned long *new; |
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new = btree_node_alloc(head, gfp); |
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if (!new) |
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return -ENOMEM; |
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err = btree_insert_level(head, geo, |
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bkey(geo, node, fill / 2 - 1), |
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new, level + 1, gfp); |
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if (err) { |
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mempool_free(new, head->mempool); |
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return err; |
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} |
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for (i = 0; i < fill / 2; i++) { |
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setkey(geo, new, i, bkey(geo, node, i)); |
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setval(geo, new, i, bval(geo, node, i)); |
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setkey(geo, node, i, bkey(geo, node, i + fill / 2)); |
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setval(geo, node, i, bval(geo, node, i + fill / 2)); |
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clearpair(geo, node, i + fill / 2); |
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} |
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if (fill & 1) { |
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setkey(geo, node, i, bkey(geo, node, fill - 1)); |
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setval(geo, node, i, bval(geo, node, fill - 1)); |
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clearpair(geo, node, fill - 1); |
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} |
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goto retry; |
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} |
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BUG_ON(fill >= geo->no_pairs); |
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/* shift and insert */ |
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for (i = fill; i > pos; i--) { |
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setkey(geo, node, i, bkey(geo, node, i - 1)); |
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setval(geo, node, i, bval(geo, node, i - 1)); |
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} |
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setkey(geo, node, pos, key); |
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setval(geo, node, pos, val); |
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return 0; |
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} |
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int btree_insert(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key, void *val, gfp_t gfp) |
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{ |
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BUG_ON(!val); |
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return btree_insert_level(head, geo, key, val, 1, gfp); |
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} |
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EXPORT_SYMBOL_GPL(btree_insert); |
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|
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static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key, int level); |
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static void merge(struct btree_head *head, struct btree_geo *geo, int level, |
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unsigned long *left, int lfill, |
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unsigned long *right, int rfill, |
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unsigned long *parent, int lpos) |
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{ |
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int i; |
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for (i = 0; i < rfill; i++) { |
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/* Move all keys to the left */ |
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setkey(geo, left, lfill + i, bkey(geo, right, i)); |
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setval(geo, left, lfill + i, bval(geo, right, i)); |
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} |
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/* Exchange left and right child in parent */ |
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setval(geo, parent, lpos, right); |
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setval(geo, parent, lpos + 1, left); |
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/* Remove left (formerly right) child from parent */ |
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btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1); |
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mempool_free(right, head->mempool); |
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} |
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static void rebalance(struct btree_head *head, struct btree_geo *geo, |
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unsigned long *key, int level, unsigned long *child, int fill) |
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{ |
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unsigned long *parent, *left = NULL, *right = NULL; |
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int i, no_left, no_right; |
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|
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if (fill == 0) { |
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/* Because we don't steal entries from a neighbour, this case |
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* can happen. Parent node contains a single child, this |
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* node, so merging with a sibling never happens. |
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*/ |
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btree_remove_level(head, geo, key, level + 1); |
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mempool_free(child, head->mempool); |
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return; |
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} |
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parent = find_level(head, geo, key, level + 1); |
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i = getpos(geo, parent, key); |
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BUG_ON(bval(geo, parent, i) != child); |
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|
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if (i > 0) { |
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left = bval(geo, parent, i - 1); |
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no_left = getfill(geo, left, 0); |
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if (fill + no_left <= geo->no_pairs) { |
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merge(head, geo, level, |
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left, no_left, |
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child, fill, |
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parent, i - 1); |
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return; |
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} |
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} |
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if (i + 1 < getfill(geo, parent, i)) { |
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right = bval(geo, parent, i + 1); |
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no_right = getfill(geo, right, 0); |
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if (fill + no_right <= geo->no_pairs) { |
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merge(head, geo, level, |
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child, fill, |
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right, no_right, |
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parent, i); |
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return; |
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} |
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} |
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/* |
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* We could also try to steal one entry from the left or right |
|
* neighbor. By not doing so we changed the invariant from |
|
* "all nodes are at least half full" to "no two neighboring |
|
* nodes can be merged". Which means that the average fill of |
|
* all nodes is still half or better. |
|
*/ |
|
} |
|
|
|
static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo, |
|
unsigned long *key, int level) |
|
{ |
|
unsigned long *node; |
|
int i, pos, fill; |
|
void *ret; |
|
|
|
if (level > head->height) { |
|
/* we recursed all the way up */ |
|
head->height = 0; |
|
head->node = NULL; |
|
return NULL; |
|
} |
|
|
|
node = find_level(head, geo, key, level); |
|
pos = getpos(geo, node, key); |
|
fill = getfill(geo, node, pos); |
|
if ((level == 1) && (keycmp(geo, node, pos, key) != 0)) |
|
return NULL; |
|
ret = bval(geo, node, pos); |
|
|
|
/* remove and shift */ |
|
for (i = pos; i < fill - 1; i++) { |
|
setkey(geo, node, i, bkey(geo, node, i + 1)); |
|
setval(geo, node, i, bval(geo, node, i + 1)); |
|
} |
|
clearpair(geo, node, fill - 1); |
|
|
|
if (fill - 1 < geo->no_pairs / 2) { |
|
if (level < head->height) |
|
rebalance(head, geo, key, level, node, fill - 1); |
|
else if (fill - 1 == 1) |
|
btree_shrink(head, geo); |
|
} |
|
|
|
return ret; |
|
} |
|
|
|
void *btree_remove(struct btree_head *head, struct btree_geo *geo, |
|
unsigned long *key) |
|
{ |
|
if (head->height == 0) |
|
return NULL; |
|
|
|
return btree_remove_level(head, geo, key, 1); |
|
} |
|
EXPORT_SYMBOL_GPL(btree_remove); |
|
|
|
int btree_merge(struct btree_head *target, struct btree_head *victim, |
|
struct btree_geo *geo, gfp_t gfp) |
|
{ |
|
unsigned long key[MAX_KEYLEN]; |
|
unsigned long dup[MAX_KEYLEN]; |
|
void *val; |
|
int err; |
|
|
|
BUG_ON(target == victim); |
|
|
|
if (!(target->node)) { |
|
/* target is empty, just copy fields over */ |
|
target->node = victim->node; |
|
target->height = victim->height; |
|
__btree_init(victim); |
|
return 0; |
|
} |
|
|
|
/* TODO: This needs some optimizations. Currently we do three tree |
|
* walks to remove a single object from the victim. |
|
*/ |
|
for (;;) { |
|
if (!btree_last(victim, geo, key)) |
|
break; |
|
val = btree_lookup(victim, geo, key); |
|
err = btree_insert(target, geo, key, val, gfp); |
|
if (err) |
|
return err; |
|
/* We must make a copy of the key, as the original will get |
|
* mangled inside btree_remove. */ |
|
longcpy(dup, key, geo->keylen); |
|
btree_remove(victim, geo, dup); |
|
} |
|
return 0; |
|
} |
|
EXPORT_SYMBOL_GPL(btree_merge); |
|
|
|
static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo, |
|
unsigned long *node, unsigned long opaque, |
|
void (*func)(void *elem, unsigned long opaque, |
|
unsigned long *key, size_t index, |
|
void *func2), |
|
void *func2, int reap, int height, size_t count) |
|
{ |
|
int i; |
|
unsigned long *child; |
|
|
|
for (i = 0; i < geo->no_pairs; i++) { |
|
child = bval(geo, node, i); |
|
if (!child) |
|
break; |
|
if (height > 1) |
|
count = __btree_for_each(head, geo, child, opaque, |
|
func, func2, reap, height - 1, count); |
|
else |
|
func(child, opaque, bkey(geo, node, i), count++, |
|
func2); |
|
} |
|
if (reap) |
|
mempool_free(node, head->mempool); |
|
return count; |
|
} |
|
|
|
static void empty(void *elem, unsigned long opaque, unsigned long *key, |
|
size_t index, void *func2) |
|
{ |
|
} |
|
|
|
void visitorl(void *elem, unsigned long opaque, unsigned long *key, |
|
size_t index, void *__func) |
|
{ |
|
visitorl_t func = __func; |
|
|
|
func(elem, opaque, *key, index); |
|
} |
|
EXPORT_SYMBOL_GPL(visitorl); |
|
|
|
void visitor32(void *elem, unsigned long opaque, unsigned long *__key, |
|
size_t index, void *__func) |
|
{ |
|
visitor32_t func = __func; |
|
u32 *key = (void *)__key; |
|
|
|
func(elem, opaque, *key, index); |
|
} |
|
EXPORT_SYMBOL_GPL(visitor32); |
|
|
|
void visitor64(void *elem, unsigned long opaque, unsigned long *__key, |
|
size_t index, void *__func) |
|
{ |
|
visitor64_t func = __func; |
|
u64 *key = (void *)__key; |
|
|
|
func(elem, opaque, *key, index); |
|
} |
|
EXPORT_SYMBOL_GPL(visitor64); |
|
|
|
void visitor128(void *elem, unsigned long opaque, unsigned long *__key, |
|
size_t index, void *__func) |
|
{ |
|
visitor128_t func = __func; |
|
u64 *key = (void *)__key; |
|
|
|
func(elem, opaque, key[0], key[1], index); |
|
} |
|
EXPORT_SYMBOL_GPL(visitor128); |
|
|
|
size_t btree_visitor(struct btree_head *head, struct btree_geo *geo, |
|
unsigned long opaque, |
|
void (*func)(void *elem, unsigned long opaque, |
|
unsigned long *key, |
|
size_t index, void *func2), |
|
void *func2) |
|
{ |
|
size_t count = 0; |
|
|
|
if (!func2) |
|
func = empty; |
|
if (head->node) |
|
count = __btree_for_each(head, geo, head->node, opaque, func, |
|
func2, 0, head->height, 0); |
|
return count; |
|
} |
|
EXPORT_SYMBOL_GPL(btree_visitor); |
|
|
|
size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo, |
|
unsigned long opaque, |
|
void (*func)(void *elem, unsigned long opaque, |
|
unsigned long *key, |
|
size_t index, void *func2), |
|
void *func2) |
|
{ |
|
size_t count = 0; |
|
|
|
if (!func2) |
|
func = empty; |
|
if (head->node) |
|
count = __btree_for_each(head, geo, head->node, opaque, func, |
|
func2, 1, head->height, 0); |
|
__btree_init(head); |
|
return count; |
|
} |
|
EXPORT_SYMBOL_GPL(btree_grim_visitor); |
|
|
|
static int __init btree_module_init(void) |
|
{ |
|
btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0, |
|
SLAB_HWCACHE_ALIGN, NULL); |
|
return 0; |
|
} |
|
|
|
static void __exit btree_module_exit(void) |
|
{ |
|
kmem_cache_destroy(btree_cachep); |
|
} |
|
|
|
/* If core code starts using btree, initialization should happen even earlier */ |
|
module_init(btree_module_init); |
|
module_exit(btree_module_exit); |
|
|
|
MODULE_AUTHOR("Joern Engel <[email protected]>"); |
|
MODULE_AUTHOR("Johannes Berg <[email protected]>"); |
|
MODULE_LICENSE("GPL");
|
|
|