--- lib/btree.c | 797 +++++++++++++ diff --git a/lib/btree.c b/lib/btree.c new file mode 100644 index 0000000..41859a8 --- /dev/null +++ b/lib/btree.c @@ -0,0 +1,797 @@ +/* + * lib/btree.c - Simple In-memory B+Tree + * + * As should be obvious for Linux kernel code, license is GPLv2 + * + * Copyright (c) 2007-2008 Joern Engel <joern@xxxxxxxxx> + * Bits and pieces stolen from Peter Zijlstra's code, which is + * Copyright 2007, Red Hat Inc. Peter Zijlstra <pzijlstr@xxxxxxxxxx> + * GPLv2 + * + * see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch + * + * A relatively simple B+Tree implementation. I have written it as a learning + * excercise to understand how B+Trees work. Turned out to be useful as well. + * + * B+Trees can be used similar to Linux radix trees (which don't have anything + * in common with textbook radix trees, beware). Prerequisite for them working + * well is that access to a random tree node is much faster than a large number + * of operations within each node. + * + * Disks have fulfilled the prerequisite for a long time. More recently DRAM + * has gained similar properties, as memory access times, when measured in cpu + * cycles, have increased. Cacheline sizes have increased as well, which also + * helps B+Trees. + * + * Compared to radix trees, B+Trees are more efficient when dealing with a + * sparsely populated address space. Between 25% and 50% of the memory is + * occupied with valid pointers. When densely populated, radix trees contain + * ~98% pointers - hard to beat. Very sparse radix trees contain only ~2% + * pointers. + * + * This particular implementation stores pointers identified by a long value. + * Storing NULL pointers is illegal, lookup will return NULL when no entry + * was found. + * + * A tricks was used that is not commonly found in textbooks. The lowest + * values are to the right, not to the left. All used slots within a node + * are on the left, all unused slots contain NUL values. Most operations + * simply loop once over all slots and terminate on the first NUL. + */ + +#include <linux/btree.h> +#include <linux/cache.h> +#include <linux/kernel.h> +#include <linux/slab.h> +#include <linux/module.h> + +#define MAX(a, b) ((a) > (b) ? (a) : (b)) +#define NODESIZE MAX(L1_CACHE_BYTES, 128) + +struct btree_geo { + int keylen; + int no_pairs; + int no_longs; +}; + +struct btree_geo btree_geo32 = { + .keylen = 1, + .no_pairs = NODESIZE / sizeof(long) / 2, + .no_longs = NODESIZE / sizeof(long) / 2, +}; +EXPORT_SYMBOL_GPL(btree_geo32); + +#define LONG_PER_U64 (64 / BITS_PER_LONG) +struct btree_geo btree_geo64 = { + .keylen = LONG_PER_U64, + .no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64), + .no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)), +}; +EXPORT_SYMBOL_GPL(btree_geo64); + +struct btree_geo btree_geo128 = { + .keylen = 2 * LONG_PER_U64, + .no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64), + .no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)), +}; +EXPORT_SYMBOL_GPL(btree_geo128); + +static struct kmem_cache *btree_cachep; + +void *btree_alloc(gfp_t gfp_mask, void *pool_data) +{ + return kmem_cache_alloc(btree_cachep, gfp_mask); +} +EXPORT_SYMBOL_GPL(btree_alloc); + +void btree_free(void *element, void *pool_data) +{ + kmem_cache_free(btree_cachep, element); +} +EXPORT_SYMBOL_GPL(btree_free); + +static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp) +{ + unsigned long *node; + + node = mempool_alloc(head->mempool, gfp); + memset(node, 0, NODESIZE); + return node; +} + +static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n) +{ + size_t i; + + for (i = 0; i < n; i++) { + if (l1[i] < l2[i]) + return -1; + if (l1[i] > l2[i]) + return 1; + } + return 0; +} + +static unsigned long *longcpy(unsigned long *dest, const unsigned long *src, + size_t n) +{ + size_t i; + + for (i = 0; i < n; i++) + dest[i] = src[i]; + return dest; +} + +static unsigned long *longset(unsigned long *s, unsigned long c, size_t n) +{ + size_t i; + + for (i = 0; i < n; i++) + s[i] = c; + return s; +} + +static void dec_key(struct btree_geo *geo, unsigned long *key) +{ + unsigned long val; + int i; + + for (i = geo->keylen - 1; i >= 0; i--) { + val = key[i]; + key[i] = val - 1; + if (val) + break; + } +} + +static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n) +{ + return &node[n * geo->keylen]; +} + +static void *bval(struct btree_geo *geo, unsigned long *node, int n) +{ + return (void *)node[geo->no_longs + n]; +} + +static void setkey(struct btree_geo *geo, unsigned long *node, int n, + unsigned long *key) +{ + longcpy(bkey(geo, node, n), key, geo->keylen); +} + +static void setval(struct btree_geo *geo, unsigned long *node, int n, + void *val) +{ + node[geo->no_longs + n] = (unsigned long) val; +} + +static void clearpair(struct btree_geo *geo, unsigned long *node, int n) +{ + longset(bkey(geo, node, n), 0, geo->keylen); + node[geo->no_longs + n] = 0; +} + +static inline void __btree_init(struct btree_head *head) +{ + head->node = NULL; + head->height = 0; +} + +void btree_init_mempool(struct btree_head *head, mempool_t *mempool) +{ + __btree_init(head); + head->mempool = mempool; +} +EXPORT_SYMBOL_GPL(btree_init_mempool); + +int btree_init(struct btree_head *head) +{ + __btree_init(head); + head->mempool = mempool_create(0, btree_alloc, btree_free, NULL); + if (!head->mempool) + return -ENOMEM; + return 0; +} +EXPORT_SYMBOL_GPL(btree_init); + +void btree_destroy(struct btree_head *head) +{ + mempool_destroy(head->mempool); + head->mempool = NULL; +} +EXPORT_SYMBOL_GPL(btree_destroy); + +void *btree_last(struct btree_head *head, struct btree_geo *geo, + unsigned long *key) +{ + int height = head->height; + unsigned long *node = head->node; + + if (height == 0) + return NULL; + + for ( ; height > 1; height--) + node = bval(geo, node, 0); + + longcpy(key, bkey(geo, node, 0), geo->keylen); + return bval(geo, node, 0); +} +EXPORT_SYMBOL_GPL(btree_last); + +static int keycmp(struct btree_geo *geo, unsigned long *node, int pos, + unsigned long *key) +{ + return longcmp(bkey(geo, node, pos), key, geo->keylen); +} + +static int keyzero(struct btree_geo *geo, unsigned long *key) +{ + int i; + + for (i = 0; i < geo->keylen; i++) + if (key[i]) + return 0; + + return 1; +} + +void *btree_lookup(struct btree_head *head, struct btree_geo *geo, + unsigned long *key) +{ + int i, height = head->height; + unsigned long *node = head->node; + + if (height == 0) + return NULL; + + for ( ; height > 1; height--) { + for (i = 0; i < geo->no_pairs; i++) + if (keycmp(geo, node, i, key) <= 0) + break; + if (i == geo->no_pairs) + return NULL; + node = bval(geo, node, i); + if (!node) + return NULL; + } + + if (!node) + return NULL; + + for (i = 0; i < geo->no_pairs; i++) + if (keycmp(geo, node, i, key) == 0) + return bval(geo, node, i); + return NULL; +} +EXPORT_SYMBOL_GPL(btree_lookup); + +int btree_update(struct btree_head *head, struct btree_geo *geo, + unsigned long *key, void *val) +{ + int i, height = head->height; + unsigned long *node = head->node; + + if (height == 0) + return -ENOENT; + + for ( ; height > 1; height--) { + for (i = 0; i < geo->no_pairs; i++) + if (keycmp(geo, node, i, key) <= 0) + break; + if (i == geo->no_pairs) + return -ENOENT; + node = bval(geo, node, i); + if (!node) + return -ENOENT; + } + + if (!node) + return -ENOENT; + + for (i = 0; i < geo->no_pairs; i++) + if (keycmp(geo, node, i, key) == 0) { + setval(geo, node, i, val); + return 0; + } + return -ENOENT; +} +EXPORT_SYMBOL_GPL(btree_update); + +/* + * Usually this function is quite similar to normal lookup. But the key of + * a parent node may be smaller than the smallest key of all its siblings. + * In such a case we cannot just return NULL, as we have only proven that no + * key smaller than __key, but larger than this parent key exists. + * So we set __key to the parent key and retry. We have to use the smallest + * such parent key, which is the last parent key we encountered. + */ +void *btree_get_prev(struct btree_head *head, struct btree_geo *geo, + unsigned long *__key) +{ + int i, height; + unsigned long *node, *oldnode; + unsigned long *retry_key = NULL, key[geo->keylen]; + + if (keyzero(geo, __key)) + return NULL; + + if (head->height == 0) + return NULL; +retry: + longcpy(key, __key, geo->keylen); + dec_key(geo, key); + + node = head->node; + for (height = head->height ; height > 1; height--) { + for (i = 0; i < geo->no_pairs; i++) + if (keycmp(geo, node, i, key) <= 0) + break; + if (i == geo->no_pairs) + goto miss; + oldnode = node; + node = bval(geo, node, i); + if (!node) + goto miss; + retry_key = bkey(geo, oldnode, i); + } + + if (!node) + goto miss; + + for (i = 0; i < geo->no_pairs; i++) { + if (keycmp(geo, node, i, key) <= 0) { + if (bval(geo, node, i)) { + longcpy(__key, bkey(geo, node, i), geo->keylen); + return bval(geo, node, i); + } else + goto miss; + } + } +miss: + if (retry_key) { + __key = retry_key; + retry_key = NULL; + goto retry; + } + return NULL; +} + +static int getpos(struct btree_geo *geo, unsigned long *node, + unsigned long *key) +{ + int i; + + for (i = 0; i < geo->no_pairs; i++) { + if (keycmp(geo, node, i, key) <= 0) + break; + } + return i; +} + +static int getfill(struct btree_geo *geo, unsigned long *node, int start) +{ + int i; + + for (i = start; i < geo->no_pairs; i++) + if (!bval(geo, node, i)) + break; + return i; +} + +/* + * locate the correct leaf node in the btree + */ +static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo, + unsigned long *key, int level) +{ + unsigned long *node = head->node; + int i, height; + + for (height = head->height; height > level; height--) { + for (i = 0; i < geo->no_pairs; i++) + if (keycmp(geo, node, i, key) <= 0) + break; + + if ((i == geo->no_pairs) || !bval(geo, node, i)) { + /* right-most key is too large, update it */ + /* FIXME: If the right-most key on higher levels is + * always zero, this wouldn't be necessary. */ + i--; + setkey(geo, node, i, key); + } + BUG_ON(i < 0); + node = bval(geo, node, i); + } + BUG_ON(!node); + return node; +} + +static int btree_grow(struct btree_head *head, struct btree_geo *geo, + gfp_t gfp) +{ + unsigned long *node; + int fill; + + node = btree_node_alloc(head, gfp); + if (!node) + return -ENOMEM; + if (head->node) { + fill = getfill(geo, head->node, 0); + setkey(geo, node, 0, bkey(geo, head->node, fill - 1)); + setval(geo, node, 0, head->node); + } + head->node = node; + head->height++; + return 0; +} + +static void btree_shrink(struct btree_head *head, struct btree_geo *geo) +{ + unsigned long *node; + int fill; + + if (head->height <= 1) + return; + + node = head->node; + fill = getfill(geo, node, 0); + BUG_ON(fill > 1); + head->node = bval(geo, node, 0); + head->height--; + mempool_free(node, head->mempool); +} + +static int btree_insert_level(struct btree_head *head, struct btree_geo *geo, + unsigned long *key, void *val, int level, + gfp_t gfp) +{ + unsigned long *node; + int i, pos, fill, err; + + BUG_ON(!val); + if (head->height < level) { + err = btree_grow(head, geo, gfp); + if (err) + return err; + } + +retry: + node = find_level(head, geo, key, level); + pos = getpos(geo, node, key); + fill = getfill(geo, node, pos); + /* two identical keys are not allowed */ + BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0); + + if (fill == geo->no_pairs) { + /* need to split node */ + unsigned long *new; + + new = btree_node_alloc(head, gfp); + if (!new) + return -ENOMEM; + err = btree_insert_level(head, geo, + bkey(geo, node, fill / 2 - 1), + new, level + 1, gfp); + if (err) { + mempool_free(new, head->mempool); + return err; + } + for (i = 0; i < fill / 2; i++) { + setkey(geo, new, i, bkey(geo, node, i)); + setval(geo, new, i, bval(geo, node, i)); + setkey(geo, node, i, bkey(geo, node, i + fill / 2)); + setval(geo, node, i, bval(geo, node, i + fill / 2)); + clearpair(geo, node, i + fill / 2); + } + if (fill & 1) { + setkey(geo, node, i, bkey(geo, node, fill - 1)); + setval(geo, node, i, bval(geo, node, fill - 1)); + clearpair(geo, node, fill - 1); + } + goto retry; + } + BUG_ON(fill >= geo->no_pairs); + + /* shift and insert */ + for (i = fill; i > pos; i--) { + setkey(geo, node, i, bkey(geo, node, i - 1)); + setval(geo, node, i, bval(geo, node, i - 1)); + } + setkey(geo, node, pos, key); + setval(geo, node, pos, val); + + return 0; +} + +int btree_insert(struct btree_head *head, struct btree_geo *geo, + unsigned long *key, void *val, gfp_t gfp) +{ + return btree_insert_level(head, geo, key, val, 1, gfp); +} +EXPORT_SYMBOL_GPL(btree_insert); + +static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo, + unsigned long *key, int level); +static void merge(struct btree_head *head, struct btree_geo *geo, int level, + unsigned long *left, int lfill, + unsigned long *right, int rfill, + unsigned long *parent, int lpos) +{ + int i; + + for (i = 0; i < rfill; i++) { + /* Move all keys to the left */ + setkey(geo, left, lfill + i, bkey(geo, right, i)); + setval(geo, left, lfill + i, bval(geo, right, i)); + } + /* Exchange left and right child in parent */ + setval(geo, parent, lpos, right); + setval(geo, parent, lpos + 1, left); + /* Remove left (formerly right) child from parent */ + btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1); + mempool_free(right, head->mempool); +} + +static void rebalance(struct btree_head *head, struct btree_geo *geo, + unsigned long *key, int level, unsigned long *child, int fill) +{ + unsigned long *parent, *left = NULL, *right = NULL; + int i, no_left, no_right; + + if (fill == 0) { + /* Because we don't steal entries from a neigbour, this case + * can happen. Parent node contains a single child, this + * node, so merging with a sibling never happens. + */ + btree_remove_level(head, geo, key, level + 1); + mempool_free(child, head->mempool); + return; + } + + parent = find_level(head, geo, key, level + 1); + i = getpos(geo, parent, key); + BUG_ON(bval(geo, parent, i) != child); + + if (i > 0) { + left = bval(geo, parent, i - 1); + no_left = getfill(geo, left, 0); + if (fill + no_left <= geo->no_pairs) { + merge(head, geo, level, + left, no_left, + child, fill, + parent, i - 1); + return; + } + } + if (i + 1 < getfill(geo, parent, i)) { + right = bval(geo, parent, i + 1); + no_right = getfill(geo, right, 0); + if (fill + no_right <= geo->no_pairs) { + merge(head, geo, level, + child, fill, + right, no_right, + parent, i); + return; + } + } + /* + * 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[geo->keylen]; + unsigned long dup[geo->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 <joern@xxxxxxxxx>"); +MODULE_AUTHOR("Johannes Berg <johannes@xxxxxxxxxxxxxxxx>"); +MODULE_LICENSE("GPL"); -- To unsubscribe from this list: send the line "unsubscribe linux-fsdevel" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
