--- /dev/null 2008-04-02 16:29:12.813336657 +0200
+++ linux-2.6.24logfs/fs/logfs/memtree.c 2008-04-01 21:43:14.593326689 +0200
@@ -0,0 +1,405 @@
+/*
+ * fs/logfs/memtree.c - Simple In-memory B+Tree
+ *
+ * As should be obvious for Linux kernel code, license is GPLv2
+ *
+ * Copyright (c) 2007 Joern Engel <joern@xxxxxxxxx>
+ *
+ *
+ * This could possibly get moved to lib/.
+ *
+ * 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 prerequite 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.
+ *
+ * Two tricks were used that are not commonly found in textbooks. First, 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.
+ *
+ * Second trick is to special-case the key "0" or NUL. As seen above, this
+ * value indicates an unused slot, so such a value should not be stored in the
+ * tree itself. Instead it is stored in the null_ptr field in the btree_head.
+ */
+/* FIXME: use mempool for allocations */
+#include "logfs.h"
+
+/*
+ * Prerequisite of B+Trees performing well is that node lookup is much slower
+ * than a large number of operations within a node. That can be true if the
+ * node size is identical to cacheline size. All that is highly
+ * machine-dependent, just like the #define below is not.
+ *
+ * Patches to do something smarter are welcome. Just beware that too small
+ * node with less than 8 slots have a bad fan-out and won't perform well
+ * either.
+ */
+#if BITS_PER_LONG == 32
+#define BTREE_NODES 20 /* 32bit, 240 byte nodes */
+#else
+#define BTREE_NODES 16 /* 64bit, 256 byte nodes */
+#endif
+
+struct btree_node {
+ u64 key;
+ struct btree_node *node;
+};
+
+void btree_init(struct btree_head *head)
+{
+ head->node = NULL;
+ head->height = 0;
+ head->null_ptr = NULL;
+}
+
+#if 0
+static void __dump_tree(struct btree_node *node, int height)
+{
+ int i;
+
+ if (!height)
+ return;
+
+ printk(KERN_DEBUG"%p ", node);
+ for (i = 0; i < BTREE_NODES; i++)
+ printk("(%llx,%p) ", node[i].key, node[i].node);
+ printk("\n");
+
+ for (i = 0; i < BTREE_NODES; i++)
+ if (node[i].key)
+ __dump_tree(node[i].node, height-1);
+}
+
+static void dump_tree(struct btree_head *head)
+{
+ printk(KERN_DEBUG"%p\n", head->null_ptr);
+ __dump_tree(head->node, head->height);
+}
+#endif
+
+static u64 btree_last(struct btree_head *head)
+{
+ int height = head->height;
+ struct btree_node *node = head->node;
+
+ if (height == 0)
+ return 0;
+
+ for ( ; height > 1; height--)
+ node = node[0].node;
+
+ return node[0].key;
+}
+
+void *btree_lookup(struct btree_head *head, u64 key)
+{
+ int i, height = head->height;
+ struct btree_node *node = head->node;
+
+ if (key == 0)
+ return head->null_ptr;
+
+ if (height == 0)
+ return NULL;
+
+ for ( ; height > 1; height--) {
+ for (i = 0; i < BTREE_NODES; i++)
+ if (node[i].key <= key)
+ break;
+ node = node[i].node;
+ if (!node)
+ return NULL;
+ }
+
+ if (!node)
+ return NULL;
+
+ for (i = 0; i < BTREE_NODES; i++)
+ if (node[i].key == key)
+ return node[i].node;
+
+ return NULL;
+}
+
+/*
+ * Returns two values:
+ * pos - the position of the first slot equal or less than key
+ * fill - the number of positions filled with any value
+ */
+static void find_pos(struct btree_node *node, u64 key, int *pos, int *fill)
+{
+ int i;
+
+ for (i = 0; i < BTREE_NODES; i++)
+ if (node[i].key <= key)
+ break;
+ *pos = i;
+ for (i = *pos; i < BTREE_NODES; i++)
+ if (node[i].key == 0)
+ break;
+ *fill = i;
+}
+
+/*
+ * locate the correct leaf node in the btree
+ */
+static struct btree_node *find_level(struct btree_head *head, u64 key,
+ int level)
+{
+ struct btree_node *node = head->node;
+ int i, height;
+
+ for (height = head->height; height > level; height--) {
+ for (i = 0; i < BTREE_NODES; i++)
+ if (node[i].key <= key)
+ break;
+
+ if ((i == BTREE_NODES) || !node[i].key) {
+ /* right-most key is too large, update it */
+ i--;
+ node[i].key = key;
+ }
+ BUG_ON(i < 0);
+ node = node[i].node;
+ }
+ BUG_ON(!node);
+ return node;
+}
+
+static int btree_grow(struct btree_head *head)
+{
+ struct btree_node *node;
+
+ node = kcalloc(BTREE_NODES, sizeof(*node), GFP_KERNEL);
+ BUG_ON(!node);
+ if (!node)
+ return -ENOMEM;
+ if (head->node) {
+ node->key = head->node[BTREE_NODES-1].key;
+ node->node = head->node;
+ }
+ head->node = node;
+ head->height++;
+ return 0;
+}
+
+static int btree_insert_level(struct btree_head *head, u64 key, void *ptr,
+ int level)
+{
+ struct btree_node *node;
+ int i, pos, fill, err;
+
+ BUG_ON(!ptr);
+ if (key == 0) {
+ /* 0 identifies empty slots, so special-case this */
+ BUG_ON(level != 1);
+ head->null_ptr = ptr;
+ return 0;
+ }
+
+ if (head->height < level) {
+ err = btree_grow(head);
+ if (err)
+ return err;
+ }
+
+retry:
+ node = find_level(head, key, level);
+ find_pos(node, key, &pos, &fill);
+ BUG_ON(node[pos].key == key);
+
+ if (fill == BTREE_NODES) {
+ /* need to split node */
+ struct btree_node *new;
+
+ new = kcalloc(BTREE_NODES, sizeof(*node), GFP_KERNEL);
+ BUG_ON(!new);
+ if (!new)
+ return -ENOMEM;
+ err = btree_insert_level(head, node[BTREE_NODES/2 - 1].key, new,
+ level+1);
+ if (err) {
+ kfree(new);
+ return err;
+ }
+ for (i = 0; i < BTREE_NODES / 2; i++) {
+ new[i].key = node[i].key;
+ new[i].node = node[i].node;
+ node[i].key = node[i + BTREE_NODES/2].key;
+ node[i].node = node[i + BTREE_NODES/2].node;
+ node[i + BTREE_NODES/2].key = 0;
+ node[i + BTREE_NODES/2].node = NULL;
+ }
+ goto retry;
+ }
+ BUG_ON(fill >= BTREE_NODES);
+
+ /* shift and insert */
+ for (i = fill; i > pos; i--) {
+ node[i].key = node[i-1].key;
+ node[i].node = node[i-1].node;
+ }
+ node[pos].key = key;
+ node[pos].node = ptr;
+
+ return 0;
+}
+
+int btree_insert(struct btree_head *head, u64 key, void *ptr)
+{
+ BUG_ON(!ptr);
+ return btree_insert_level(head, key, ptr, 1);
+}
+
+static void *btree_remove_level(struct btree_head *head, u64 key, int level)
+{
+ struct btree_node *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, key, level);
+ find_pos(node, key, &pos, &fill);
+ if ((level == 1) && (node[pos].key != key))
+ return NULL;
+ ret = node[pos].node;
+
+ /* remove and shift */
+ for (i = pos; i < fill-1; i++) {
+ node[i].key = node[i+1].key;
+ node[i].node = node[i+1].node;
+ }
+ node[fill-1].key = 0;
+ node[fill-1].node = NULL;
+
+ if (fill-1 < BTREE_NODES/2) {
+ /*
+ * At this point there *should* be code to either merge with
+ * a neighboring node or steal some entries from it to preserve
+ * the btree invariant of only having nodes with n/2..n
+ * elements.
+ *
+ * As you can see, that code is left as an excercise to the
+ * reader or anyone noticing severe performance problems in
+ * very rare cases.
+ *
+ * As-is this code "implements" a method called lazy deletion,
+ * which according to text books is relatively common in
+ * databases and usually works quite well.
+ * Not so usually, the btree can degrade into very long lists
+ * of 1-element nodes and perform accordingly.
+ */
+ }
+ if (fill-1 == 0) {
+ btree_remove_level(head, key, level+1);
+ kfree(node);
+ }
+
+ return ret;
+}
+
+void *btree_remove(struct btree_head *head, u64 key)
+{
+ void *ret;
+
+ if (key == 0) {
+ /* 0 identifies empty slots, so special-case this */
+ ret = head->null_ptr;
+ head->null_ptr = NULL;
+ return ret;
+ }
+ if (head->height == 0)
+ return NULL;
+
+ return btree_remove_level(head, key, 1);
+}
+
+int btree_merge(struct btree_head *target, struct btree_head *victim)
+{
+ struct btree_node *node;
+ u64 key;
+ int err;
+
+ BUG_ON(target == victim);
+
+ if (!(target->node || target->null_ptr)) {
+ /* target is empty, just copy fields over */
+ target->null_ptr = victim->null_ptr;
+ target->node = victim->node;
+ target->height = victim->height;
+ btree_init(victim);
+ return 0;
+ }
+
+ for (;;) {
+ key = btree_last(victim);
+ node = btree_remove(victim, key);
+ if (!node)
+ break;
+ err = btree_insert(target, key, node);
+ if (err)
+ return err;
+ }
+ return 0;
+}
+
+static void __btree_for_each(struct btree_node *node, long opaque,
+ void (*func)(void *elem, long opaque, u64 key), int reap,
+ int height)
+{
+ int i;
+
+ for (i = 0; i < BTREE_NODES && node[i].key; i++) {
+ if (height > 1)
+ __btree_for_each(node[i].node, opaque, func, reap,
+ height-1);
+ else
+ func(node[i].node, opaque, node[i].key);
+ }
+ if (reap)
+ kfree(node);
+}
+
+void btree_visitor(struct btree_head *head, long opaque,
+ void (*func)(void *elem, long opaque, u64 key))
+{
+ if (head->node)
+ __btree_for_each(head->node, opaque, func, 0, head->height);
+ if (head->null_ptr)
+ func(head->null_ptr, opaque, 0);
+}
+
+void btree_grim_visitor(struct btree_head *head, long opaque,
+ void (*func)(void *elem, long opaque, u64 key))
+{
+ if (head->node)
+ __btree_for_each(head->node, opaque, func, 1, head->height);
+ if (head->null_ptr)
+ func(head->null_ptr, opaque, 0);
+ btree_init(head);
+}
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