--- /dev/null 2007-03-13 19:15:28.862769062 +0100
+++ linux-2.6.21logfs/fs/logfs/memtree.c 2007-06-03 19:18:57.000000000 +0200
@@ -0,0 +1,258 @@
+/*
+ * 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
+ *
+ *
+ * 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.
+ */
+#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.
+ */
+#define BTREE_NODES 16 /* 32bit, 128 byte cacheline */
+
+struct btree_node {
+ long val;
+ struct btree_node *node;
+};
+
+void btree_init(struct btree_head *head)
+{
+ head->node = NULL;
+ head->height = 0;
+ head->null_ptr = NULL;
+}
+
+void *btree_lookup(struct btree_head *head, long val)
+{
+ int i, height = head->height;
+ struct btree_node *node = head->node;
+
+ if (val == 0)
+ return head->null_ptr;
+
+ if (height == 0)
+ return NULL;
+
+ for ( ; height > 1; height--) {
+ for (i=0; i<BTREE_NODES; i++)
+ if (node[i].val <= val)
+ break;
+ node = node[i].node;
+ }
+
+ for (i=0; i<BTREE_NODES; i++)
+ if (node[i].val == val)
+ return node[i].node;
+
+ return NULL;
+}
+
+static void find_pos(struct btree_node *node, long val, int *pos, int *fill)
+{
+ int i;
+
+ for (i=0; i<BTREE_NODES; i++)
+ if (node[i].val <= val)
+ break;
+ *pos = i;
+ for (i=*pos; i<BTREE_NODES; i++)
+ if (node[i].val == 0)
+ break;
+ *fill = i;
+}
+
+static struct btree_node *find_level(struct btree_head *head, long val,
+ int level)
+{
+ struct btree_node *node = head->node;
+ int i, height = head->height;
+
+ for ( ; height > level; height--) {
+ for (i=0; i<BTREE_NODES; i++)
+ if (node[i].val <= val)
+ break;
+ node = node[i].node;
+ }
+ return node;
+}
+
+static int btree_grow(struct btree_head *head)
+{
+ struct btree_node *node;
+
+ node = kcalloc(BTREE_NODES, sizeof(*node), GFP_KERNEL);
+ if (!node)
+ return -ENOMEM;
+ if (head->node) {
+ node->val = head->node[BTREE_NODES-1].val;
+ node->node = head->node;
+ }
+ head->node = node;
+ head->height++;
+ return 0;
+}
+
+static int btree_insert_level(struct btree_head *head, long val, void *ptr,
+ int level)
+{
+ struct btree_node *node;
+ int i, pos, fill, err;
+
+ if (val == 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, val, level);
+ find_pos(node, val, &pos, &fill);
+ BUG_ON(node[pos].val == val);
+
+ if (fill == BTREE_NODES) {
+ /* need to split node */
+ struct btree_node *new;
+
+ new = kcalloc(BTREE_NODES, sizeof(*node), GFP_KERNEL);
+ if (!new)
+ return -ENOMEM;
+ err = btree_insert_level(head, node[BTREE_NODES/2 - 1].val, new,
+ level+1);
+ if (err) {
+ kfree(new);
+ return err;
+ }
+ for (i=0; i<BTREE_NODES/2; i++) {
+ new[i].val = node[i].val;
+ new[i].node = node[i].node;
+ node[i].val = node[i + BTREE_NODES/2].val;
+ node[i].node = node[i + BTREE_NODES/2].node;
+ node[i + BTREE_NODES/2].val = 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].val = node[i-1].val;
+ node[i].node = node[i-1].node;
+ }
+ node[pos].val = val;
+ node[pos].node = ptr;
+
+ return 0;
+}
+
+int btree_insert(struct btree_head *head, long val, void *ptr)
+{
+ return btree_insert_level(head, val, ptr, 1);
+}
+
+static int btree_remove_level(struct btree_head *head, long val, int level)
+{
+ struct btree_node *node;
+ int i, pos, fill;
+
+ if (val == 0) {
+ /* 0 identifies empty slots, so special-case this */
+ head->null_ptr = NULL;
+ return 0;
+ }
+
+ node = find_level(head, val, level);
+ find_pos(node, val, &pos, &fill);
+ if (level == 1)
+ BUG_ON(node[pos].val != val);
+
+ /* remove and shift */
+ for (i=pos; i<fill-1; i++) {
+ node[i].val = node[i+1].val;
+ node[i].node = node[i+1].node;
+ }
+ node[fill-1].val = 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, val, level+1);
+ kfree(node);
+ return 0;
+ }
+
+ return 0;
+}
+
+int btree_remove(struct btree_head *head, long val)
+{
+ return btree_remove_level(head, val, 1);
+}
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