btree.c

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/*
 * 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 <[email protected]>
 * Bits and pieces stolen from Peter Zijlstra's code, which is
 * Copyright 2007, Red Hat Inc. Peter Zijlstra <[email protected]>
 * 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
 * exercise 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);
    if (likely(node))
        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;
    longcpy(key, __key, geo->keylen);
retry:
    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) {
        longcpy(key, retry_key, geo->keylen);
        retry_key = NULL;
        goto retry;
    }
    return NULL;
}
EXPORT_SYMBOL_GPL(btree_get_prev);

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)
{
    BUG_ON(!val);
    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 neighbour, 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 <[email protected]>");
MODULE_AUTHOR("Johannes Berg <[email protected]>");
MODULE_LICENSE("GPL");