1.     单值查找radix_tree_lookup

函数radix_tree_lookup执行查找操作，查找方法是：从叶子到树顶，通过数组索引键值值查看数组元素的方法，一层层地查找slot。其列出如下

void *radix_tree_lookup(struct radix_tree_root *root, unsigned long index)
{
    unsigned int height, shift;
    struct radix_tree_node *node, **slot;

    node = rcu_dereference(root->rnode); /*获取根结点*/
    if (node == NULL)
        return NULL;

/*间接指针指向结点而非数据条目，通过设置root->rnode的低位表示是否是间指针。对于间接指针来说，树高度值root->height大于0，但是RCU查找需要测试间接指针，因为root->height 值不可靠。这种问题仅的RCU下需要考虑*/ 
    if (!radix_tree_is_indirect_ptr(node)) { /*非间接指针，说明只有根结点*/
        if (index > 0)
            return NULL;
        return node;
    }

 /*获取真正结点指针，因为根结点指针的第0位设置为1表示为间接指针。当使用结点指针时，必须将第0位设置为0，因为地址以字对齐*/
    node = radix_tree_indirect_to_ptr(node);

    height = node->height;
    if (index > radix_tree_maxindex(height)) /*索引键值不能超过最大索引值*/
        return NULL;

    /*每层索引偏移值为RADIX_TREE_MAP_SHIFT，叶子索引值偏移基数为（树高-1）*每层索引偏移值*/ 
    shift = (height-1) * RADIX_TREE_MAP_SHIFT;

    do { /*从叶子到树顶，通过树路径组成的索引查找指定索引键值的slot*/
        slot = (struct radix_tree_node **)(node->slots + ((index>>shift) & RADIX_TREE_MAP_MASK)); /*如：slots +1*/
        node = rcu_dereference(*slot);
        if (node == NULL)
            return NULL;

        shift -= RADIX_TREE_MAP_SHIFT; /*向上移一层，再迭代查找*/
        height--;
    } while (height > 0);

   return node;
}

2.     多值查找radix_tree_gang_lookup

函数执行多个索引键值的查找，其列出如下：

unsigned int radix_tree_gang_lookup(struct radix_tree_root *root, void **results, unsigned long first_index, unsigned int max_items)
{
    unsigned long max_index;
    struct radix_tree_node *node;
    unsigned long cur_index = first_index;
    unsigned int ret;

    node = rcu_dereference(root->rnode);
    if (!node)
        return 0;

    if (!radix_tree_is_indirect_ptr(node)) { /*如果为非间接指针，表示只有根节点*/
        if (first_index > 0)
            return 0;
        results[0] = node;
        return 1;
    }
    node = radix_tree_indirect_to_ptr(node); /*清除用于间接指针标识的第0位*/

    max_index = radix_tree_maxindex(node->height); /*获取树的最大索引键值*/

    ret = 0;
    while (ret < max_items) { /* max_items为查找的最大条目数*/
        unsigned int nr_found;
        unsigned long next_index; /* 下一个搜索的索引键值*/

        if (cur_index > max_index) /*已查询完所需查询的索引键值*/
            break;
        nr_found = __lookup(node, results + ret, cur_index,
        max_items - ret, &next_index);
        ret += nr_found;
        if (next_index == 0)
            break;
        cur_index = next_index;
    }

    return ret;
}

static unsigned int
__lookup(struct radix_tree_node *slot, void **results, unsigned long index, unsigned int max_items, unsigned long *next_index)
{
    unsigned int nr_found = 0;
    unsigned int shift, height;
    unsigned long i;

    height = slot->height;
    if (height == 0)
        goto out;
    /*所有叶子slot的索引键值基数偏移*/
    shift = (height-1) * RADIX_TREE_MAP_SHIFT; 

    /*从底层向树顶层，
    for ( ; height > 1; height--) { /*从叶子向树顶查找*/
        i = (index >> shift) & RADIX_TREE_MAP_MASK;
        for (;;) { /*遍历每一层的各个路径，由树顶到当前层一条路径组成索引键值*/
            /*如果slot不为空，那么它挂有子结点，跳出本循环，进入子结点层进行本循环*/
            if (slot->slots[i] != NULL)
                break;
           /*如果slot为空，就跳过slot对应的所有索引键值*/ 
           /*清除索引号低位.将索引号与该层slot的起始索引号对齐*/
           index &= ~((1UL << shift) - 1);
           /*跳过一个slot的索引键值数*/
          index += 1UL << shift;
          if (index == 0)
              goto out; /* 32-bit wraparound */
          i++; /*找到多个slot*/
          if (i == RADIX_TREE_MAP_SIZE)
              goto out;
       }

       shift -= RADIX_TREE_MAP_SHIFT; /*向上移一层，基数偏移减少*/
       slot = rcu_dereference(slot->slots[i]);
       if (slot == NULL)
           goto out;

    }

    /* 返回找到的多个slot*/
    for (i = index & RADIX_TREE_MAP_MASK; i < RADIX_TREE_MAP_SIZE; i++) {
        struct radix_tree_node *node;
        index++;
        node = slot->slots[i];
        if (node) {
            results[nr_found++] = rcu_dereference(node);
           if (nr_found == max_items)
               goto out;
        }
    }
    out:
    *next_index = index;
    return nr_found;
}

3.     插入操作radix_tree_insert

函数radix_tree_insert找到索引键值对应的结点，将item加到该结点的slot指针上。其列出如下：

int radix_tree_insert(struct radix_tree_root *root, unsigned long index, void *item)
{
    struct radix_tree_node *node = NULL, *slot;
    unsigned int height, shift;
    int offset;
    int error;

    BUG_ON(radix_tree_is_indirect_ptr(item));

    /* 如果树的高度不够，就扩展树。函数radix_tree_maxindex计算树高容纳的最大索引*/
    if (index > radix_tree_maxindex(root->height)) {
        error = radix_tree_extend(root, index);
        if (error)
            return error;
    }

    slot = radix_tree_indirect_to_ptr(root->rnode);

    height = root->height;
    shift = (height-1) * RADIX_TREE_MAP_SHIFT; /*计算偏移基数*/

    offset = 0; 
    while (height > 0) {
        if (slot == NULL) { /*如果slot为空，则需要加入孩子结点*/
            /* 分配slot */
            if (!(slot = radix_tree_node_alloc(root)))
                return -ENOMEM;
            slot->height = height;
            if (node) {/*添加slot*/
                rcu_assign_pointer(node->slots[offset], slot);
             node->count++;
         } else
             rcu_assign_pointer(root->rnode,radix_tree_ptr_to_indirect(slot));
        }

        /* 进入上一层*/
        offset = (index >> shift) & RADIX_TREE_MAP_MASK;
        node = slot;
        slot = node->slots[offset];
        shift -= RADIX_TREE_MAP_SHIFT;
        height--;
    }
    /*如果index对应的slot已有映射页面，返回-EEXIST*/
    if (slot != NULL)
        return -EEXIST;

    if (node) {
        node->count++; /*增加子结点的计数*/
        rcu_assign_pointer(node->slots[offset], item);
        BUG_ON(tag_get(node, 0, offset));
        BUG_ON(tag_get(node, 1, offset));
    } else { /*为顶层结点*/
        rcu_assign_pointer(root->rnode, item);
        BUG_ON(root_tag_get(root, 0));
        BUG_ON(root_tag_get(root, 1));
    }

return 0;
}

4.     扩展树radix_tree_extend

如果当前树高度不足以存放index，就需要扩展树，扩展方法是在旧树顶上加新的根结点，并将原根结点的tag信息移到新根结点的第1个slot。函数radix_tree_extend 列出如下：
static int radix_tree_extend(struct radix_tree_root *root, unsigned long index)
{
    struct radix_tree_node *node;
    unsigned int height;
    int tag;

    /* 计算扩展的深度*/
    height = root->height + 1;
    /*如果index超过树高所容纳的最大索引值，树高递增*/
    while (index > radix_tree_maxindex(height)) 
        height++;

    /*到这里已计算好合适的高度height*/ 
    if (root->rnode == NULL) { /*只有根结点，设置好树高度就可返回*/
        root->height = height;
        goto out;
    }

    /*将当前树扩展到高度height*/
    do {
        unsigned int newheight;
        if (!(node = radix_tree_node_alloc(root))) /*分配一个结点*/
            return -ENOMEM;

        /* 增加树高，在树顶点之上增加一个结点*/
        node->slots[0] = radix_tree_indirect_to_ptr(root->rnode);

        /*传播tag信息到新根结点*/
        /*以前的根结点现成为新顶结点的第1个插槽。 如果以前的根结点打上了tag，就将新增结点的第1个插槽对应的子节点打上相应的tag*/
        for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++) {
            if (root_tag_get(root, tag))
               tag_set(node, tag, 0);
        }

        newheight = root->height+1;
        node->height = newheight;
        node->count = 1;
        node = radix_tree_ptr_to_indirect(node);
        rcu_assign_pointer(root->rnode, node);
        root->height = newheight;
    } while (height > root->height);
out:
    return 0;
}

5.     删除操作radix_tree_delete

函数radix_tree_delete删除index对应的条目，并返回删除条目的地址。其列出如下：
void *radix_tree_delete(struct radix_tree_root *root, unsigned long index)
{
    /*数组path用于保存路径上的结点及索引偏移值*/
    struct radix_tree_path path[RADIX_TREE_MAX_PATH + 1], *pathp = path;
    struct radix_tree_node *slot = NULL;
    struct radix_tree_node *to_free;
    unsigned int height, shift;
    int tag;
    int offset;

    height = root->height;
    if (index > radix_tree_maxindex(height)) /*index不能超过树的最大索引值*/
        goto out;

    slot = root->rnode;
    if (height == 0) { /*只有根结点*/
        root_tag_clear_all(root);
        root->rnode = NULL;
        goto out;
    }
    slot = radix_tree_indirect_to_ptr(slot);

    shift = (height - 1) * RADIX_TREE_MAP_SHIFT;
    pathp->node = NULL;
    /*获取删除条目的路径*/
    /*将index从根到叶子的路径所经过的结点及相应索引偏移值存放在数组pathp中*/
    do {
        if (slot == NULL)
            goto out;

        pathp++;
        offset = (index >> shift) & RADIX_TREE_MAP_MASK;
        pathp->offset = offset;
        pathp->node = slot;
        slot = slot->slots[offset];
        shift -= RADIX_TREE_MAP_SHIFT;
        height--;
    } while (height > 0);

    if (slot == NULL)
        goto out;

    /*清除与删除条目相关的所有标签*/
    for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++) {
        if (tag_get(pathp->node, tag, pathp->offset))
            radix_tree_tag_clear(root, index, tag);
    }

    to_free = NULL;
    /*释放不再需要的结点 */
    while (pathp->node) { /*删除
        pathp->node->slots[pathp->offset] = NULL; /*清除slot*/
        pathp->node->count--; /*孩子数量减1*/
        /*调用RCU机制的函数call_rcu在最后一个引用结束时延迟释放结点to_free */
        if (to_free)
            radix_tree_node_free(to_free);

        if (pathp->node->count) { /*还有孩子存在*/
           if (pathp->node == radix_tree_indirect_to_ptr(root->rnode)) /*为根结点的孩子*/
                radix_tree_shrink(root); /*树缩小*/
           goto out;
        }

        /*释放有0个slot的结点 */
        to_free = pathp->node;
        pathp--;

    }
    /*运行到这里，说明是根结点*/
    root_tag_clear_all(root);
    root->height = 0;
    root->rnode = NULL;
    if (to_free)
        radix_tree_node_free(to_free);

out:
    return slot;
}

6.     压缩树radix_tree_shrink

函数radix_tree_shrink缩小树的高度到最小。其列出如下：

static inline void radix_tree_shrink(struct radix_tree_root *root)
{
    /* 尝试缩小树的高度*/
    while (root->height > 0) {
        struct radix_tree_node *to_free = root->rnode;
        void *newptr;

        BUG_ON(!radix_tree_is_indirect_ptr(to_free));
        to_free = radix_tree_indirect_to_ptr(to_free);

        /*候选结点多于一个孩子或孩子不在最左边slot，不能缩小树的高度，跳出循环*/
        if (to_free->count != 1)
            break;
        if (!to_free->slots[0])
            break;

  /*不需要调用rcu_assign_pointer()，因为仅从树的一部分到另一部分移动结点。如果释放旧指针的引用to_free->slots[0]是安全的，那么释放新指针的引用root->rnode也是安全的*/ 
       newptr = to_free->slots[0];
       if (root->height > 1)
           newptr = radix_tree_ptr_to_indirect(newptr);
       root->rnode = newptr;
       root->height--; 
       /* 仅释放0结点*/
       tag_clear(to_free, 0, 0);
       tag_clear(to_free, 1, 0);
       to_free->slots[0] = NULL;
       to_free->count = 0;
       radix_tree_node_free(to_free);
    }
}

Linux内核Radix Tree（三）：API介绍