【LevelDB源码阅读】SkipList

是什么

skiplist特点

• 有几个层组成，每层是一个有序的链表
• 第一层包含所有元素，如果元素x出现在第i层，则所有比i小的层都包含x
• 头指针指向最高处的第一个元素

参考LevelDB源码剖析之基础部件-SkipList中示意图：

skiplist结构

图1.1中红色部分为初始化状态，即head各个level中next节点均为NULL。

查找和插入示例：

为什么要用

• 实现比平衡树简单，性能和平衡树媲美

学到什么

• 通过类模板解决多种数据类型

源码分析

SkipList是一个模板类

template <typename Key, class Comparator>
class SkipList

其中Key是要存储的数据类型，Comparator实现Key的比较。

对外接口

主要提供两个接口Insert和Contains，即插入和查找，没有Delete接口。

  // Insert key into the list.
  // REQUIRES: nothing that compares equal to key is currently in the list.
  void Insert(const Key &key);

  // Returns true iff an entry that compares equal to key is in the list.
  bool Contains(const Key &key) const;

数据成员

  enum { kMaxHeight = 12 };  //最大层数
  
  // Immutable after construction
  Comparator const compare_;
  Arena* const arena_;  // Arena used for allocations of nodes
  Node* const head_;    // SkipList头节点

  // Modified only by Insert().  Read racily by readers, but stale
  // values are ok.
  std::atomic<int> max_height_;  // Height of the entire list

  // Read/written only by Insert().
  Random rnd_;

构造函数

初始化head_高度为kMaxHeight，并设置每一层的后继节点为nullptr。

template <typename Key, class Comparator>
SkipList<Key, Comparator>::SkipList(Comparator cmp, Arena *arena)
    : compare_(cmp),
      arena_(arena),
      head_(NewNode(0 /* any key will do */, kMaxHeight)),
      max_height_(1),
      rnd_(0xdeadbeef) {
  for (int i = 0; i < kMaxHeight; i++) {
    head_->SetNext(i, nullptr);  // 设置每层后继节点为nullptr
  }
}

Node和NewNode

Node对应SkipList中的节点，包含了key以及若干层级信息。

// Implementation details follow
template <typename Key, class Comparator>
struct SkipList<Key, Comparator>::Node {
  explicit Node(const Key &k) : key(k) {}
  Key const key;

  // Accessors/mutators for links.  Wrapped in methods so we can
  // add the appropriate barriers as necessary.
  Node *Next(int n) {
    assert(n >= 0);
    // Use an 'acquire load' so that we observe a fully initialized
    // version of the returned Node.
    return next_[n].load(std::memory_order_acquire);
  }
  void SetNext(int n, Node *x) {
    assert(n >= 0);
    // Use a 'release store' so that anybody who reads through this
    // pointer observes a fully initialized version of the inserted node.
    next_[n].store(x, std::memory_order_release);  // 设置当前节点下一个节点
  }

  // No-barrier variants that can be safely used in a few locations.
  Node *NoBarrier_next(int n) {
    assert(n >= 0);
    return next_[n].load(std::memory_order_relaxed);
  }
  void NoBarrier_SetNext(int n, Node *x) {
    assert(n >= 0);
    next_[n].store(std::memory_order_relaxed);
  }

 private:
  // Array of length equal to the node height.  next_[0] is lowest level link.
  std::atomic<Node *> next_[1];
};

所有Node对象都通过NewNode构造，先通过arena_分配内存，然后通过placement new的方式调用Node的构造函数。

为什么使用placement new？
主要为了在预分配的内存上构建对象。

template <typename Key, class Comparator>
typename SkipList<Key, Comparator>::Node* SkipList<Key, Comparator>::NewNode(
    const Key &key, int height) {
  char *const node_memory = arena_->AllocateAligned(
      sizeof(Node) + sizeof(std::atomic<Node*>) * (height - 1));
  return new (node_memory) Node(key);
}

插入

插入时需要找到多个前后节点。

template <typename Key, class Comparator>
void SkipList<Key, Comparator>::Insert(const Key &key) {
  // TODO(opt): We can use a barrier-free variant of FindGreaterOrEqual()
  // here since Insert() is externally synchronized.
  Node* prev[kMaxHeight];
  Node* x = FindGreatOrEqual(key, prev);

  // Our data structure does not allow duplicate insertion
  assert(x == nullptr || !Equal(key, x->key));
  int height = RandomHeight();  // 随机决定插入节点高度
  if (height > GetMaxHeight()) {
    for (int i = GetMaxHeight(); i < height; ++i) {
      prev[i] = head_;  //如果当前节点的高度大于最高节点，则高出部分的的前节点都是头节点
    }
    // It is ok to mutate max_height_ without any synchronization
    // with concurrent readers.  A concurrent reader that observes
    // the new value of max_height_ will see either the old value of
    // new level pointers from head_ (nullptr), or a new value set in
    // the loop below.  In the former case the reader will
    // immediately drop to the next level since nullptr sorts after all
    // keys.  In the latter case the reader will use the new node.
    max_height_.store(height, std::memory_order_relaxed);
  }

  x = NewNode(key, height);  // 构造节点，高度为height
  for (int i = 0; i < height; ++i) {  // 每层断开链表插入新节点
    // NoBarrier_SetNext() suffices since we will add a barrier when
    // we publish a pointer to "x" in prev[i].
    x->NoBarrier_SetNext(i, prev[i]->NoBarrier_Next(i));
    prev[i]->SetNext(i, x);  // 先修改x节点，再修改prev节点
  }
}

其中RandomHeight通过破硬币的方法随机决定该节点高度

template <typename Key, class Comparator>
int SkipList<Key, Comparator>::RandomHeight() {
  // Increase height with probability 1 in kBranching
  static const unsigned int kBranching = 4;
  int height = 1;
  while (height < kMaxHeight && ((rnd.Next() % kBranching) == 0)) {
    ++height;
  }
  assert(height > 0);
  assert(height <= kMaxHeight);
  return height;
}

FindGreatOrEqual实现如下：

//返回第一个大于等于key的节点
template <typename Key, class Comparator>
typename SkipList<Key, Comparator>::Node*
SkipList<Key, Comparator>::FindGreatOrEqual(const Key &key, Node **prev) const {
  Node *x = head_;
  int level = GetMaxHeight() - 1;  // 下标从0层开始
  while (true) {
    Node *next = x->Next(level);
    if (KeyIsAfterNode(key, next)) {
      // Keep searching in this list
      x = next;
    } else {  // key <= next->key
      if (prev != nullptr) prev[level] = x;
      if (level == 0) {
        return next;
      } else {
        // Switch to next list
        --level;
      }
    }
  }
}

其中KeyIsAfterNode实现如下：

template <typename Key, class Comparator>
bool SkipList<Key, Comparator>::KeyIsAfterNode(const Key &key, Node *n) const {
  // null n is considered infinite
  return (n != nullptr) && (compare_(n->key, key) < 0);
}

查找

template <typename Key, class Comparator>
bool SkipList<Key, Comparator>::Contains(const Key &key) const {
  Node *x = FindGreatOrEqual(key, nullptr);
  if (x != nullptr && Equal(key, x->key)) {
    return true;
  } else {
    return false;
  }
}

迭代器

MemTable在读取时使用的是SkipList::Iterator，定义如下：

  // Iteration over the contents of a skip list
  class Iterator {
   public:
    // Initialize an iterator over the specified list.
    // The returned iterator is not valid.
    explicit Iterator(const SkipList *list);

    // Returns true iff the iterator is positioned at a valid node.
    bool Valid() const;

    // Returns the key at the current position.
    // REQUIRES: Valid()
    const Key &key() const;

    // Advances to the next position.
    // REQUIRES: Valid()
    void Next();

    // Advances to the previous position.
    // REQUIRES: Valid()
    void Prev();

    // Advance to the first entry with a key >= target
    void Seek(const Key &target);

    // Position at the first entry in list.
    // Final state of iterator is Valid() iff list is not empty.
    void SeekToFirst();

    // Position at the last entry in list.
    // Final state of iterator is Valid() iff list is not empty.
    void SeekToLast();

   private:
    const SkipList *list_;  // 需迭代的skiplist
    Node *node_;            // 当前迭代的节点
    // Intentionally copyable
  };