leveldb阅读-Skiplist

Skiplist是一种随机化的链表，通过并联链表，可以实现数据的快速插入和查找，同时能够取得比较好的时间开销和空间开销。详细的实现原理可以参照http://blog.youkuaiyun.com/haidao2009/article/details/8206856。leveldb采用skiplist来实现k-value的处理应该也是综合考虑到空间开销和时间开销的成本。

在介绍leveldb中的Skiplist之前，首先需要看一下其Node的定义，也就是Skiplist中存储信息的节点是如何定义的；

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

  //key值不可修改
  Key const key;

  //获得下一个节点的地址,为了防止冲突，因此Release_Store版本中采用了内存屏障，
  //这样可以有效的确保线程获得数据都是完整的，但不一定是同步的；
  // 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 reinterpret_cast<Node*>(next_[n].Acquire_Load());
  }
  //设置下一个节点的地址，通过内存屏障或者系统提供的原语，这样确保任何线程读的数据都是完整的，当然不一定是同步的；
  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].Release_Store(x);
  }

  // No-barrier variants that can be safely used in a few locations.
  Node* NoBarrier_Next(int n) {
    assert(n >= 0);
    return reinterpret_cast<Node*>(next_[n].NoBarrier_Load());
  }
  void NoBarrier_SetNext(int n, Node* x) {
    assert(n >= 0);
    next_[n].NoBarrier_Store(x);
  }

 private:
  // Array of length equal to the node height.  next_[0] is lowest level link.
  //弹性指针，并且采用原子性的指针来确保数据进行读写的时候的完整性；
  port::AtomicPointer next_[1];
};

其中，Atomicpointer的定义如下，由于leveldb需要适应不同的平台，因此，AtomicPointer有不同平台版本的定义，为了理解，只看一下比较简单版本的，也就是支持atomic的平台上的代码；

// AtomicPointer based on <cstdatomic>
#elif defined(LEVELDB_ATOMIC_PRESENT)
class AtomicPointer {
 private:
  std::atomic<void*> rep_;
 public:
  AtomicPointer() { }
  explicit AtomicPointer(void* v) : rep_(v) { }
  inline void* Acquire_Load() const {
    return rep_.load(std::memory_order_acquire);
  }
  inline void Release_Store(void* v) {
    rep_.store(v, std::memory_order_release);
  }
  inline void* NoBarrier_Load() const {
    return rep_.load(std::memory_order_relaxed);
  }
  inline void NoBarrier_Store(void* v) {
    rep_.store(v, std::memory_order_relaxed);
  }
};

可以从上面看出，所有的操作都是原子性的，因此就可以确保不同线程对next_数据读取和写入的时候，可以保证原子性；

SKiplist的定义如下：

//需要提供compare仿函数
template<typename Key, class Comparator>
class SkipList {
 private:
  struct Node;

 public:

  //利用arena进行内存管理，cmp用于对key进行比较
  // Create a new SkipList object that will use "cmp" for comparing keys,
  // and will allocate memory using "*arena".  Objects allocated in the arena
  // must remain allocated for the lifetime of the skiplist object.
  explicit SkipList(Comparator cmp, Arena* arena);


  //插入数据，要求不能有相同键值的数据存在列表中；
  // Insert key into the list.
  // REQUIRES: nothing that compares equal to key is currently in the list.
  void Insert(const Key& key);

  //判断指定的键值是否已经存在list中；
  // Returns true iff an entry that compares equal to key is in the list.
  bool Contains(const Key& key) const;

  // 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_;
    Node* node_;//head节点
    // Intentionally copyable
  };

 private:
  //skiplist最大并行列表的数量；
  enum { kMaxHeight = 12 };

  //用于比较键值对大小；
  // Immutable after construction
  Comparator const compare_;
  //用于分配和管理node内存；
  Arena* const arena_;    // Arena used for allocations of nodes

  //skiplist的heaed指针；
  Node* const head_;

  // Modified only by Insert().  Read racily by readers, but stale
  // values are ok.
  //链表的并行度，在insert的时候可能会被修改；
  port::AtomicPointer max_height_;   // Height of the entire list

  inline int GetMaxHeight() const {
    return static_cast<int>(
        reinterpret_cast<intptr_t>(max_height_.NoBarrier_Load()));
  }

  //产生随机数；
  // Read/written only by Insert().
  Random rnd_;

  //产生新的节点；
  Node* NewNode(const Key& key, int height);
  //随机产生并行高度；
  int RandomHeight();
  //判断两个键值对是否相等；
  bool Equal(const Key& a, const Key& b) const { return (compare_(a, b) == 0); }

  //判断key值是否比n中存储的值要大；
  // Return true if key is greater than the data stored in "n"
  bool KeyIsAfterNode(const Key& key, Node* n) const;

  // Return the earliest node that comes at or after key.
  // Return NULL if there is no such node.
  //
  // If prev is non-NULL, fills prev[level] with pointer to previous
  // node at "level" for every level in [0..max_height_-1].
  Node* FindGreaterOrEqual(const Key& key, Node** prev) const;

  // Return the latest node with a key < key.
  // Return head_ if there is no such node.
  Node* FindLessThan(const Key& key) const;

  // Return the last node in the list.
  // Return head_ if list is empty.
  Node* FindLast() const;

  //禁止复制
  // No copying allowed
  SkipList(const SkipList&);
  void operator=(const SkipList&);
};

其中随机数产生器Radom的定义如下：

// Copyright (c) 2011 The LevelDB Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file. See the AUTHORS file for names of contributors.

#ifndef STORAGE_LEVELDB_UTIL_RANDOM_H_
#define STORAGE_LEVELDB_UTIL_RANDOM_H_

#include <stdint.h>

namespace leveldb {

//
//简单的随机数产生器，不能产生真正的随机数，但是在leveldb中足够使用
// A very simple random number generator.  Not especially good at
// generating truly random bits, but good enough for our needs in this
// package.
class Random {
 private:
  uint32_t seed_;
 public:
  explicit Random(uint32_t s) : seed_(s & 0x7fffffffu) {
    // Avoid bad seeds.
    if (seed_ == 0 || seed_ == 2147483647L) {
      seed_ = 1;
    }
  }
  //获得下一个随机数；
  uint32_t Next() {
    static const uint32_t M = 2147483647L;   // 2^31-1
    static const uint64_t A = 16807;  // bits 14, 8, 7, 5, 2, 1, 0
    // We are computing
    //       seed_ = (seed_ * A) % M,    where M = 2^31-1
    //
    // seed_ must not be zero or M, or else all subsequent computed values
    // will be zero or M respectively.  For all other values, seed_ will end
    // up cycling through every number in [1,M-1]
    uint64_t product = seed_ * A;

    // Compute (product % M) using the fact that ((x << 31) % M) == x.
    seed_ = static_cast<uint32_t>((product >> 31) + (product & M));
    // The first reduction may overflow by 1 bit, so we may need to
    // repeat.  mod == M is not possible; using > allows the faster
    // sign-bit-based test.
    if (seed_ > M) {
      seed_ -= M;
    }
    return seed_;
  }
  // Returns a uniformly distributed value in the range [0..n-1]
  // REQUIRES: n > 0
  uint32_t Uniform(int n) { return Next() % n; }

  // Randomly returns true ~"1/n" of the time, and false otherwise.
  // REQUIRES: n > 0
  bool OneIn(int n) { return (Next() % n) == 0; }

  // Skewed: pick "base" uniformly from range [0,max_log] and then
  // return "base" random bits.  The effect is to pick a number in the
  // range [0,2^max_log-1] with exponential bias towards smaller numbers.
  uint32_t Skewed(int max_log) {
    return Uniform(1 << Uniform(max_log + 1));
  }
};

}  // namespace leveldb

#endif  // STORAGE_LEVELDB_UTIL_RANDOM_H_

其中，next中求mod的值的原理如下：

Skiplist的具体实现如下；

//产生新的节点
template<typename Key, class Comparator>
typename SkipList<Key,Comparator>::Node*
SkipList<Key,Comparator>::NewNode(const Key& key, int height) {
  char* mem = arena_->AllocateAligned(
      sizeof(Node) + sizeof(port::AtomicPointer) * (height - 1));
  return new (mem) Node(key);
}

template<typename Key, class Comparator>
inline SkipList<Key,Comparator>::Iterator::Iterator(const SkipList* list) {
  list_ = list;
  node_ = NULL;
}

template<typename Key, class Comparator>
inline bool SkipList<Key,Comparator>::Iterator::Valid() const {
  return node_ != NULL;
}

template<typename Key, class Comparator>
inline const Key& SkipList<Key,Comparator>::Iterator::key() const {
  assert(Valid());
  return node_->key;
}

template<typename Key, class Comparator>
inline void SkipList<Key,Comparator>::Iterator::Next() {
  assert(Valid());
  node_ = node_->Next(0);
}

template<typename Key, class Comparator>
inline void SkipList<Key,Comparator>::Iterator::Prev() {
  // Instead of using explicit "prev" links, we just search for the
  // last node that falls before key.
  assert(Valid());
  node_ = list_->FindLessThan(node_->key);
  if (node_ == list_->head_) {
    node_ = NULL;
  }
}

template<typename Key, class Comparator>
inline void SkipList<Key,Comparator>::Iterator::Seek(const Key& target) {
  node_ = list_->FindGreaterOrEqual(target, NULL);
}

template<typename Key, class Comparator>
inline void SkipList<Key,Comparator>::Iterator::SeekToFirst() {
  node_ = list_->head_->Next(0);
}

template<typename Key, class Comparator>
inline void SkipList<Key,Comparator>::Iterator::SeekToLast() {
  node_ = list_->FindLast();
  if (node_ == list_->head_) {
    node_ = NULL;
  }
}

//随机random出node节点的高度；
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;
  //利用<span style="font-family: Arial, Helvetica, sans-serif;">kBranching，可以控制不同点出现的概率，如1出现的概率为3/4,2出现的概率为3/4 *1/4  ,3出现的概率为 1/4*1/4*3/4；</span>
  while (height < kMaxHeight && ((rnd_.Next() % kBranching) == 0)) {
    height++;
  }
  assert(height > 0);
  assert(height <= kMaxHeight);
  return height;
}

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

//找到第一个大于或者等于key值的节点
template<typename Key, class Comparator>
typename SkipList<Key,Comparator>::Node* SkipList<Key,Comparator>::FindGreaterOrEqual(const Key& key, Node** prev)
    const {
  Node* x = head_;
  int level = GetMaxHeight() - 1;
  //快速查找并填充prev，这样就可以快速的查找到大于或者等于key的第一个值
  //prev[1-level]填充的是每一层大于key的值的第一个node节点；
  while (true) {
    Node* next = x->Next(level);
    if (KeyIsAfterNode(key, next)) {
      // Keep searching in this list
      x = next;
    } else {
      if (prev != NULL) prev[level] = x;
      if (level == 0) {
        return next;
      } else {
        // Switch to next list
        level--;
      }
    }
  }
}

//找到小于key的最大值
template<typename Key, class Comparator>
typename SkipList<Key,Comparator>::Node*
SkipList<Key,Comparator>::FindLessThan(const Key& key) const {
  Node* x = head_;
  int level = GetMaxHeight() - 1;
  while (true) {
    assert(x == head_ || compare_(x->key, key) < 0);
    Node* next = x->Next(level);
    if (next == NULL || compare_(next->key, key) >= 0) {
      if (level == 0) {
        return x;
      } else {
        // Switch to next list
        level--;
      }
    } else {
      x = next;
    }
  }
}

//快速的找到最后一个值
template<typename Key, class Comparator>
typename SkipList<Key,Comparator>::Node* SkipList<Key,Comparator>::FindLast()
    const {
  Node* x = head_;
  int level = GetMaxHeight() - 1;
  while (true) {
    Node* next = x->Next(level);
    if (next == NULL) {
      if (level == 0) {
        return x;
      } else {
        // Switch to next list
        level--;
      }
    } else {
      x = next;
    }
  }
}

//初始化；
//最大高度= kMaxHeight = 12
//random初始化种子为 0xdeadbeef
//初始高度为1
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_(reinterpret_cast<void*>(1)),
      rnd_(0xdeadbeef) {
  for (int i = 0; i < kMaxHeight; i++) {
    head_->SetNext(i, NULL);
  }
}

//插入节点，插入的时候会改变maxheght；
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 = FindGreaterOrEqual(key, prev);

  // Our data structure does not allow duplicate insertion
  assert(x == NULL || !Equal(key, x->key));
  int height = RandomHeight();
  if (height > GetMaxHeight()) {
    for (int i = GetMaxHeight(); i < height; i++) {
      prev[i] = head_;
    }
    //fprintf(stderr, "Change height from %d to %d\n", max_height_, height);

    // 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_ (NULL), or a new value set in
    // the loop below.  In the former case the reader will
    // immediately drop to the next level since NULL sorts after all
    // keys.  In the latter case the reader will use the new node.
    //更新最大高度
    max_height_.NoBarrier_Store(reinterpret_cast<void*>(height));
  }

  x = NewNode(key, height);
  for (int i = 0; i < height; i++) {
    // 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));
    //增加了memory barrier
    prev[i]->SetNext(i, x);
  }
}

//判断skiplist中是否存在目标键值
template<typename Key, class Comparator>
bool SkipList<Key,Comparator>::Contains(const Key& key) const {
  Node* x = FindGreaterOrEqual(key, NULL);
  if (x != NULL && Equal(key, x->key)) {
    return true;
  } else {
    return false;
  }
}

可以看到，在leveldb中，skiplist没有删除节点的接口，主要是在leveldb中，skiplist中没有节点删除这一说，利用arena进行内存管理，可以有效的防止内存泄漏，并避免内存管理的复杂性；