Redis中LFU算法的深入分析

前言

在Redis中的LRU算法文中说到，LRU有一个缺陷，在如下情况下：

~~~~~A~~~~~A~~~~~A~~~~A~~~~~A~~~~~A~~|
~~B~~B~~B~~B~~B~~B~~B~~B~~B~~B~~B~~B~|
~~~~~~~~~~C~~~~~~~~~C~~~~~~~~~C~~~~~~|
~~~~~D~~~~~~~~~~D~~~~~~~~~D~~~~~~~~~D|

会将数据D误认为将来最有可能被访问到的数据。

Redis作者曾想改进LRU算法，但发现Redis的LRU算法受制于随机采样数maxmemory_samples，在maxmemory_samples等于10的情况下已经很接近于理想的LRU算法性能，也就是说，LRU算法本身已经很难再进一步了。

于是，将思路回到原点，淘汰算法的本意是保留那些将来最有可能被再次访问的数据，而LRU算法只是预测最近被访问的数据将来最有可能被访问到。我们可以转变思路，采用一种LFU(Least Frequently Used)算法，也就是最频繁被访问的数据将来最有可能被访问到。在上面的情况中，根据访问频繁情况，可以确定保留优先级：B>A>C=D。

Redis中的LFU思路

在LFU算法中，可以为每个key维护一个计数器。每次key被访问的时候，计数器增大。计数器越大，可以约等于访问越频繁。

上述简单算法存在两个问题：

• 在LRU算法中可以维护一个双向链表，然后简单的把被访问的节点移至链表开头，但在LFU中是不可行的，节点要严格按照计数器进行排序，新增节点或者更新节点位置时，时间复杂度可能达到O(N)。
• 只是简单的增加计数器的方法并不完美。访问模式是会频繁变化的，一段时间内频繁访问的key一段时间之后可能会很少被访问到，只增加计数器并不能体现这种趋势。

第一个问题很好解决，可以借鉴LRU实现的经验，维护一个待淘汰key的pool。第二个问题的解决办法是，记录key最后一个被访问的时间，然后随着时间推移，降低计数器。

Redis对象的结构如下：

typedef struct redisObject {  unsigned type:4;  unsigned encoding:4;  unsigned lru:LRU_BITS; /* LRU time (relative to global lru_clock) or              * LFU data (least significant 8 bits frequency              * and most significant 16 bits access time). */  int refcount;  void *ptr;} robj;

在LRU算法中，24 bits的lru是用来记录LRU time的，在LFU中也可以使用这个字段，不过是分成16 bits与8 bits使用：

      16 bits   8 bits   +----------------+--------+   + Last decr time | LOG_C |   +----------------+--------+

高16 bits用来记录最近一次计数器降低的时间ldt，单位是分钟，低8 bits记录计数器数值counter。

LFU配置

Redis4.0之后为maxmemory_policy淘汰策略添加了两个LFU模式：

• volatile-lfu：对有过期时间的key采用LFU淘汰算法
• allkeys-lfu：对全部key采用LFU淘汰算法

还有2个配置可以调整LFU算法：

lfu-log-factor 10lfu-decay-time 1

lfu-log-factor可以调整计数器counter的增长速度，lfu-log-factor越大，counter增长的越慢。

lfu-decay-time是一个以分钟为单位的数值，可以调整counter的减少速度

源码实现

在lookupKey中:

robj *lookupKey(redisDb *db, robj *key, int flags) {  dictEntry *de = dictFind(db->dict,key->ptr);  if (de) {    robj *val = dictGetVal(de);    /* Update the access time for the ageing algorithm.     * Don't do it if we have a saving child, as this will trigger     * a copy on write madness. */    if (server.rdb_child_pid == -1 &&      server.aof_child_pid == -1 &&      !(flags & LOOKUP_NOTOUCH))    {      if (server.maxmemory_policy & MAXMEMORY_FLAG_LFU) {        updateLFU(val);      } else {        val->lru = LRU_CLOCK();      }    }    return val;  } else {    return NULL;  }}

当采用LFU策略时，updateLFU更新lru：

/* Update LFU when an object is accessed. * Firstly, decrement the counter if the decrement time is reached. * Then logarithmically increment the counter, and update the access time. */void updateLFU(robj *val) {  unsigned long counter = LFUDecrAndReturn(val);  counter = LFULogIncr(counter);  val->lru = (LFUGetTimeInMinutes()<<8) | counter;}

降低LFUDecrAndReturn

首先，LFUDecrAndReturn对counter进行减少操作：

/* If the object decrement time is reached decrement the LFU counter but * do not update LFU fields of the object, we update the access time * and counter in an explicit way when the object is really accessed. * And we will times halve the counter according to the times of * elapsed time than server.lfu_decay_time. * Return the object frequency counter. * * This function is used in order to scan the dataset for the best object * to fit: as we check for the candidate, we incrementally decrement the * counter of the scanned objects if needed. */unsigned long LFUDecrAndReturn(robj *o) {  unsigned long ldt = o->lru >> 8;  unsigned long counter = o->lru & 255;  unsigned long num_periods = server.lfu_decay_time ? LFUTimeElapsed(ldt) / server.lfu_decay_time : 0;  if (num_periods)    counter = (num_periods > counter) ? 0 : counter - num_periods;  return counter;}

函数首先取得高16 bits的最近降低时间ldt与低8 bits的计数器counter，然后根据配置的lfu_decay_time计算应该降低多少。

LFUTimeElapsed用来计算当前时间与ldt的差值：

/* Return the current time in minutes, just taking the least significant * 16 bits. The returned time is suitable to be stored as LDT (last decrement * time) for the LFU implementation. */unsigned long LFUGetTimeInMinutes(void) {  return (server.unixtime/60) & 65535;}/* Given an object last access time, compute the minimum number of minutes * that elapsed since the last access. Handle overflow (ldt greater than * the current 16 bits minutes time) considering the time as wrapping * exactly once. */unsigned long LFUTimeElapsed(unsigned long ldt) {  unsigned long now = LFUGetTimeInMinutes();  if (now >= ldt) return now-ldt;  return 65535-ldt+now;}

具体是当前时间转化成分钟数后取低16 bits，然后计算与ldt的差值now-ldt。当ldt > now时，默认为过了一个周期(16 bits，最大65535)，取值65535-ldt+now。

然后用差值与配置lfu_decay_time相除，LFUTimeElapsed(ldt) / server.lfu_decay_time，已过去n个lfu_decay_time，则将counter减少n，counter - num_periods。

增长LFULogIncr

增长函数LFULogIncr如下：

/* Logarithmically increment a counter. The greater is the current counter value * the less likely is that it gets really implemented. Saturate it at 255. */uint8_t LFULogIncr(uint8_t counter) {  if (counter == 255) return 255;  double r = (double)rand()/RAND_MAX;  double baseval = counter - LFU_INIT_VAL;  if (baseval < 0) baseval = 0;  double p = 1.0/(baseval*server.lfu_log_factor+1);  if (r < p) counter++;  return counter;}

counter并不是简单的访问一次就+1，而是采用了一个0-1之间的p因子控制增长。counter最大值为255。取一个0-1之间的随机数r与p比较，当r

+--------+------------+------------+------------+------------+------------+
| factor | 100 hits | 1000 hits | 100K hits | 1M hits | 10M hits |
+--------+------------+------------+------------+------------+------------+
| 0 | 104 | 255 | 255 | 255 | 255 |
+--------+------------+------------+------------+------------+------------+
| 1 | 18 | 49 | 255 | 255 | 255 |
+--------+------------+------------+------------+------------+------------+
| 10 | 10 | 18 | 142 | 255 | 255 |
+--------+------------+------------+------------+------------+------------+
| 100 | 8 | 11 | 49 | 143 | 255 |
+--------+------------+------------+------------+------------+------------+

可见counter增长与访问次数呈现对数增长的趋势，随着访问次数越来越大，counter增长的越来越慢。

新生key策略

另外一个问题是，当创建新对象的时候，对象的counter如果为0，很容易就会被淘汰掉，还需要为新生key设置一个初始counter，createObject:

robj *createObject(int type, void *ptr) {  robj *o = zmalloc(sizeof(*o));  o->type = type;  o->encoding = OBJ_ENCODING_RAW;  o->ptr = ptr;  o->refcount = 1;  /* Set the LRU to the current lruclock (minutes resolution), or   * alternatively the LFU counter. */  if (server.maxmemory_policy & MAXMEMORY_FLAG_LFU) {    o->lru = (LFUGetTimeInMinutes()<<8) | LFU_INIT_VAL;  } else {    o->lru = LRU_CLOCK();  }  return o;}

counter会被初始化为LFU_INIT_VAL，默认5。

pool

pool算法就与LRU算法一致了：

    if (server.maxmemory_policy & (MAXMEMORY_FLAG_LRU|MAXMEMORY_FLAG_LFU) ||      server.maxmemory_policy == MAXMEMORY_VOLATILE_TTL)

计算idle时有所不同：

    } else if (server.maxmemory_policy & MAXMEMORY_FLAG_LFU) {      /* When we use an LRU policy, we sort the keys by idle time       * so that we expire keys starting from greater idle time.       * However when the policy is an LFU one, we have a frequency       * estimation, and we want to evict keys with lower frequency       * first. So inside the pool we put objects using the inverted       * frequency subtracting the actual frequency to the maximum       * frequency of 255. */      idle = 255-LFUDecrAndReturn(o);

使用了255-LFUDecrAndReturn(o)当做排序的依据。

参考链接

• Random notes on improving the Redis LRU algorithm
• Using Redis as an LRU cache

总结

以上就是这篇文章的全部内容了，希望本文的内容对大家的学习或者工作具有一定的参考学习价值，谢谢大家对的支持。