Redis中的LFU演算法
在Redis中的LRU演算法文中說到，LRU有一個缺陷，在如下情況下：
~~~~~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|
會將資料D誤認為將來最有可能被訪問到的資料。
Redis作者曾想改進LRU演算法，但發現Redis的LRU演算法受制於隨機取樣數maxmemory_samples，在maxmemory_samples
LRU演算法效能，也就是說，LRU演算法本身已經很難再進一步了。
於是，將思路回到原點，淘汰演算法的本意是保留那些將來最有可能被再次訪問的資料，而LRU演算法只是預測最近被訪問的資料將來最有可能被訪問到。我們可以轉變思路，採用一種LFU(Least Frequently Used)演算法，也就是最頻繁被訪問的資料將來最有可能被訪問到。在上面的情況中，根據訪問頻繁情況，可以確定保留優先順序：B>A>C=D。
Redis中的LFU思路
在LFU演算法中，可以為每個key維護一個計數器。每次key被訪問的時候，計數器增大。計數器越大，可以約等於訪問越頻繁。
上述簡單演算法存在兩個問題：
- 在
LRU演算法中可以維護一個雙向連結串列，然後簡單的把被訪問的節點移至連結串列開頭，但在LFU中是不可行的，節點要嚴格按照計數器進行排序，新增節點或者更新節點位置時，時間複雜度可能達到O(N)。 - 只是簡單的增加計數器的方法並不完美。訪問模式是會頻繁變化的，一段時間內頻繁訪問的key一段時間之後可能會很少被訪問到，只增加計數器並不能體現這種趨勢。
第一個問題很好解決，可以借鑑LRU實現的經驗，維護一個待淘汰key的pool。第二個問題的解決辦法是，記錄key最後一個被訪問的時間，然後隨著時間推移，降低計數器。
Redis物件的結構如下：
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演算法中，24 bits的lru是用來記錄LRU time的，在LFU中也可以使用這個欄位，不過是分成16 bits與8 bits使用：
16 bits 8 bits
+----------------+--------+
+ Last decr time | LOG_C |
+----------------+--------+
高16 bits用來記錄最近一次計數器降低的時間ldt，單位是分鐘，低8 bits記錄計數器數值counter。
LFU配置
Redis4.0之後為maxmemory_policy淘汰策略添加了兩個LFU模式：
volatile-lfu：對有過期時間的key採用LFU淘汰演算法allkeys-lfu：對全部key採用LFU淘汰演算法
還有2個配置可以調整LFU演算法：
lfu-log-factor 10
lfu-decay-time 1
lfu-log-factor可以調整計數器counter的增長速度，lfu-log-factor越大，counter增長的越慢。
lfu-decay-time是一個以分鐘為單位的數值，可以調整counter的減少速度
原始碼實現
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;
}
}
當採用LFU策略時，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對counter進行減少操作：
/* 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;
}
函式首先取得高16 bits的最近降低時間ldt與低8 bits的計數器counter，然後根據配置的lfu_decay_time計算應該降低多少。
LFUTimeElapsed用來計算當前時間與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;
}
具體是當前時間轉化成分鐘數後取低16 bits，然後計算與ldt的差值now-ldt。當ldt > now時，預設為過了一個週期(16 bits，最大65535)，取值65535-ldt+now。
然後用差值與配置lfu_decay_time相除，LFUTimeElapsed(ldt) / server.lfu_decay_time，已過去n個lfu_decay_time，則將counter減少n，counter - num_periods。
增長LFULogIncr
增長函式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並不是簡單的訪問一次就+1，而是採用了一個0-1之間的p因子控制增長。counter最大值為255。取一個0-1之間的隨機數r與p比較，當r<p時，才增加counter，這和比特幣中控制產出的策略類似。p取決於當前counter值與lfu_log_factor因子，counter值與lfu_log_factor因子越大，p越小，r<p的概率也越小，counter增長的概率也就越小。增長情況如下：
+--------+------------+------------+------------+------------+------------+
| 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 |
+--------+------------+------------+------------+------------+------------+
可見counter增長與訪問次數呈現對數增長的趨勢，隨著訪問次數越來越大，counter增長的越來越慢。
新生key策略
另外一個問題是，當建立新物件的時候，物件的counter如果為0，很容易就會被淘汰掉，還需要為新生key設定一個初始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會被初始化為LFU_INIT_VAL，預設5。
pool
pool演算法就與LRU演算法一致了：
if (server.maxmemory_policy & (MAXMEMORY_FLAG_LRU|MAXMEMORY_FLAG_LFU) ||
server.maxmemory_policy == MAXMEMORY_VOLATILE_TTL)
計算idle時有所不同：
} 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)當做排序的依據。
參考連結
- Random notes on improving the Redis LRU algorithm
- Using Redis as an LRU cache