Redis中的LFU算法

在Redis中的LRU算法文中说到，

LRU

~~~~~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

LRU

Redis

LRU

maxmemory_samples

maxmemory_samples

LRU

LRU

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

LFU(Least Frequently Used)

Redis中的LFU思路

在

LFU

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

Redis

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

lru

LRU time

LFU

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

counter

LFU配置

Redis

maxmemory_policy

LFU

• 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

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

lfu-log-factor

counter

lfu-log-factor

counter

lfu-decay-time

counter

源码实现

在

lookupKey

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

updateLFU

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

counter

/* 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

counter

lfu_decay_time

LFUTimeElapsed

ldt

/* 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

now-ldt

ldt > now

65535-ldt+now

然后用差值与配置

lfu_decay_time

LFUTimeElapsed(ldt) / server.lfu_decay_time

lfu_decay_time

counter

counter - num_periods

增长LFULogIncr

增长函数

LFULogIncr

/* 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

counter

r<p

counter

counter

lfu_log_factor

counter

lfu_log_factor

r<p

counter

+--------+------------+------------+------------+------------+------------+
| 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

counter

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

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

LFU_INIT_VAL

pool

pool算法就与

LRU

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

计算

idle

} 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)

参考链接

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