通過原始碼學習@functools.lru_cache

一、前言

　　通常在一些代碼中包含了重復運算，而這些重復運算會大大增加代碼運行所耗費的時間，比如使用遞回實作斐波那契數列，

　　舉個例子，當求 fibonacci(5) 時，需要求得 fibonacci(3) 和 fibonacci(4) 的結果，而求 fibonacci(4) 時，又需要求 fibonacci(2) 和 fibonacci(3) ，但此時 fibonacci(3) 就被重新計算一遍了，繼續遞回下去，重復計算的內容就更多了，求 fibonacci(5) 的代碼和運行結果如下：

 1 def fibonacci(n):
 2     # 遞回實作斐波那契數列
 3     print("n is {}".format(n))
 4     if n < 2:
 5         return n
 6     return fibonacci(n - 2) + fibonacci(n - 1)
 7 
 8 
 9 if __name__ == '__main__':
10     fibonacci(5)
11 
12 # n is 5
13 # n is 3
14 # n is 1
15 # n is 2
16 # n is 0
17 # n is 1
18 # n is 4
19 # n is 2
20 # n is 0
21 # n is 1
22 # n is 3
23 # n is 1
24 # n is 2
25 # n is 0
26 # n is 1

　　從列印的結果來看，有很多重復計算的部分，傳入的 n 越大，重復計算的部分就越多，程式的耗時也大大增加，例如當 n = 40 時，運行耗時已經很長了，代碼如下：

 1 import time
 2 
 3 
 4 def fibonacci(n):
 5     # 遞回實作斐波那契數列
 6     if n < 2:
 7         return n
 8     return fibonacci(n - 2) + fibonacci(n - 1)
 9 
10 
11 if __name__ == '__main__':
12     print("Start: {}".format(time.time()))
13     print("Fibonacci(40) = {}".format(fibonacci(40)))
14     print("End: {}".format(time.time()))
15 
16 # Start: 1594197671.6210408
17 # Fibonacci(40) = 102334155
18 # End: 1594197717.8520994

二、@functools.lru_cache

1.使用方法

　　@functools.lru_cache 是一個裝飾器，所謂裝飾器，就是在不改變原有代碼的基礎上，為其增加額外的功能，例如列印日志、計算運行時間等，該裝飾器的用法如下：

 1 import functools
 2 
 3 
 4 @functools.lru_cache(100)
 5 def fibonacci(n):
 6     # 遞回實作斐波那契數列
 7     print("n is {}".format(n))
 8     if n < 2:
 9         return n
10     return fibonacci(n - 2) + fibonacci(n - 1)
11 
12 
13 if __name__ == '__main__':
14     fibonacci(5)
15 
16 # n is 5
17 # n is 3
18 # n is 1
19 # n is 2
20 # n is 0
21 # n is 4

　　從列印的結果來看，從0到5都只計算了一遍，沒有出現重復計算的情況，那當 n = 40 時，程式的耗時情況又是如何呢？代碼如下：

 1 import time
 2 import functools
 3 
 4 
 5 @functools.lru_cache(100)
 6 def fibonacci(n):
 7     # 遞回實作斐波那契數列
 8     if n < 2:
 9         return n
10     return fibonacci(n - 2) + fibonacci(n - 1)
11 
12 
13 if __name__ == '__main__':
14     print("Start: {}".format(time.time()))
15     print("Fibonacci(40) = {}".format(fibonacci(40)))
16     print("End: {}".format(time.time()))
17 
18 # Start: 1594197813.2185402
19 # Fibonacci(40) = 102334155
20 # End: 1594197813.2185402

　　從結果可知，沒有了這些重復計算，程式運行所耗費的時間也大大減少了，

2.原始碼決議

　　在 Pycharm 中點擊 lru_cache 可以查看原始碼，其原始碼如下：

def lru_cache(maxsize=128, typed=False):
    """Least-recently-used cache decorator.

    If *maxsize* is set to None, the LRU features are disabled and the cache
    can grow without bound.

    If *typed* is True, arguments of different types will be cached separately.
    For example, f(3.0) and f(3) will be treated as distinct calls with
    distinct results.

    Arguments to the cached function must be hashable.

    View the cache statistics named tuple (hits, misses, maxsize, currsize)
    with f.cache_info().  Clear the cache and statistics with f.cache_clear().
    Access the underlying function with f.__wrapped__.

    See:  http://en.wikipedia.org/wiki/Cache_algorithms#Least_Recently_Used

    """

    # Users should only access the lru_cache through its public API:
    #       cache_info, cache_clear, and f.__wrapped__
    # The internals of the lru_cache are encapsulated for thread safety and
    # to allow the implementation to change (including a possible C version).

    # Early detection of an erroneous call to @lru_cache without any arguments
    # resulting in the inner function being passed to maxsize instead of an
    # integer or None.
    if maxsize is not None and not isinstance(maxsize, int):
        raise TypeError('Expected maxsize to be an integer or None')

    def decorating_function(user_function):
        wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
        return update_wrapper(wrapper, user_function)

    return decorating_function

　　注釋的第一行就指明了這是一個 LRU 快取裝飾器（“Least-recently-used cache decorator”），如果 maxsize 引數被設定為 None，則禁用了 LRU 特性，且快取可以無限制地增長；如果 typed 引數被設定為 True，則不同型別的引數會被視為不同的呼叫，例如 f(3.0) 和 f(3) 就會被視為不同的呼叫，其結果也就不同了，

　　再看代碼部分，maxsize 只能為 None 或者 int 型別資料，然后就是一個裝飾的函式 decorating_function，包含了兩個函式 _lru_cache_wrapper 和 update_wrapper，而其中主要功能包含在 _lru_cache_wrapper() 函式中，其原始碼如下：

  1 def _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo):
  2     # Constants shared by all lru cache instances:
  3     sentinel = object()          # unique object used to signal cache misses
  4     make_key = _make_key         # build a key from the function arguments
  5     PREV, NEXT, KEY, RESULT = 0, 1, 2, 3   # names for the link fields
  6 
  7     cache = {}
  8     hits = misses = 0
  9     full = False
 10     cache_get = cache.get    # bound method to lookup a key or return None
 11     cache_len = cache.__len__  # get cache size without calling len()
 12     lock = RLock()           # because linkedlist updates aren't threadsafe
 13     root = []                # root of the circular doubly linked list
 14     root[:] = [root, root, None, None]     # initialize by pointing to self
 15 
 16     if maxsize == 0:
 17 
 18         def wrapper(*args, **kwds):
 19             # No caching -- just a statistics update after a successful call
 20             nonlocal misses
 21             result = user_function(*args, **kwds)
 22             misses += 1
 23             return result
 24 
 25     elif maxsize is None:
 26 
 27         def wrapper(*args, **kwds):
 28             # Simple caching without ordering or size limit
 29             nonlocal hits, misses
 30             key = make_key(args, kwds, typed)
 31             result = cache_get(key, sentinel)
 32             if result is not sentinel:
 33                 hits += 1
 34                 return result
 35             result = user_function(*args, **kwds)
 36             cache[key] = result
 37             misses += 1
 38             return result
 39 
 40     else:
 41 
 42         def wrapper(*args, **kwds):
 43             # Size limited caching that tracks accesses by recency
 44             nonlocal root, hits, misses, full
 45             key = make_key(args, kwds, typed)
 46             with lock:
 47                 link = cache_get(key)
 48                 if link is not None:
 49                     # Move the link to the front of the circular queue
 50                     link_prev, link_next, _key, result = link
 51                     link_prev[NEXT] = link_next
 52                     link_next[PREV] = link_prev
 53                     last = root[PREV]
 54                     last[NEXT] = root[PREV] = link
 55                     link[PREV] = last
 56                     link[NEXT] = root
 57                     hits += 1
 58                     return result
 59             result = user_function(*args, **kwds)
 60             with lock:
 61                 if key in cache:
 62                     # Getting here means that this same key was added to the
 63                     # cache while the lock was released.  Since the link
 64                     # update is already done, we need only return the
 65                     # computed result and update the count of misses.
 66                     pass
 67                 elif full:
 68                     # Use the old root to store the new key and result.
 69                     oldroot = root
 70                     oldroot[KEY] = key
 71                     oldroot[RESULT] = result
 72                     # Empty the oldest link and make it the new root.
 73                     # Keep a reference to the old key and old result to
 74                     # prevent their ref counts from going to zero during the
 75                     # update. That will prevent potentially arbitrary object
 76                     # clean-up code (i.e. __del__) from running while we're
 77                     # still adjusting the links.
 78                     root = oldroot[NEXT]
 79                     oldkey = root[KEY]
 80                     oldresult = root[RESULT]
 81                     root[KEY] = root[RESULT] = None
 82                     # Now update the cache dictionary.
 83                     del cache[oldkey]
 84                     # Save the potentially reentrant cache[key] assignment
 85                     # for last, after the root and links have been put in
 86                     # a consistent state.
 87                     cache[key] = oldroot
 88                 else:
 89                     # Put result in a new link at the front of the queue.
 90                     last = root[PREV]
 91                     link = [last, root, key, result]
 92                     last[NEXT] = root[PREV] = cache[key] = link
 93                     # Use the cache_len bound method instead of the len() function
 94                     # which could potentially be wrapped in an lru_cache itself.
 95                     full = (cache_len() >= maxsize)
 96                 misses += 1
 97             return result
 98 
 99     def cache_info():
100         """Report cache statistics"""
101         with lock:
102             return _CacheInfo(hits, misses, maxsize, cache_len())
103 
104     def cache_clear():
105         """Clear the cache and cache statistics"""
106         nonlocal hits, misses, full
107         with lock:
108             cache.clear()
109             root[:] = [root, root, None, None]
110             hits = misses = 0
111             full = False
112 
113     wrapper.cache_info = cache_info
114     wrapper.cache_clear = cache_clear
115     return wrapper

　　可以看到根據 maxsize 的值會回傳不同的 wrapper 函式，當 maxsize 為零時，定義了一個區域變數 misses，并在每次呼叫時加1；當 maxsize 為 None 時，在函式呼叫時會先從快取中獲取，若快取中有就回傳結果，若快取中沒有則運行函式并將結果加入到快取中；當 maxsize 為非零整數時，可以快取最多 maxsize 個此函式的呼叫結果，此時使用了一個雙向鏈表 root，其初始化如下：

root = []     # root of the circular doubly linked list
root[:] = [root, root, None, None]      # initialize by pointing to self

　　當呼叫時也會先從快取中進行獲取，如果有則更新 root 并回傳結果，如果沒有則呼叫函式，此時需要判斷快取是否達到最大數量，若已滿，則洗掉 root 中最久未訪問的資料并更新 root 和快取，

三、LRU Cache

1.基本認識

　　我們知道計算機的快取容量有限，如果快取滿了就要洗掉一些內容，給新內容騰位置，但問題是，洗掉哪些內容呢？

　　LRU 快取策略就是一種常用的策略，LRU，全稱 least recently used，表示最近最少使用，LRU 快取策略認為最近使用過的資料應該是是有用的，而很久都沒用過的資料應該是無用的，記憶體滿了就優先刪那些很久沒用過的資料，

 2.自定義實作

　　實作 lru cache 需要兩個資料結構：雙向鏈表和哈希表，雙向鏈表用于記錄存盤資料的順序，用于淘汰最久未使用的資料，哈希表用于記錄元素位置，可在 O(1) 的時間復雜度下獲取元素，

　　然后要實作兩個操作，分別是 get 和 put：

　　1）get 操作：根據傳入的 key 從哈希表中獲取元素的位置，若沒有回傳 None，若有則從鏈表中獲取元素并將該元素移到鏈表尾部；

　　2）put 操作：首先判斷傳入的 key 是否在哈希表中存在，若有則進行更新，并將該元素移到鏈表尾部；若沒有，表示是一個新元素，需要添加到哈希表中，再判斷資料量是否超過最大容量，若達到最大容量則洗掉最久未使用的資料，即鏈表頭部元素，再將新元素添加到鏈表尾部，若未達到最大容量則直接添加到鏈表尾部，

　　首先要實作雙向鏈表，代碼如下：

 1 # Node of the list
 2 class Node:
 3     def __init__(self, val):
 4         self.val = val
 5         self.prev = None
 6         self.next = None
 7 
 8     def __str__(self):
 9         return "The value is " + str(self.val)
10 
11 
12 # Double Linked List
13 class DoubleList:
14     def __init__(self):
15         self.head = None
16         self.tail = None
17 
18     def is_empty(self):
19         """
20         returns true if the list is empty, false otherwise
21         :return:
22         """
23         return self.head is None
24 
25     def append(self, value):
26         """
27         append element after the list
28         :param value: the value of node
29         :return:
30         """
31         node = Node(value)
32         if self.is_empty():
33             self.head = node
34             self.tail = node
35             return
36         cur = self.head
37         # find the tail of the list
38         while cur.next:
39             cur = cur.next
40         cur.next = node
41         node.prev = cur
42         self.tail = node
43 
44     def remove(self, value):
45         """
46         if value in the list, remove the element
47         :param value: the value of node
48         :return:
49         """
50         if self.is_empty():
51             return
52         cur = self.head
53         while cur:
54             if cur.val == value:
55                 if len(self) == 1:
56                     # when the list has only one node
57                     self.head, self.tail = None, None
58                 else:
59                     if cur == self.head:
60                         self.head = cur.next
61                     elif cur == self.tail:
62                         self.tail = cur.prev
63                     else:
64                         cur.prev.next = cur.next
65                 return
66             else:
67                 cur = cur.next
68 
69     def traverse(self):
70         """
71         iterate through the list
72         :return:
73         """
74         cur = self.head
75         index = 1
76         while cur:
77             print("Index: {}".format(index) + cur)
78             cur = cur.next
79             index += 1
80 
81     def __len__(self):
82         count = 0
83         cur = self.head
84         while cur:
85             count += 1
86             cur = cur.next
87         return count
88 
89     def __str__(self):
90         cur = self.head
91         ret = ""
92         while cur:
93             ret += str(cur.val) + "->" if cur.next else str(cur.val)
94             cur = cur.next
95         return ret

　　其中實作了添加節點、洗掉節點、獲取長度等方法，已經足夠作為我們需要的雙向鏈表來使用了，最后就是實作 LRU Cache，主要實作 get（獲取資料） 和 put（添加資料）方法，下面是自定義實作的 LRU Cache 類的代碼：

 1 # LRU Cache
 2 class LRU:
 3     def __init__(self, size):
 4         self.size = size
 5         self._list = DoubleList()
 6         self._cache = dict()
 7 
 8     def _set_recent(self, node):
 9         """
10         set the node to most recently used
11         :param node: node
12         :return:
13         """
14         # when the node is the tail of the list
15         if node == self._list.tail:
16             return
17         cur = self._list.head
18         while cur:
19             # remove the node from the list
20             if cur == node:
21                 if cur == self._list.head:
22                     self._list.head = cur.next
23                 else:
24                     prev = cur.prev
25                     prev.next = cur.next
26             if cur.next:
27                 cur = cur.next
28             else:
29                 break
30         # set node to the tail of the list
31         cur.next = node
32         node.next = None
33         node.prev = cur
34         self._list.tail = node
35 
36     def get(self, key):
37         """
38         get value of the key
39         :param key: key
40         :return:
41         """
42         node = self._cache.get(key, None)
43         if not node:
44             return
45         self._set_recent(node)
46         return node.val
47 
48     def put(self, key, value):
49         """
50         set value of the key and add to the cache
51         :param key: key
52         :param value: value
53         :return:
54         """
55         node = self._cache.get(key, None)
56         if not node:
57             if len(self._list) < self.size:
58                 self._list.append(value)
59             else:
60                 # when the quantity reaches the maximum, delete the head node
61                 name = None
62                 for k, v in self._cache.items():
63                     if v == self._list.head:
64                         name = k
65                 if name:
66                     del self._cache[name]
67                 self._list.head = self._list.head.next
68                 self._list.append(value)
69         else:
70             self._set_recent(node)
71             self._list.tail.val = value
72         # add to cache
73         self._cache[key] = self._list.tail
74 
75     def show(self):
76         """
77         show data of the list
78         :return:
79         """
80         return "The list is: {}".format(self._list)

　　下面是測驗代碼：

 1 if __name__ == '__main__':
 2     lru = LRU(8)
 3     for i in range(10):
 4         lru.put(str(i), i)
 5     print(lru.show())
 6     for i in range(10):
 7         if i % 3 == 0:
 8             print("Get {}: {}".format(i, lru.get(str(i))))
 9     print(lru.show())
10     lru.put("2", 22)
11     lru.put("4", 44)
12     lru.put("6", 66)
13     print(lru.show())

　　最后是運行結果的截圖：

• 當插入資料時，因為最大容量為8，而插入了10個資料，那么最開始添加進去的0和1就會被刪掉；
• 當獲取資料時，不存在則回傳None，存在則回傳對應的值，并將該節點移到鏈表的尾部；
• 當更新資料時，會將對應節點的值進行更新，并將節點移到鏈表的尾部，

完整代碼已上傳到 GitHub！

標籤：Python

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