1 NOTES ON OPTIMIZING DICTIONARIES 2 ================================ 3 4 5 Principal Use Cases for Dictionaries 6 ------------------------------------ 7 8 Passing keyword arguments 9 Typically, one read and one write for 1 to 3 elements. 10 Occurs frequently in normal python code. 11 12 Class method lookup 13 Dictionaries vary in size with 8 to 16 elements being common. 14 Usually written once with many lookups. 15 When base classes are used, there are many failed lookups 16 followed by a lookup in a base class. 17 18 Instance attribute lookup and Global variables 19 Dictionaries vary in size. 4 to 10 elements are common. 20 Both reads and writes are common. 21 22 Builtins 23 Frequent reads. Almost never written. 24 Size 126 interned strings (as of Py2.3b1). 25 A few keys are accessed much more frequently than others. 26 27 Uniquification 28 Dictionaries of any size. Bulk of work is in creation. 29 Repeated writes to a smaller set of keys. 30 Single read of each key. 31 Some use cases have two consecutive accesses to the same key. 32 33 * Removing duplicates from a sequence. 34 dict.fromkeys(seqn).keys() 35 36 * Counting elements in a sequence. 37 for e in seqn: 38 d[e] = d.get(e,0) + 1 39 40 * Accumulating references in a dictionary of lists: 41 42 for pagenumber, page in enumerate(pages): 43 for word in page: 44 d.setdefault(word, []).append(pagenumber) 45 46 Note, the second example is a use case characterized by a get and set 47 to the same key. There are similar use cases with a __contains__ 48 followed by a get, set, or del to the same key. Part of the 49 justification for d.setdefault is combining the two lookups into one. 50 51 Membership Testing 52 Dictionaries of any size. Created once and then rarely changes. 53 Single write to each key. 54 Many calls to __contains__() or has_key(). 55 Similar access patterns occur with replacement dictionaries 56 such as with the % formatting operator. 57 58 Dynamic Mappings 59 Characterized by deletions interspersed with adds and replacements. 60 Performance benefits greatly from the re-use of dummy entries. 61 62 63 Data Layout (assuming a 32-bit box with 64 bytes per cache line) 64 ---------------------------------------------------------------- 65 66 Smalldicts (8 entries) are attached to the dictobject structure 67 and the whole group nearly fills two consecutive cache lines. 68 69 Larger dicts use the first half of the dictobject structure (one cache 70 line) and a separate, continuous block of entries (at 12 bytes each 71 for a total of 5.333 entries per cache line). 72 73 74 Tunable Dictionary Parameters 75 ----------------------------- 76 77 * PyDict_MINSIZE. Currently set to 8. 78 Must be a power of two. New dicts have to zero-out every cell. 79 Each additional 8 consumes 1.5 cache lines. Increasing improves 80 the sparseness of small dictionaries but costs time to read in 81 the additional cache lines if they are not already in cache. 82 That case is common when keyword arguments are passed. 83 84 * Maximum dictionary load in PyDict_SetItem. Currently set to 2/3. 85 Increasing this ratio makes dictionaries more dense resulting 86 in more collisions. Decreasing it improves sparseness at the 87 expense of spreading entries over more cache lines and at the 88 cost of total memory consumed. 89 90 The load test occurs in highly time sensitive code. Efforts 91 to make the test more complex (for example, varying the load 92 for different sizes) have degraded performance. 93 94 * Growth rate upon hitting maximum load. Currently set to *2. 95 Raising this to *4 results in half the number of resizes, 96 less effort to resize, better sparseness for some (but not 97 all dict sizes), and potentially doubles memory consumption 98 depending on the size of the dictionary. Setting to *4 99 eliminates every other resize step. 100 101 * Maximum sparseness (minimum dictionary load). What percentage 102 of entries can be unused before the dictionary shrinks to 103 free up memory and speed up iteration? (The current CPython 104 code does not represent this parameter directly.) 105 106 * Shrinkage rate upon exceeding maximum sparseness. The current 107 CPython code never even checks sparseness when deleting a 108 key. When a new key is added, it resizes based on the number 109 of active keys, so that the addition may trigger shrinkage 110 rather than growth. 111 112 Tune-ups should be measured across a broad range of applications and 113 use cases. A change to any parameter will help in some situations and 114 hurt in others. The key is to find settings that help the most common 115 cases and do the least damage to the less common cases. Results will 116 vary dramatically depending on the exact number of keys, whether the 117 keys are all strings, whether reads or writes dominate, the exact 118 hash values of the keys (some sets of values have fewer collisions than 119 others). Any one test or benchmark is likely to prove misleading. 120 121 While making a dictionary more sparse reduces collisions, it impairs 122 iteration and key listing. Those methods loop over every potential 123 entry. Doubling the size of dictionary results in twice as many 124 non-overlapping memory accesses for keys(), items(), values(), 125 __iter__(), iterkeys(), iteritems(), itervalues(), and update(). 126 Also, every dictionary iterates at least twice, once for the memset() 127 when it is created and once by dealloc(). 128 129 Dictionary operations involving only a single key can be O(1) unless 130 resizing is possible. By checking for a resize only when the 131 dictionary can grow (and may *require* resizing), other operations 132 remain O(1), and the odds of resize thrashing or memory fragmentation 133 are reduced. In particular, an algorithm that empties a dictionary 134 by repeatedly invoking .pop will see no resizing, which might 135 not be necessary at all because the dictionary is eventually 136 discarded entirely. 137 138 139 Results of Cache Locality Experiments 140 ------------------------------------- 141 142 When an entry is retrieved from memory, 4.333 adjacent entries are also 143 retrieved into a cache line. Since accessing items in cache is *much* 144 cheaper than a cache miss, an enticing idea is to probe the adjacent 145 entries as a first step in collision resolution. Unfortunately, the 146 introduction of any regularity into collision searches results in more 147 collisions than the current random chaining approach. 148 149 Exploiting cache locality at the expense of additional collisions fails 150 to payoff when the entries are already loaded in cache (the expense 151 is paid with no compensating benefit). This occurs in small dictionaries 152 where the whole dictionary fits into a pair of cache lines. It also 153 occurs frequently in large dictionaries which have a common access pattern 154 where some keys are accessed much more frequently than others. The 155 more popular entries *and* their collision chains tend to remain in cache. 156 157 To exploit cache locality, change the collision resolution section 158 in lookdict() and lookdict_string(). Set i^=1 at the top of the 159 loop and move the i = (i << 2) + i + perturb + 1 to an unrolled 160 version of the loop. 161 162 This optimization strategy can be leveraged in several ways: 163 164 * If the dictionary is kept sparse (through the tunable parameters), 165 then the occurrence of additional collisions is lessened. 166 167 * If lookdict() and lookdict_string() are specialized for small dicts 168 and for largedicts, then the versions for large_dicts can be given 169 an alternate search strategy without increasing collisions in small dicts 170 which already have the maximum benefit of cache locality. 171 172 * If the use case for a dictionary is known to have a random key 173 access pattern (as opposed to a more common pattern with a Zipf's law 174 distribution), then there will be more benefit for large dictionaries 175 because any given key is no more likely than another to already be 176 in cache. 177 178 * In use cases with paired accesses to the same key, the second access 179 is always in cache and gets no benefit from efforts to further improve 180 cache locality. 181 182 Optimizing the Search of Small Dictionaries 183 ------------------------------------------- 184 185 If lookdict() and lookdict_string() are specialized for smaller dictionaries, 186 then a custom search approach can be implemented that exploits the small 187 search space and cache locality. 188 189 * The simplest example is a linear search of contiguous entries. This is 190 simple to implement, guaranteed to terminate rapidly, never searches 191 the same entry twice, and precludes the need to check for dummy entries. 192 193 * A more advanced example is a self-organizing search so that the most 194 frequently accessed entries get probed first. The organization 195 adapts if the access pattern changes over time. Treaps are ideally 196 suited for self-organization with the most common entries at the 197 top of the heap and a rapid binary search pattern. Most probes and 198 results are all located at the top of the tree allowing them all to 199 be located in one or two cache lines. 200 201 * Also, small dictionaries may be made more dense, perhaps filling all 202 eight cells to take the maximum advantage of two cache lines. 203 204 205 Strategy Pattern 206 ---------------- 207 208 Consider allowing the user to set the tunable parameters or to select a 209 particular search method. Since some dictionary use cases have known 210 sizes and access patterns, the user may be able to provide useful hints. 211 212 1) For example, if membership testing or lookups dominate runtime and memory 213 is not at a premium, the user may benefit from setting the maximum load 214 ratio at 5% or 10% instead of the usual 66.7%. This will sharply 215 curtail the number of collisions but will increase iteration time. 216 The builtin namespace is a prime example of a dictionary that can 217 benefit from being highly sparse. 218 219 2) Dictionary creation time can be shortened in cases where the ultimate 220 size of the dictionary is known in advance. The dictionary can be 221 pre-sized so that no resize operations are required during creation. 222 Not only does this save resizes, but the key insertion will go 223 more quickly because the first half of the keys will be inserted into 224 a more sparse environment than before. The preconditions for this 225 strategy arise whenever a dictionary is created from a key or item 226 sequence and the number of *unique* keys is known. 227 228 3) If the key space is large and the access pattern is known to be random, 229 then search strategies exploiting cache locality can be fruitful. 230 The preconditions for this strategy arise in simulations and 231 numerical analysis. 232 233 4) If the keys are fixed and the access pattern strongly favors some of 234 the keys, then the entries can be stored contiguously and accessed 235 with a linear search or treap. This exploits knowledge of the data, 236 cache locality, and a simplified search routine. It also eliminates 237 the need to test for dummy entries on each probe. The preconditions 238 for this strategy arise in symbol tables and in the builtin dictionary. 239 240 241 Readonly Dictionaries 242 --------------------- 243 Some dictionary use cases pass through a build stage and then move to a 244 more heavily exercised lookup stage with no further changes to the 245 dictionary. 246 247 An idea that emerged on python-dev is to be able to convert a dictionary 248 to a read-only state. This can help prevent programming errors and also 249 provide knowledge that can be exploited for lookup optimization. 250 251 The dictionary can be immediately rebuilt (eliminating dummy entries), 252 resized (to an appropriate level of sparseness), and the keys can be 253 jostled (to minimize collisions). The lookdict() routine can then 254 eliminate the test for dummy entries (saving about 1/4 of the time 255 spent in the collision resolution loop). 256 257 An additional possibility is to insert links into the empty spaces 258 so that dictionary iteration can proceed in len(d) steps instead of 259 (mp->mask + 1) steps. Alternatively, a separate tuple of keys can be 260 kept just for iteration. 261 262 263 Caching Lookups 264 --------------- 265 The idea is to exploit key access patterns by anticipating future lookups 266 based on previous lookups. 267 268 The simplest incarnation is to save the most recently accessed entry. 269 This gives optimal performance for use cases where every get is followed 270 by a set or del to the same key. 271
