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.