| [/ Copyright 2006-2008 Daniel James. |
| / Distributed under the Boost Software License, Version 1.0. (See accompanying |
| / file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) ] |
| |
| [def __wang__ |
| [@http://web.archive.org/web/20121102023700/http://www.concentric.net/~Ttwang/tech/inthash.htm |
| Thomas Wang's article on integer hash functions]] |
| |
| [section:rationale Implementation Rationale] |
| |
| The intent of this library is to implement the unordered |
| containers in the draft standard, so the interface was fixed. But there are |
| still some implementation decisions to make. The priorities are |
| conformance to the standard and portability. |
| |
| The [@http://en.wikipedia.org/wiki/Hash_table Wikipedia article on hash tables] |
| has a good summary of the implementation issues for hash tables in general. |
| |
| [h2 Data Structure] |
| |
| By specifying an interface for accessing the buckets of the container the |
| standard pretty much requires that the hash table uses chained addressing. |
| |
| It would be conceivable to write a hash table that uses another method. For |
| example, it could use open addressing, and use the lookup chain to act as a |
| bucket but there are some serious problems with this: |
| |
| * The draft standard requires that pointers to elements aren't invalidated, so |
| the elements can't be stored in one array, but will need a layer of |
| indirection instead - losing the efficiency and most of the memory gain, |
| the main advantages of open addressing. |
| |
| * Local iterators would be very inefficient and may not be able to |
| meet the complexity requirements. |
| |
| * There are also the restrictions on when iterators can be invalidated. Since |
| open addressing degrades badly when there are a high number of collisions the |
| restrictions could prevent a rehash when it's really needed. The maximum load |
| factor could be set to a fairly low value to work around this - but the |
| standard requires that it is initially set to 1.0. |
| |
| * And since the standard is written with a eye towards chained |
| addressing, users will be surprised if the performance doesn't reflect that. |
| |
| So chained addressing is used. |
| |
| [/ (Removing for now as this is out of date) |
| |
| For containers with unique keys I store the buckets in a single-linked list. |
| There are other possible data structures (such as a double-linked list) |
| that allow for some operations to be faster (such as erasing and iteration) |
| but the possible gain seems small compared to the extra memory needed. |
| The most commonly used operations (insertion and lookup) would not be improved |
| at all. |
| |
| But for containers with equivalent keys a single-linked list can degrade badly |
| when a large number of elements with equivalent keys are inserted. I think it's |
| reasonable to assume that users who choose to use `unordered_multiset` or |
| `unordered_multimap` do so because they are likely to insert elements with |
| equivalent keys. So I have used an alternative data structure that doesn't |
| degrade, at the expense of an extra pointer per node. |
| |
| This works by adding storing a circular linked list for each group of equivalent |
| nodes in reverse order. This allows quick navigation to the end of a group (since |
| the first element points to the last) and can be quickly updated when elements |
| are inserted or erased. The main disadvantage of this approach is some hairy code |
| for erasing elements. |
| ] |
| |
| [/ (Starting to write up new structure, might not be ready in time) |
| The node used to be stored in a linked list for each bucket but that |
| didn't meet the complexity requirements for C++11, so now the nodes |
| are stored in one long single linked list. But there needs a way to get |
| the bucket from the node, to do that a copy of the key's hash value is |
| stored in the node. Another possibility would be to store a pointer to |
| the bucket, or the bucket's index, but storing the hash value allows |
| some operations to be faster. |
| ] |
| |
| [h2 Number of Buckets] |
| |
| There are two popular methods for choosing the number of buckets in a hash |
| table. One is to have a prime number of buckets, another is to use a power |
| of 2. |
| |
| Using a prime number of buckets, and choosing a bucket by using the modulus |
| of the hash function's result will usually give a good result. The downside |
| is that the required modulus operation is fairly expensive. This is what the |
| containers do in most cases. |
| |
| Using a power of 2 allows for much quicker selection of the bucket |
| to use, but at the expense of losing the upper bits of the hash value. |
| For some specially designed hash functions it is possible to do this and |
| still get a good result but as the containers can take arbitrary hash |
| functions this can't be relied on. |
| |
| To avoid this a transformation could be applied to the hash function, for an |
| example see __wang__. Unfortunately, a transformation like Wang's requires |
| knowledge of the number of bits in the hash value, so it isn't portable enough |
| to use as a default. It can applicable in certain cases so the containers |
| have a policy based implementation that can use this alternative technique. |
| |
| Currently this is only done on 64 bit architectures, where prime number |
| modulus can be expensive. Although this varies depending on the architecture, |
| so I probably should revisit it. |
| |
| I'm also thinking of introducing a mechanism whereby a hash function can |
| indicate that it's safe to be used directly with power of 2 buckets, in |
| which case a faster plain power of 2 implementation can be used. |
| |
| [endsect] |