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| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="unordered.rationale"></a><a class="link" href="rationale.html" title="Implementation Rationale">Implementation Rationale</a> |
| </h2></div></div></div> |
| <p> |
| 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. |
| </p> |
| <p> |
| The <a href="http://en.wikipedia.org/wiki/Hash_table" target="_top">wikipedia article |
| on hash tables</a> has a good summary of the implementation issues for |
| hash tables in general. |
| </p> |
| <h3> |
| <a name="unordered.rationale.h0"></a> |
| <span class="phrase"><a name="unordered.rationale.data_structure"></a></span><a class="link" href="rationale.html#unordered.rationale.data_structure">Data |
| Structure</a> |
| </h3> |
| <p> |
| By specifying an interface for accessing the buckets of the container the standard |
| pretty much requires that the hash table uses chained addressing. |
| </p> |
| <p> |
| 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 a some serious problems with this: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| 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. |
| </li> |
| <li class="listitem"> |
| Local iterators would be very inefficient and may not be able to meet the |
| complexity requirements. |
| </li> |
| <li class="listitem"> |
| 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. |
| </li> |
| <li class="listitem"> |
| And since the standard is written with a eye towards chained addressing, |
| users will be surprised if the performance doesn't reflect that. |
| </li> |
| </ul></div> |
| <p> |
| So chained addressing is used. |
| </p> |
| <h3> |
| <a name="unordered.rationale.h1"></a> |
| <span class="phrase"><a name="unordered.rationale.number_of_buckets"></a></span><a class="link" href="rationale.html#unordered.rationale.number_of_buckets">Number |
| of Buckets</a> |
| </h3> |
| <p> |
| 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. |
| </p> |
| <p> |
| 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. |
| </p> |
| <p> |
| Using a power of 2 allows for much quicker selection of the bucket to use, |
| but at the expense of loosing 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. |
| </p> |
| <p> |
| To avoid this a transformation could be applied to the hash function, for an |
| example see <a href="http://web.archive.org/web/20121102023700/http://www.concentric.net/~Ttwang/tech/inthash.htm" target="_top">Thomas |
| Wang's article on integer hash functions</a>. 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. |
| </p> |
| <p> |
| Currently this is only done on 64 bit architecures, where prime number modulus |
| can be expensive. Although this varies depending on the architecture, so I |
| probably should revisit it. |
| </p> |
| <p> |
| 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. |
| </p> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2003, 2004 Jeremy B. Maitin-Shepard<br>Copyright © 2005-2008 Daniel |
| James<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
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