Exit Zen
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The standard requires that pointers to elements aren't invalidated, so
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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.
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Local iterators would be very inefficient and may not be able to
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meet the complexity requirements.
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13
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There are also the restrictions on when iterators can be invalidated. Since
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14
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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.
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And since the standard is written with a eye towards closed
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addressing, users will be surprised if the performance doesn't reflect that.
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17
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So closed addressing is used.
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Number of Buckets
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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.
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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 used to do in most cases.
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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.
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To avoid this a transformation could be applied to the hash function, for an example see http://web.archive.org/web/20121102023700/http://www.concentric.net/~Ttwang/tech/inthash.htm[Thomas Wang's article on integer hash functions^]. Unfortunately, a transformation like Wang's requires knowledge of the number of bits in the hash value, so it was only used when `size_t` was 64 bit.
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Since release 1.79.0, https://en.wikipedia.org/wiki/Hash_function#Fibonacci_hashing[Fibonacci hashing] is used instead. With this implementation, the bucket number is determined by using `(h * m) >> (w - k)`, where `h` is the hash value, `m` is `2^w` divided by the golden ratio, `w` is the word size (32 or 64), and `2^k` is the number of buckets. This provides a good compromise between speed and distribution.
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Since release 1.80.0, prime numbers are chosen for the number of buckets in tandem with sophisticated modulo arithmetic. This removes the need for "mixing" the result of the user's hash function as was used for release 1.79.0.
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Open-addresing Containers
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The C++ standard specification of unordered associative containers impose severe limitations on permissible implementations, the most important being that closed addressing is implicitly assumed. Slightly relaxing this specification opens up the possibility of providing container variations taking full advantage of open-addressing techniques.
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The design of `boost::unordered_flat_set`/`unordered_node_set` and `boost::unordered_flat_map`/`unordered_node_map` has been guided by Peter Dimov's https://pdimov.github.io/articles/unordered_dev_plan.html[Development Plan for Boost.Unordered^]. We discuss here the most relevant principles.
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Hash Function
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