[/ 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://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 a 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[/ (Removing for now as this is out of date)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.

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.

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.
This leaves more expensive methods, such as Knuth's Multiplicative Method
(mentioned in Wang's article). These don't tend to work as well as taking the
modulus of a prime, and the extra computation required might negate
efficiency advantage of power of 2 hash tables.

So, this implementation uses a prime number for the hash table size.

[endsect]
