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## 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 wikipedia article on hash tables has a good summary of the implementation issues for hash tables in general.

### 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.

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.

### 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 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 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.

### Equality operators

`operator==` and `operator!=` are not included in the standard, but I've added them as I think they could be useful and can be implemented fairly efficiently. They are specified differently to the other standard containers, comparing keys using the equality predicate rather than `operator==`.

It's also different to the proposal n2944. which uses the equality operators for the whole of `value_type`. This implementation just uses the key equality function for the key, and `mapped_type`'s equality operator in `unordered_map` and `unordered_multimap` for the mapped part of the element.

Also, in `unordered_multimap`, the mapped values for a group of elements with equivalent keys are only considered equal if they are in the same order, in n2944 they just need to be a permutation of each other. Since the order of elements with equal keys is now defined to be stable, it seems to me that their order can be considered part of the container's value.

### Active Issues and Proposals

#### C++0x allocators

Recent drafts have included an overhaul of the allocators, but this was dependent on concepts which are no longer in the standard. n2946 attempts to respecify them without concepts. I'll try to implement this (or an appropriate later version) in a future version of boost, possibly changed a little to accomodate non-C++0x compilers.

#### Swapping containers with unequal allocators

It isn't clear how to swap containers when their allocators aren't equal. This is Issue 431: Swapping containers with unequal allocators. This has been resolved with the new allocator specification, so this should be fixed when support is added.

#### Are insert and erase stable for unordered_multiset and unordered_multimap?

It wan't specified if `unordered_multiset` and `unordered_multimap` preserve the order of elements with equivalent keys (i.e. if they're stable under `insert` and `erase`). Since n2691 it's been specified that they do and this implementation follows that.