[#hash_equality]

:idprefix: hash_equality_

= Equality Predicates and Hash Functions

While the associative containers use an ordering relation to specify how the
elements are stored, the unordered associative containers use an equality
predicate and a hash function. For example, `xref:reference/unordered_map.adoc[boost::unordered_map]`
is declared as:

```cpp
template <
    class Key, class Mapped,
    class Hash = boost::hash<Key>,
    class Pred = std::equal_to<Key>,
    class Alloc = std::allocator<std::pair<Key const, Mapped> > >
class unordered_map;
```

The hash function comes first as you might want to change the hash function
but not the equality predicate. For example, if you wanted to use the
https://en.wikipedia.org/wiki/Fowler%E2%80%93Noll%E2%80%93Vo_hash_function#FNV-1a_hash[FNV-1a hash^] you could write:

```cpp
boost::unordered_map<std::string, int, hash::fnv_1a>
    dictionary;
```

There is an link:../../../examples/fnv1.hpp[implementation of FNV-1a^] in the examples directory.

If you wish to use a different equality function, you will also need to use a matching hash function. For example, to implement a case insensitive dictionary you need to define a case insensitive equality predicate and hash function:

```cpp
struct iequal_to
{
    bool operator()(std::string const& x,
        std::string const& y) const
    {
        return boost::algorithm::iequals(x, y, std::locale());
    }
};

struct ihash
{
    std::size_t operator()(std::string const& x) const
    {
        std::size_t seed = 0;
        std::locale locale;

        for(std::string::const_iterator it = x.begin();
            it != x.end(); ++it)
        {
            boost::hash_combine(seed, std::toupper(*it, locale));
        }

        return seed;
    }
};
```

Which you can then use in a case insensitive dictionary:
```cpp
boost::unordered_map<std::string, int, ihash, iequal_to>
    idictionary;
```

This is a simplified version of the example at
link:../../../examples/case_insensitive.hpp[/libs/unordered/examples/case_insensitive.hpp^] which supports other locales and string types.

CAUTION: Be careful when using the equality (`==`) operator with custom equality
predicates, especially if you're using a function pointer. If you compare two
containers with different equality predicates then the result is undefined.
For most stateless function objects this is impossible - since you can only
compare objects with the same equality predicate you know the equality
predicates must be equal. But if you're using function pointers or a stateful
equality predicate (e.g. `boost::function`) then you can get into trouble.

== Custom Types

Similarly, a custom hash function can be used for custom types:

```cpp
struct point {
    int x;
    int y;
};

bool operator==(point const& p1, point const& p2)
{
    return p1.x == p2.x && p1.y == p2.y;
}

struct point_hash
{
    std::size_t operator()(point const& p) const
    {
        std::size_t seed = 0;
        boost::hash_combine(seed, p.x);
        boost::hash_combine(seed, p.y);
        return seed;
    }
};

boost::unordered_multiset<point, point_hash> points;
```

Since the default hash function is link:../../../../container_hash/index.html[Boost.Hash^],
we can extend it to support the type so that the hash function doesn't need to be explicitly given:

```cpp
struct point {
    int x;
    int y;
};

bool operator==(point const& p1, point const& p2)
{
    return p1.x == p2.x && p1.y == p2.y;
}

std::size_t hash_value(point const& p) {
    std::size_t seed = 0;
    boost::hash_combine(seed, p.x);
    boost::hash_combine(seed, p.y);
    return seed;
}

// Now the default function objects work.
boost::unordered_multiset<point> points;
```

See the link:../../../../container_hash/index.html[Boost.Hash documentation^] for more detail on how to
do this. Remember that it relies on extensions to the standard - so it
won't work for other implementations of the unordered associative containers,
you'll need to explicitly use Boost.Hash.

[caption=, title='Table {counter:table-counter} Methods for accessing the hash and equality functions']
[cols="1,.^1", frame=all, grid=rows]
|===
|Method |Description

|`hasher hash_function() const`
|Returns the container's hash function.

|`key_equal key_eq() const`
|Returns the container's key equality function..

|===