: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. 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; } 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. Method Description `hasher hash_function() const` Returns the container\'s hash function. `key_equal key_eq() const` Returns the container\'s key equality function..