Editing Hash function (section)

== Overview ==
In a hash table, a hash function takes a key as an input, which is associated with a datum or record and used to identify it to the data storage and retrieval application. The keys may be fixed-length, like an integer, or variable-length, like a name.  In some cases, the key is the datum itself.  The output is a hash code used to index a hash table holding the data or records, or pointers to them.

A hash function may be considered to perform three functions:
*Convert variable-length keys into fixed-length (usually [[Machine word|machine-word]]-length or less) values, by folding them by words or other units using a [[Parity function|parity-preserving operator]] like ADD or XOR,
*Scramble the bits of the key so that the resulting values are uniformly distributed over the [[Key space (cryptography)|keyspace]], and
*Map the key values into ones less than or equal to the size of the table.
A good hash function satisfies two basic properties: it should be very fast to compute, and it should minimize duplication of output values ([[Hash collision|collisions]]).  Hash functions rely on generating favorable [[probability distribution]]s for their effectiveness, reducing access time to nearly constant.  High table loading factors, [[Pathological (mathematics)|pathological]] key sets, and poorly designed hash functions can result in access times approaching linear in the number of items in the table. Hash functions can be designed to give the best worst-case performance,<ref group=Notes>This is useful in cases where keys are devised by a malicious agent, for example in pursuit of a DOS attack.</ref> good performance under high table loading factors, and in special cases, perfect (collisionless) mapping of keys into hash codes. Implementation is based on parity-preserving bit operations (XOR and ADD), multiply, or divide. A necessary adjunct to the hash function is a collision-resolution method that employs an auxiliary data structure like [[linked list]]s, or systematic probing of the table to find an empty slot.