<P> This principle is widely used in computer graphics, computational geometry and many other disciplines, to solve many proximity problems in the plane or in three - dimensional space, such as finding closest pairs in a set of points, similar shapes in a list of shapes, similar images in an image database, and so on . In these applications, the set of all inputs is some sort of metric space, and the hashing function can be interpreted as a partition of that space into a grid of cells . The table is often an array with two or more indices (called a grid file, grid index, bucket grid, and similar names), and the hash function returns an index tuple . This special case of hashing is known as geometric hashing or the grid method . Geometric hashing is also used in telecommunications (usually under the name vector quantization) to encode and compress multi-dimensional signals . </P> <P> Some standard applications that employ hash functions include authentication, message integrity (using an HMAC (Hashed MAC)), message fingerprinting, data corruption detection, and digital signature efficiency . </P> <P> Good hash functions, in the original sense of the term, are usually required to satisfy certain properties listed below . The exact requirements are dependent on the application, for example a hash function well suited to indexing data will probably be a poor choice for a cryptographic hash function . </P> <P> A hash procedure must be deterministic--meaning that for a given input value it must always generate the same hash value . In other words, it must be a function of the data to be hashed, in the mathematical sense of the term . This requirement excludes hash functions that depend on external variable parameters, such as pseudo-random number generators or the time of day . It also excludes functions that depend on the memory address of the object being hashed in cases that the address may change during execution (as may happen on systems that use certain methods of garbage collection), although sometimes rehashing of the item is possible . </P>

Where does a good hash function for numerical data come from
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