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Better hashing

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Problem

Clojure’s hashing strategy for numbers, sequences/vectors, sets, and maps mimics Java’s.  In Clojure, however, it is far more common than in Java to use longs, vectors, sets, maps and compound objects comprised of those components (e.g., a map from vectors of longs to sets) as keys in other hash maps.  It appears that Java’s hash strategy is not well-tuned for this kind of usage.  Clojure’s hashing for longs, vectors, sets, and maps each suffer from some weaknesses that can multiply together to create a crippling number of collisions.

For example, Paul Butcher wrote a simple Clojure program that produces a set of solutions to a chess problem.  Each solution in the set was itself a set of vectors of the form [piece-keyword [row-int col-int]].  Clojure 1.5.1's current hash function hashed about 20 million different solutions to about 20 thousand different hash values, for an average of about 1000 solutions per unique hash value.  This causes PersistentHashSet and PersistentHashMap to use long linear searches for testing set/map membership or adding new elements/keys.  There is nothing intentionally pathological about these values – they simply happened to expose this behavior in a dramatic way.  Others have come across similarly bad performance without any obvious reason why, but some of those cases are likely be due to this same root cause.

Proposed solutions

Mark Engelberg document on the subject of the hash function in Clojure, its behavior, and potential improvements, is here:

A summary of his proposed hash function modifications is:

• Change the hash of integers that fit within a long to the return value of longHashMunge (see Longs section of doc for more details)
• Change the current multiplier of 31 used for vectors, sequences, and queues to a different constant such as -1640531527 or 524287 (see Vectors section)
• For sets, instead of adding together the hash value of the elements, add together the return value of a function xorShift32 called on the hash value of each element (see Sets section)
• For maps and records, instead of adding together hash(key) ^ hash(val) for each hash,val pair, instead add together hash(key)^xorShift32(hash(val)) (see Maps section)

Andy Fingerhut's modified version of Paul Butcher's N-queens solver, with extra code for printing stats with several different hash functions.  The README has instructions for retrieving and installing locally a version of Clojure modified with one of Mark's proposed alternate hash functions: