Hash array mapped trie

A HAMT is an array mapped trie where the keys are first hashed to ensure an even distribution of keys and a constant key length.

In a typical implementation of HAMT's array mapped trie, each node contains a table with some fixed number N of slots with each slot containing either a nil pointer or a pointer to another node. N is commonly 32. As allocating space for N pointers for each node would be expensive, each node instead contains a bitmap which is N bits long where each bit indicates the presence of a non-nil pointer. This is followed by an array of pointers equal in length to the number of ones in the bitmap (its Hamming weight).

The hash array mapped trie achieves almost hash table-like speed while using memory much more economically. Also, a hash table may have to be periodically resized, an expensive operation, whereas HAMTs grow dynamically. Generally, HAMT performance is improved by a larger root table with some multiple of N slots; some HAMT variants allow the root to grow lazily with negligible impact on performance.

Implementation of a HAMT involves the use of the population count function, which counts the number of ones in the binary representation of a number. This operation is available in many instruction set architectures, but it is available in only some high-level languages. Although population count can be implemented in software in O(1) time using a series of shift and add instructions, doing so may perform the operation an order of magnitude slower.{{citation needed|date=October 2016}}

The programming languages Clojure,{{cite web|url=https://github.com/clojure/clojure/blob/master/src/jvm/clojure/lang/PersistentHashMap.java|title=clojure/clojure|website=GitHub|date=8 December 2022 }} Scala, and Frege{{cite web|url=https://github.com/Frege/frege/blob/master/frege/data/HashMap.fr|title=Frege/frege|website=GitHub|date=7 December 2022 }} use a persistent variant of hash array mapped tries for their native hash map type. The Haskell library "unordered-containers" uses the same to implement persistent map and set data structures.Johan Tibell, A. [http://blog.johantibell.com/2012/03/announcing-unordered-containers-02.html Announcing unordered-containers 0.2] Another Haskell library "stm-containers" adapts the algorithm for use in the context of software transactional memory.Nikita Volkov, [https://nikita-volkov.github.io/stm-containers/ Announcing the "stm-containers" library], 2014 A Javascript HAMT library {{cite web|url=https://github.com/mattbierner/hamt|title=mattbierner/hamt|website=GitHub|date=27 November 2022 }} based on the Clojure implementation is also available. The Rubinius{{cite web|url=https://github.com/rubinius/rubinius/blob/540a4b446991e4d5c956023d37ec4f95372d539d/kernel/common/hash_hamt.rb|title=Ruby source file of Rubinius's HAMT|website=GitHub|publisher=}} implementation of Ruby includes a HAMT, mostly written in Ruby but with 3https://github.com/rubinius/rubinius/blob/master/machine/builtin/system.cpp#L1724-L1802 {{Dead link|date=February 2022}} primitives. Large maps in Erlang use a persistent HAMT representation internally since release 18.0.{{Cite web | url=http://www.erlang.org/news/86 | title=Erlang Programming Language}} The Pony programming language uses a HAMT for the hash map in its persistent collections package.{{Cite web | url=https://github.com/ponylang/ponyc/blob/master/packages/collections/persistent/map.pony | title=horse: Pony is an open-source, actor-model, capabilities-secure, high performance programming language: Ponylang/ponyc| website=GitHub| date=2018-11-26}}

The im and im-rc crates, which provide persistent collection types for the Rust programming language, use a HAMT for their persistent hash tables and hash sets.

{{cite web|url=https://docs.rs/im/|title=API docs for Rust im-rc crate}}

The concurrent lock-free versionProkopec, A. [https://github.com/axel22/Ctries Implementation of Concurrent Hash Tries on GitHub] of the hash trie called Ctrie is a mutable thread-safe implementation which ensures progress. The data-structure has been proven to be correctProkopec, A. et al. (2011) [http://infoscience.epfl.ch/record/166908/files/ctries-techreport.pdf Cache-Aware Lock-Free Concurrent Hash Tries]. Technical Report, 2011. - Ctrie operations have been shown to have the atomicity, linearizability and lock-freedom properties.

• Judy array
• Radix tree

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Category:Associative arrays

Category:Hashing