Hash array mapped trie

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A hash array mapped trie[1] (HAMT) is an implementation of an associative array that combines the characteristics of a hash table and an array mapped trie.[1] It is a refined version of the more general notion of a hash tree.


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).

Advantages of HAMTs[edit]

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[1] with negligible impact on performance.

Implementation details[edit]

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]


The programming languages Clojure,[2] Scala, and Frege[3] 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.[4] Another Haskell library "stm-containers" adapts the algorithm for use in the context of software transactional memory.[5] A Javascript HAMT library [6] based on the Clojure implementation is also available. The Rubinius[7] implementation of Ruby includes a HAMT, mostly written in Ruby but with 3[8] primitives. Large maps in Erlang use a persistent HAMT representation internally since release 18.0.[9] The Pony programming language uses a HAMT for the hash map in its persistent collections package.[10] 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. [11]

The concurrent lock-free version[12] of the hash trie called Ctrie is a mutable thread-safe implementation which ensures progress. The data-structure has been proven to be correct[13] - Ctrie operations have been shown to have the atomicity, linearizability and lock-freedom properties.

See also[edit]


  1. ^ a b c Phil Bagwell (2000). Ideal Hash Trees (PDF) (Report). Infoscience Department, École Polytechnique Fédérale de Lausanne.
  2. ^ "clojure/clojure". GitHub. 8 December 2022.
  3. ^ "Frege/frege". GitHub. 7 December 2022.
  4. ^ Johan Tibell, A. Announcing unordered-containers 0.2
  5. ^ Nikita Volkov, Announcing the "stm-containers" library, 2014
  6. ^ "mattbierner/hamt". GitHub. 27 November 2022.
  7. ^ "Ruby source file of Rubinius's HAMT". GitHub.
  8. ^ https://github.com/rubinius/rubinius/blob/master/machine/builtin/system.cpp#L1724-L1802[dead link]
  9. ^ "Erlang Programming Language".
  10. ^ "horse: Pony is an open-source, actor-model, capabilities-secure, high performance programming language: Ponylang/ponyc". GitHub. 2018-11-26.
  11. ^ "API docs for Rust im-rc crate".
  12. ^ Prokopec, A. Implementation of Concurrent Hash Tries on GitHub
  13. ^ Prokopec, A. et al. (2011) Cache-Aware Lock-Free Concurrent Hash Tries. Technical Report, 2011.