[postfuturist]

> They are a data structure invented by Rich Hickey for Clojure

It is an implementation of a data structure invented by Phil Bagwell: http://lampwww.epfl.ch/papers/idealhashtrees.pdf

[JeanPierre]

Author here: I think you talk about the persistent hashmaps, not the persistent vectors. I've been looking for papers explaining Clojure's persistent collections, and Bagwell seems to cover the hash maps and hash sets quite well. However, I've not seen a paper on the persistent vectors, which was quite a bummer, and that was the reason I started explaining them in the first place.

If you have a reference to a paper explaining something similar (or the actual implementation), I'd love to put it in the post for others.

[jasonwatkinspdx]

https://github.com/clojure/clojure/blob/c6756a8bab137128c811...

Looking at the source the persistent vectors are virtually identical to Bagwell's paper. Rich did add a couple tweaks, namely moving the bitvector that indicates what slots of a node are occupied from being a word in the node object to being embedded in the 64bit integers stored in each node slot. When a node is filled enough to span 2 cache lines, around 9 slots on typical hardware with 64 byte lines, and the next desired index fragment is the 9th slot or higher, this avoids touching the first cache line, potentially saving a cache miss. This is why the nodes are 32 way: 32bits for the bitvector and 32bits for the offset in the underlying storage array fit in one 64bit word which can be written atomically (inside a transient obviously). Rich goes through this in one of his talks but I don't recall which.

The modification to go from mutable to immutable isn't an invention either. Anyone who's read any of the functional data structure literature will be familiar with path copying being one of the two general ways of making any data structure persistent.

From the perspective of these data structures there's little difference between a vector with integer indexes and a hashmap. The hashmap just requires a preliminary step of hashing the key to an integer.

[swannodette]

Tiark & Bagwell cover Rich Hickey's modifications and come up with some pretty cool improvements of their own in their paper on RRB-Trees, http://infoscience.epfl.ch/record/169879/files/RMTrees.pdf

[swannodette]

Note Phil's version is mutable and lacks the performance tweaks suited for an array-like data structure. There are enough modifications to the original idea to say that Rich Hickey invented the immutable Bitmapped Vector Trie.