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Understanding Clojure's Persistent Vectors, Part 1 (hypirion.com)
106 points by llambda on Sept 25, 2013 | hide | past | favorite | 23 comments

Does anyone have benchmarks comparing the performance of Clojure's PersistentVectors to standard arrays in Java and/or C? O(1) is pretty useless if the constant factor is huge. Anecdotally, I've heard that they are "fast" but it would be interesting to know what that really means.

W/o benchmarks, but from theory - it's a rather different data structure.

1) for pure lookup-by-random-int-index, the standard array is much faster - in C you just calculate a memory location and there your data is; this structure requires, say, 4-6 such lookups depending on the array size, and is that many times slower.

2) On the other hand, iteration through large consecutive parts of the array is almost the same as pure arrays; there is some overhead but that's tiny.

3) Insertion is much faster than standard C/Java arrays - you can't really insert in the middle of an array w/o copying almost all of it, but you can do it here.

4) If you need "modification while keeping the old version as well" - then again, arrays need to make a full copy, but this beast can do it cheaply, faster than a raw C array.

As for any data structures, there are no "faster data structures" since preferences greatly depend on what you want to do with them, some data structures are faster for X and others are faster for Y. The efficiency of this structure greatly depends if your array/vector is mostly used as random-access-lookup or as a list where you need to process all/many sequential items.

Clojure's standard persistent vectors don't allow insertion in the middle without copying the entire vector, they only allow fast insertion at the end. There is an alternative implementation here [1] which does allow insertion (anywhere) without copying the entire vector.

[1] https://github.com/clojure/core.rrb-vector

This might be a little hard to compare, because, as others have said, Clojure's vectors have different goals from Java arrays, with persistence being the most important one, and the one at the core of Clojure's entire philosophy.

Persistent data structures do have performance costs that are probably significant. First, each "modification" generates garbage; garbage on the JVM has different collection costs – from virtually nonexistent to quite significant – but persistent DS might generate the most expensive kind of garbage: medium-duration-lived objects. The second is caching effects. Mutable data structures reuse cache lines, while persistent DS cause cache faults and pollute the cache. Clojure's transients help with that. Of course, persistence is an essential element of Clojure's beautiful values-and-states philosophy, so you do get something extremely valuable in exchange for some performance cost.

There's another issue with persistent DS: they can't be concurrently modified; they allow only one writer at a time. Clojure does support parallel modification using the very elegant reducers, but these only apply in data-parallel situations – not general concurrency.

> 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

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.


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.

From the paper I cited below:

The immutable vector data structure as pioneered by the programming language Clojure [4] strikes a good balance between read and write performance and supports many commonly used programming patterns in an effi- cient manner. In Clojure, immutable vectors are an essential part of the language implementation design. Ideal Hash Tries (HAMTs) [1] were used as a basis for immutable hash maps and the same structure, 32-way branching trees, was used for immutable vectors.

I'm pretty sure they picked the word pioneered for a reason. If Rich Hickey didn't invent them, then Tiark & Bagwell didn't invent RRB-Trees.

Well, it's arguable either way IMHO. I'd give priority to Bagwell because he first published his work academically in 2000. At the time he worked for Odersky, the author of the Scala language. So these structures were in Scala's implementation first, then adapted and improved for Clojure.

Phil Bagwell was loosely associated with my group in 2000 but did not work for me then. His work at the time was theoretical; the first practical implementation is Clojure's. Scala's implementations only appeared in version 2.8, in 2010.

Awesome, thanks for the correction.

Since Rich Hickey isn't in academia, but instead a working programmer, using publication dates doesn't feel like it is the best criterion for determining who did what when.

I do agree that the structure is influenced by the paper, so I've added that in. I don't agree that they are "virtually identical" however, because there are significant differences leading to a lot of performance improvements (never any hash collisions, insertion and removal only at the end, resulting in perfect balancing, etc) and, as swanodette mentioned, Bagwell himself mentioned that they were pioneered by Hickey.

> Rich goes through this in one of his talks but I don't recall which.

If you figure out which, I'd love to know! :)

There's no bitvector in clojure persistent vectors. The difference between vectors and a hashmap without the hashing stage is that a persistent vector can't be sparse!

Thanks for the link to the source. I had no idea the clojure source code was so readable :-)

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

The relevant quote from section 1:

"In Clojure, immutable vectors are an essential part of the language implementation design. Ideal Hash Tries (HAMTs) [1] were used as a basis for immutable hash maps and the same structure, 32-way branching trees, was used for immutable vectors."

I expanded your selective quoting above.

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.

"practically O(1)" is an interesting statement

I like to point out that hash tables are O(N) when people bring this up. Constant factors, average cases, and practical considerations matter a lot - it's not just nitpicking or semantics.

Awesome post! The diagrams are really great additions. I look forward to the rest of the series. :)

Branching factor 32 is great for lookups, but isn't it slower for modification? At least, one has to create more array cells in total (31 copies in each node), no?

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