Understanding Clojure's Persistent Vectors, Part 1
hypirion.com
hypirion.com
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.
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.
It is an implementation of a data structure invented by Phil Bagwell: http://lampwww.epfl.ch/papers/idealhashtrees.pdf
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.
"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."
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.
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.
> 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! :)