Bitap: My favorite string matching algorithm
jo3-l.devI also have a favourite string matching algorithm, the "Generic SIMD" from this post [1] by Wojciech Muła (I haven't really read the other two SIMD algorithms since I wasn't planning on working with intrinsics).
There were some good comments that post's thread [2], including from burntsushi of ripgrep.
Always been interested in using SIMD to speed up searching. So far though i have not found a really nice one.
Need to figure out what area they excel in - there is no one search that is the best for all types of data and pattern/search length.
I like burntsushi's string-searching work because it's well documented, split modularly into libraries/applications, and runs the gamut from low- to high-level (his blog posts and comments online are extremely helpful too). I use these three tools which he maintains:
Low level: memchr [1];
Medium level: Regex (Rust crate) [2];
High level: ripgrep [3].
Other names to look out for are the previously aforementioned Wojciech Muła, as well as Daniel Lemire (of simdjson [4][5]). Not SIMD-specific, but Data-Oriented Design can be a big help in terms of thinking about SIMD and cache-friendly data layout (as well as trimming down the work that the computer needs to do, generally). I've talked that to death, so I'll just link those comments here [6].
1. https://docs.rs/memchr/latest/memchr/
2. https://docs.rs/regex/latest/regex/
3. https://github.com/burntsushi/ripgrep
4. https://www.youtube.com/watch?v=wlvKAT7SZIQ
5. https://arxiv.org/pdf/1902.08318
6. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
I've also implemented a SIMD accelerated, but case in-sensitive (*) search algorithm as an stb-style single header library, also based on Wojciech Muła's work.
https://gitlab.com/bztsrc/fast_memcasemem
See the performance comparison in the README, it's about 6 times faster than libc.
(*) - full UTF-8 support, but only works for UNICODE codepoints where the UTF-8 encoding lengths are the same for lowercase and uppercase. There are only 27 out of 40576 pairs which aren't handled (listed in the README).
> UNICODE codepoints where the UTF-8 encoding lengths are the same for lowercase and uppercase.
This very same property got me to post this [1], which sent me down the rabbithole of learning about Unicode in earnest and building my Unicode tool. Which may have an initial release some time this millennia... maybe.
Yeah, UNICODE messed this up, really badly.
Sometimes there's an offset (like with Latin, +/- 32), sometimes lowercase and uppercase is interleaved (eg. Latin extended), and sometimes they are in totally different blocks simply because they forgot to add both letter cases at once... (the distance of the codepoints affects UTF-8 encoding difference the most).
I've also paid attention to optimize the most common case where both UTF-8 encodings' first bytes are the same (that's 40508 pairs out of 40549). But no escape, it must handle the remaining 41 pairs specially in a slower code path, which would not be needed at all should UNICODE guys did their homework better.
One of my favourite ones in the post I linked is the "ff" ligature. It uppercases to "FF", meaning in UTF-8 it goes from one encoded character to two, and from 3 bytes total to 2 bytes total.
Lots to read about here for those interested (and that's without getting into `Casefold`, `NFKC_Casefold`, simple vs complex case mappings, the CLDR, etc.):
https://www.unicode.org/versions/Unicode17.0.0/core-spec/cha...
Ah, last weekend I was just updating my own string search algorithm to use Bitap (Shift-OR variant) instead of KMP, when the pattern length is < 64. It is faster. It is a very lovely algorithm indeed.
My search algorithm, HashChain [1] is a very fast sublinear algorithm, but is uses KMP (and now Bitap) to verify matches so it has a linear worst case (instead of quadratic, like Boyer Moore Horspool).
It is a really nice derivation of Bitap from first principles. I had not seen that before. Good job!
One small nit: he says the naive algorithm is linear - maybe it is for the average case, but it has a quadratic worst case complexity. Bitap is linear even for worst case.
Interesting algorithm.
I can see how this could be advantageous for moderate length patterns up to 64 bytes.
But for short registered sized patterns (4 or 8 bytes), I am somewhat skeptical of any significant advantage over a very tight, brute force register based loop comparing multi-byte chunks.
(OP here.) You're correct that for short patterns there's little advantage over the brute-force algorithm, and in fact the brute-force algorithm should actually be faster in many cases. Indeed the per-iteration comparison against the pattern in the brute-force algorithm is essentially a memcmp, which is vectorized and runs very fast on modern hardware. Consequently all mainstream programming languages that I know of just use the brute-force algorithm as a fallback when the pattern is short, as opposed to something more complicated like bitap.
I tried to be fairly careful to not overstate the performance benefits in the original post for this reason.
Ok, so why not use a fast memcmp on the first 4-8 chars of the pattern to identify any potential match and once found, work from there to verify if a full match exists?
This is essentially what I have have been doing for years and it is very simple. I'm sure it is not always the fastest but it's not too shabby either in the real world.
Probably very effective for shorter patterns. Two reasons to use more complex algorithms for longer patterns:
1. Linearity - the naive approach is quadratic on worst case data (imagine searching for 100 0's in a text of 0's).
2. Sublinearity - sublinear search algorithms skip over text that cannot match. They typically have the somewhat counter-intuitive property that they get much faster the longer the pattern is. So long patterns will be faster using a sub linear search algorithm.
Yes but longer patterns are kind of an outlier.
Most of the everyday searching and parsing that I end up doing involves relatively short patterns. Maybe I am an outlier :-)