Simple and fast drop-in replacements for the stdlib's strstr() and memmem() sub-sequence search functions.
byteshift_strstr() can be significantly faster than most sub-string search
algorithms in various cases. Scenarios where it is expected to be significantly
faster than the alternatives when searching for relatively small sub-strings
(such as words) or when searching through text with a very small alphabet
(such as DNA sequences).
The high performance is achieved by doing very little processing for the majority of characters, by using a minimal amount of working memory and by keeping pre-processing to a minimum.
If performance is important, run some benchmarks with your actual data! This should be relatively easy since these functions have the same interface as their common counterparts.
The worst case complexity of the algorithm used by these functions is
O(n × m), where n is the length of the string and m the length of the
sub-string. This is the same as the naive brute-force algorithm.
However, in most realistic scenarios it will run with linear complexity
(O(n)). O(n) is also the best-case complexity of the algorithm, since it
processes every character of the string being searched.
The core algorithm is simple. At each index of the searched string, the first
k characters are compared with the first k characters of the sub-string
being searched for (the "needle"). If these match, the next len(needle) - k
characters are compared with the rest of the needle.
The previously mentioned k is the number of characters which fit inside a
single unsigned long ("ulong"). On 64-bit machines this is usually 8,
while on 32-bit machines it is usually either 4 or 8. This was chosen because
comparing two ulong-s is a very fast operation, and "packing" characters into
ulong-s can also be done very quickly.
The first k characters of the needle need to be "packed" into a ulong only
once. This, along with finding the needle's length, are the only pre-processing
steps required.
During the search, the "packed" ulong containing the first k characters at
an index can be quickly updated to contain the first k characters at the next
index. This is done by shifting the unsigned long 8 bits to the "left" and
then XOR-ing or OR-ing the k-th character after the next index.
If the first k characters match, the rest are compared via strcmp() or
memcmp() (as appropriate).
This implemenation also employs a number of additional optimizations:
- Single-character needles are special-cased, and the search just uses
strchr()/memchr(). strchr()/memchr()is called to find the first occurence for the first character of the needle in the searched string.- Needles of length <=
kare also special cased: nomemcmp()is required. - The initial
ulong-s for the needle and searched string are built very efficiently using some "bit magic": the memory of the firstkbytes is interpreted as aulong, and then converted to big-endian format if necessary (i.e. if the machine uses little-endian). This is equavalent to starting with zero and then shifting it and xoring the next characterktimes.
The algorithm has been benchmarked together with four other algorithms by searching all occurrences of 100 random Latin words in portions of Commentarii de Bello Gallico by Julius Caesar. Each test was run 100 times and the mean time was taken. The tests were run on a late 2012 MacBook Pro 13" Retina, which has an Intel Core i5-3210M processor.
strstris from the GNU C Library (version 2.19) and uses the Two Ways Algorithmnaive strstris a naive brute-force implementationVolnitsky's strstris an algorithm by Leonid Volnitskyfast_strstris [a similar lightweight implementation by Raphael Javaux] (https://github.com/RaphaelJ/fast_strstr).byteshift_strstris this implementation.
Scores were compared to strstr.
Sections of 10, 100, 500, 1000, 5000, 10000, 50000 characters of Bello Gallico along with the full text (147277 characters) have been used.
| Algorithm \ Size | 10 | 100 | 500 | 1000 |
|---|---|---|---|---|
| strstr | 2.9 us ( 1x) | 12.2 us ( 1x) | 59.0 us ( 1x) | 127 us ( 1x) |
| naive strstr | 6.0 us ( 2.0x) | 46.4 us ( 3.8x) | 229 us (3.9x) | 459 us (3.6x) |
| Volnitsky's strstr | 187 us (63.9x) | 198 us (16.3x) | 242 us (4.1x) | 312 us (2.5x) |
| fast_strstr | 3.0 us ( 1.0x) | 12.2 us ( 1.0x) | 61.0 us (1.0x) | 113 us (0.9x) |
| byteshift_strstr | 3.0 us ( 1.0x) | 11.8 us (1.0x) | 52.1 us (0.9x) | 104 us (0.8x) |
| Algorithm \ Size | 5000 | 10000 | 50000 | 147277 |
|---|---|---|---|---|
| strstr | 668 us ( 1x) | 1.3 ms ( 1x) | 6.7 ms ( 1x) | 19.8 ms ( 1x) |
| naive strstr | 2.3 ms (3.4x) | 4.6 ms (3.4x) | 23.1 ms (3.4x) | 67.7 ms (3.4x) |
| Volnitsky's strstr | 811 us (1.2x) | 1.6 ms (1.2x) | 12.6 ms (1.9x) | 72.6 ms (3.7x) |
| fast_strstr | 559 us (0.8x) | 1.1 ms (0.8x) | 5.5 ms (0.8x) | 16.3 ms (0.8x) |
| byteshift_strstr | 509 us (0.8x) | 1.0 ms (0.8x) | 5.1 ms (0.8x) | 15.0 ms (0.8x) |
byteshift_strstr is faster than all of the alternatives, including the native
strstr, for all but the shortest of search strings.
Note the good performance with short search strings. This is since the algorithm doesn't require complex pre-processing the sub-string.
Benchmark scripts are available here. These have been written in Haskell and require the Criterion benchmarking library to run.
If you want to run the benchmarks on your hardware, download and install the
Glasgow Haskell Compiler and its library manager Cabal. Then go in the
benchmark/ directory and ask cabal to install the required
libraries :
cabal install --only-dependencies
Then compile the benchmark executable using cabal build. The resulting
executable should be located at benchmark/dist/build/benchmark/benchmark.
This algorithm is licensed under the open-source MIT license:
The MIT License (MIT)
Copyright (c) 2014-2015 Tal Einat
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
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