Fast overlapping Boyer-Moore search of both strict and lazy ByteString values.

Descriptions of the algorithm can be found at http://www-igm.univ-mlv.fr/~lecroq/string/node14.html#SECTION00140 and http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm

Original authors: Daniel Fischer (daniel.is.fischer at googlemail.com) and Chris Kuklewicz (haskell at list.mightyreason.com).

This module exists only for backwards compatibility. Nevertheless there have been small changes in the behaviour of the functions. The module exports four search functions: matchLL, matchLS, matchSL, and matchSS. All of them return the list of all starting positions of possibly overlapping occurrences of a pattern in a string.

Formerly, all four functions returned an empty list when passed an empty pattern. Now, in accordance with the functions from the other modules, matchXY "" target = [0 .. length target].

This module is deprecated. You should use the new interface provided in Data.ByteString.Search resp. Data.ByteString.Lazy.Search.

The first parameter is always the pattern string. The second parameter is always the target string to be searched. The returned list contains the offsets of all overlapping patterns.

A returned Int or Int64 is an index into the target string which is aligned to the head of the pattern string. Strict targets return Int indices and lazy targets return Int64 indices. All returned lists are computed and returned in a lazy fashion.

matchLL and matchLS take lazy bytestrings as patterns. For performance, if the pattern is not a single strict chunk then all the the pattern chunks will copied into a concatenated strict bytestring. This limits the patterns to a length of (maxBound :: Int).

matchLL and matchSL take lazy bytestrings as targets. These are written so that while they work they will not retain a reference to all the earlier parts of the the lazy bytestring. This means the garbage collector would be able to keep only a small amount of the target string and free the rest.

In general, the Boyer-Moore algorithm is the most efficient method to search for a pattern inside a string. The advantage over other algorithms (e.g. Naïve, Knuth-Morris-Pratt, Horspool, Sunday) can be made arbitrarily large for specially selected patterns and targets, but usually, it's a factor of 2–3 versus Knuth-Morris-Pratt and of 6–10 versus the naïve algorithm. The Horspool and Sunday algorithms, which are simplified variants of the Boyer-Moore algorithm, typically have performance between Boyer-Moore and Knuth-Morris-Pratt, mostly closer to Boyer-Moore. The advantage of the Boyer-moore variants over other algorithms generally becomes larger for longer patterns. For very short patterns (or patterns with a very short period), other algorithms, e.g. Data.ByteString.Search.DFA can be faster (my tests suggest that "very short" means two, maybe three bytes).

In general, searching in a strict ByteString is slightly faster than searching in a lazy ByteString, but for long targets the smaller memory footprint of lazy ByteStrings can make searching those (sometimes much) faster. On the other hand, there are cases where searching in a strict target is much faster, even for long targets.

On 32-bit systems, Int-arithmetic is much faster than Int64-arithmetic, so when there are many matches, that can make a significant difference.

Also, the modification to ameliorate the case of periodic patterns is defeated by chunk-boundaries, so long patterns with a short period and many matches exhibit poor behaviour (consider using indices from Data.ByteString.Lazy.Search.DFA or Data.ByteString.Lazy.Search.KMP in those cases, the former for medium-length patterns, the latter for long patterns; only matchLL and matchSL suffer from this problem, though).

Preprocessing the pattern string is O(patternLength). The search performance is O(targetLength/patternLength) in the best case, allowing it to go faster than a Knuth-Morris-Pratt algorithm. With a non-periodic pattern the worst case uses O(3*targetLength) comparisons. The periodic pattern worst case is quadratic O(targetLength*patternLength) complexity for the original Boyer-Moore algorithm.

The searching functions in this module contain a modification which drastically improves the performance for periodic patterns. I believe that for strict target strings, the worst case is now O(targetLength) also for periodic patterns and for lazy target strings, my semi-educated guess is O(targetLength * (1 + patternLength / chunkSize)).

These functions can all be usefully partially applied. Given only a pattern the partially applied version will compute the supporting lookup tables only once, allowing for efficient re-use. Similarly, the partially applied matchLL and matchLS will compute the concatenated pattern only once.

The current code uses Int to keep track of the locations in the target string. If the length of the pattern plus the length of any strict chunk of the target string is greater or equal to maxBound::Int then this will overflow causing an error. We try to detect this and call error before a segfault occurs.