Data.ByteString.Lazy.Search

Fast overlapping Boyer-Moore search of lazy ByteString values. Breaking, splitting and replacing using the Boyer-Moore algorithm.

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).

Overview

This module provides functions related to searching a substring within a string, using the Boyer-Moore algorithm with minor modifications to improve the overall performance and ameliorate the worst case performance degradation of the original Boyer-Moore algorithm for periodic patterns.

Efficiency demands that the pattern be a strict ByteString, to work with a lazy pattern, convert it to a strict ByteString first via strictify (provided it is not too long). If support for long lazy patterns is needed, mail a feature-request.

When searching a pattern in a UTF-8-encoded ByteString, be aware that these functions work on bytes, not characters, so the indices are byte-offsets, not character offsets.

Performance

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.Lazy.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; none of the functions except indices suffer from this problem, though).

Caution

When working with a lazy target string, the relation between the pattern length and the chunk size can play a big rôle. Crossing chunk boundaries is relatively expensive, so when that becomes a frequent occurrence, as may happen when the pattern length is close to or larger than the chunk size, performance is likely to degrade. If it is needed, steps can be taken to ameliorate that effect, but unless entirely separate functions are introduced, that would hurt the performance for the more common case of patterns much shorter than the default chunk size.

Complexity

Preprocessing the pattern is O(patternLength + σ) in time and space (σ is the alphabet size, 256 here) for all functions. The time complexity of the searching phase for indices is O(targetLength / patternLength) in the best case. For non-periodic patterns, the worst case complexity is O(targetLength), but for periodic patterns, the worst case complexity is O(targetLength * patternLength) for the original Boyer-Moore algorithm.

The searching functions in this module contain a modification which drastically improves the performance for periodic patterns, although less for lazy targets than for strict ones. If I'm not mistaken, the worst case complexity for periodic patterns is O(targetLength * (1 + patternLength / chunkSize)).

The other functions don't have to deal with possible overlapping patterns, hence the worst case complexity for the processing phase is O(targetLength) (respectively O(firstIndex + patternLength) for the breaking functions if the pattern occurs).

Partial application

All functions can usefully be partially applied. Given only a pattern, the pattern is preprocessed only once, allowing efficient re-use.

Integer overflow

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.

Finding substrings

indices

Arguments

:: ByteString

Strict pattern to find

-> ByteString

Lazy string to search

-> [Int64]

Offsets of matches

indices finds the starting indices of all possibly overlapping occurrences of the pattern in the target string. If the pattern is empty, the result is [0 .. length target].

nonOverlappingIndices

Arguments

:: ByteString

Strict pattern to find

-> ByteString

Lazy string to search

-> [Int64]

Offsets of matches

nonOverlappingIndices finds the starting indices of all non-overlapping occurrences of the pattern in the target string. It is more efficient than removing indices from the list produced by indices.

Breaking on substrings

breakOn

Arguments

:: ByteString

Strict pattern to search for

-> ByteString

Lazy string to search in

-> (ByteString, ByteString)

Head and tail of string broken at substring

breakOn pattern target splits target at the first occurrence of pattern. If the pattern does not occur in the target, the second component of the result is empty, otherwise it starts with pattern. If the pattern is empty, the first component is empty. For a non-empty pattern, the first component is generated lazily, thus the first parts of it can be available before the pattern has been found or determined to be absent.

  uncurry append . breakOn pattern = id

breakAfter

Arguments

:: ByteString

Strict pattern to search for

-> ByteString

Lazy string to search in

-> (ByteString, ByteString)

Head and tail of string broken after substring

breakAfter pattern target splits target behind the first occurrence of pattern. An empty second component means that either the pattern does not occur in the target or the first occurrence of pattern is at the very end of target. If you need to discriminate between those cases, use breakFindAfter. If the pattern is empty, the first component is empty. For a non-empty pattern, the first component is generated lazily, thus the first parts of it can be available before the pattern has been found or determined to be absent.

  uncurry append . breakAfter pattern = id

breakFindAfter

Arguments

:: ByteString

Strict pattern to search for

-> ByteString

Lazy string to search in

-> ((ByteString, ByteString), Bool)

Head and tail of string broken after substring and presence of pattern

breakFindAfter does the same as breakAfter but additionally indicates whether the pattern is present in the target.

  fst . breakFindAfter pat = breakAfter pat

Replacing

replace

Arguments

:: Substitution rep

=> ByteString

Strict pattern to replace

-> rep

Replacement string

-> ByteString

Lazy string to modify

-> ByteString

Lazy result

replace pat sub text replaces all (non-overlapping) occurrences of pat in text with sub. If occurrences of pat overlap, the first occurrence that does not overlap with a replaced previous occurrence is substituted. Occurrences of pat arising from a substitution will not be substituted. For example:

  replace "ana" "olog" "banana" = "bologna"
  replace "ana" "o" "bananana" = "bono"
  replace "aab" "abaa" "aaabb" = "aabaab"

The result is a lazy ByteString, which is lazily produced, without copying. Equality of pattern and substitution is not checked, but

  replace pat pat text == text

holds (the internal structure is generally different). If the pattern is empty but not the substitution, the result is equivalent to (were they Strings) cycle sub.

For non-empty pat and sub a lazy ByteString,

  concat . intersperse sub . split pat = replace pat sub

and analogous relations hold for other types of sub.

Splitting

split

Arguments

:: ByteString

Strict pattern to split on

-> ByteString

Lazy string to split

-> [ByteString]

Fragments of string

split pattern target splits target at each (non-overlapping) occurrence of pattern, removing pattern. If pattern is empty, the result is an infinite list of empty ByteStrings, if target is empty but not pattern, the result is an empty list, otherwise the following relations hold (where patL is the lazy ByteString corresponding to pat):

  concat . intersperse patL . split pat = id,
  length (split pattern target) ==
              length (nonOverlappingIndices pattern target) + 1,

no fragment in the result contains an occurrence of pattern.

splitKeepEnd

Arguments

:: ByteString

Strict pattern to split on

-> ByteString

Lazy string to split

-> [ByteString]

Fragments of string

splitKeepEnd pattern target splits target after each (non-overlapping) occurrence of pattern. If pattern is empty, the result is an infinite list of empty ByteStrings, otherwise the following relations hold:

  concat . splitKeepEnd pattern = id,

all fragments in the result except possibly the last end with pattern, no fragment contains more than one occurrence of pattern.

splitKeepFront

Arguments

:: ByteString

Strict pattern to split on

-> ByteString

Lazy string to split

-> [ByteString]

Fragments of string

splitKeepFront is like splitKeepEnd, except that target is split before each occurrence of pattern and hence all fragments with the possible exception of the first begin with pattern. No fragment contains more than one non-overlapping occurrence of pattern.

Convenience

strictify :: ByteString -> ByteString

strictify converts a lazy ByteString to a strict ByteString to make it a suitable pattern.