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pattern.rs
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pattern.rs
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// Copyright 2015 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! The string Pattern API.
//!
//! For more details, see the traits `Pattern`, `Searcher`,
//! `ReverseSearcher` and `DoubleEndedSearcher`.
#![unstable(feature = "pattern",
reason = "API not fully fleshed out and ready to be stabilized")]
use prelude::*;
use core::cmp;
use usize;
// Pattern
/// A string pattern.
///
/// A `Pattern<'a>` expresses that the implementing type
/// can be used as a string pattern for searching in a `&'a str`.
///
/// For example, both `'a'` and `"aa"` are patterns that
/// would match at index `1` in the string `"baaaab"`.
///
/// The trait itself acts as a builder for an associated
/// `Searcher` type, which does the actual work of finding
/// occurrences of the pattern in a string.
pub trait Pattern<'a>: Sized {
/// Associated searcher for this pattern
type Searcher: Searcher<'a>;
/// Constructs the associated searcher from
/// `self` and the `haystack` to search in.
fn into_searcher(self, haystack: &'a str) -> Self::Searcher;
/// Checks whether the pattern matches anywhere in the haystack
#[inline]
fn is_contained_in(self, haystack: &'a str) -> bool {
self.into_searcher(haystack).next_match().is_some()
}
/// Checks whether the pattern matches at the front of the haystack
#[inline]
fn is_prefix_of(self, haystack: &'a str) -> bool {
match self.into_searcher(haystack).next() {
SearchStep::Match(0, _) => true,
_ => false,
}
}
/// Checks whether the pattern matches at the back of the haystack
#[inline]
fn is_suffix_of(self, haystack: &'a str) -> bool
where Self::Searcher: ReverseSearcher<'a>
{
match self.into_searcher(haystack).next_back() {
SearchStep::Match(_, j) if haystack.len() == j => true,
_ => false,
}
}
}
// Searcher
/// Result of calling `Searcher::next()` or `ReverseSearcher::next_back()`.
#[derive(Copy, Clone, Eq, PartialEq, Debug)]
pub enum SearchStep {
/// Expresses that a match of the pattern has been found at
/// `haystack[a..b]`.
Match(usize, usize),
/// Expresses that `haystack[a..b]` has been rejected as a possible match
/// of the pattern.
///
/// Note that there might be more than one `Reject` between two `Match`es,
/// there is no requirement for them to be combined into one.
Reject(usize, usize),
/// Expresses that every byte of the haystack has been visted, ending
/// the iteration.
Done
}
/// A searcher for a string pattern.
///
/// This trait provides methods for searching for non-overlapping
/// matches of a pattern starting from the front (left) of a string.
///
/// It will be implemented by associated `Searcher`
/// types of the `Pattern` trait.
///
/// The trait is marked unsafe because the indices returned by the
/// `next()` methods are required to lie on valid utf8 boundaries in
/// the haystack. This enables consumers of this trait to
/// slice the haystack without additional runtime checks.
pub unsafe trait Searcher<'a> {
/// Getter for the underlaying string to be searched in
///
/// Will always return the same `&str`
fn haystack(&self) -> &'a str;
/// Performs the next search step starting from the front.
///
/// - Returns `Match(a, b)` if `haystack[a..b]` matches the pattern.
/// - Returns `Reject(a, b)` if `haystack[a..b]` can not match the
/// pattern, even partially.
/// - Returns `Done` if every byte of the haystack has been visited
///
/// The stream of `Match` and `Reject` values up to a `Done`
/// will contain index ranges that are adjacent, non-overlapping,
/// covering the whole haystack, and laying on utf8 boundaries.
///
/// A `Match` result needs to contain the whole matched pattern,
/// however `Reject` results may be split up into arbitrary
/// many adjacent fragments. Both ranges may have zero length.
///
/// As an example, the pattern `"aaa"` and the haystack `"cbaaaaab"`
/// might produce the stream
/// `[Reject(0, 1), Reject(1, 2), Match(2, 5), Reject(5, 8)]`
fn next(&mut self) -> SearchStep;
/// Find the next `Match` result. See `next()`
#[inline]
fn next_match(&mut self) -> Option<(usize, usize)> {
loop {
match self.next() {
SearchStep::Match(a, b) => return Some((a, b)),
SearchStep::Done => return None,
_ => continue,
}
}
}
/// Find the next `Reject` result. See `next()`
#[inline]
fn next_reject(&mut self) -> Option<(usize, usize)> {
loop {
match self.next() {
SearchStep::Reject(a, b) => return Some((a, b)),
SearchStep::Done => return None,
_ => continue,
}
}
}
}
/// A reverse searcher for a string pattern.
///
/// This trait provides methods for searching for non-overlapping
/// matches of a pattern starting from the back (right) of a string.
///
/// It will be implemented by associated `Searcher`
/// types of the `Pattern` trait if the pattern supports searching
/// for it from the back.
///
/// The index ranges returned by this trait are not required
/// to exactly match those of the forward search in reverse.
///
/// For the reason why this trait is marked unsafe, see them
/// parent trait `Searcher`.
pub unsafe trait ReverseSearcher<'a>: Searcher<'a> {
/// Performs the next search step starting from the back.
///
/// - Returns `Match(a, b)` if `haystack[a..b]` matches the pattern.
/// - Returns `Reject(a, b)` if `haystack[a..b]` can not match the
/// pattern, even partially.
/// - Returns `Done` if every byte of the haystack has been visited
///
/// The stream of `Match` and `Reject` values up to a `Done`
/// will contain index ranges that are adjacent, non-overlapping,
/// covering the whole haystack, and laying on utf8 boundaries.
///
/// A `Match` result needs to contain the whole matched pattern,
/// however `Reject` results may be split up into arbitrary
/// many adjacent fragments. Both ranges may have zero length.
///
/// As an example, the pattern `"aaa"` and the haystack `"cbaaaaab"`
/// might produce the stream
/// `[Reject(7, 8), Match(4, 7), Reject(1, 4), Reject(0, 1)]`
fn next_back(&mut self) -> SearchStep;
/// Find the next `Match` result. See `next_back()`
#[inline]
fn next_match_back(&mut self) -> Option<(usize, usize)>{
loop {
match self.next_back() {
SearchStep::Match(a, b) => return Some((a, b)),
SearchStep::Done => return None,
_ => continue,
}
}
}
/// Find the next `Reject` result. See `next_back()`
#[inline]
fn next_reject_back(&mut self) -> Option<(usize, usize)>{
loop {
match self.next_back() {
SearchStep::Reject(a, b) => return Some((a, b)),
SearchStep::Done => return None,
_ => continue,
}
}
}
}
/// A marker trait to express that a `ReverseSearcher`
/// can be used for a `DoubleEndedIterator` implementation.
///
/// For this, the impl of `Searcher` and `ReverseSearcher` need
/// to follow these conditions:
///
/// - All results of `next()` need to be identical
/// to the results of `next_back()` in reverse order.
/// - `next()` and `next_back()` need to behave as
/// the two ends of a range of values, that is they
/// can not "walk past each other".
///
/// # Examples
///
/// `char::Searcher` is a `DoubleEndedSearcher` because searching for a
/// `char` only requires looking at one at a time, which behaves the same
/// from both ends.
///
/// `(&str)::Searcher` is not a `DoubleEndedSearcher` because
/// the pattern `"aa"` in the haystack `"aaa"` matches as either
/// `"[aa]a"` or `"a[aa]"`, depending from which side it is searched.
pub trait DoubleEndedSearcher<'a>: ReverseSearcher<'a> {}
/////////////////////////////////////////////////////////////////////////////
// Impl for a CharEq wrapper
/////////////////////////////////////////////////////////////////////////////
#[doc(hidden)]
trait CharEq {
fn matches(&mut self, char) -> bool;
fn only_ascii(&self) -> bool;
}
impl CharEq for char {
#[inline]
fn matches(&mut self, c: char) -> bool { *self == c }
#[inline]
fn only_ascii(&self) -> bool { (*self as u32) < 128 }
}
impl<F> CharEq for F where F: FnMut(char) -> bool {
#[inline]
fn matches(&mut self, c: char) -> bool { (*self)(c) }
#[inline]
fn only_ascii(&self) -> bool { false }
}
impl<'a> CharEq for &'a [char] {
#[inline]
fn matches(&mut self, c: char) -> bool {
self.iter().any(|&m| { let mut m = m; m.matches(c) })
}
#[inline]
fn only_ascii(&self) -> bool {
self.iter().all(|m| m.only_ascii())
}
}
struct CharEqPattern<C: CharEq>(C);
#[derive(Clone)]
struct CharEqSearcher<'a, C: CharEq> {
char_eq: C,
haystack: &'a str,
char_indices: super::CharIndices<'a>,
#[allow(dead_code)]
ascii_only: bool,
}
impl<'a, C: CharEq> Pattern<'a> for CharEqPattern<C> {
type Searcher = CharEqSearcher<'a, C>;
#[inline]
fn into_searcher(self, haystack: &'a str) -> CharEqSearcher<'a, C> {
CharEqSearcher {
ascii_only: self.0.only_ascii(),
haystack: haystack,
char_eq: self.0,
char_indices: haystack.char_indices(),
}
}
}
unsafe impl<'a, C: CharEq> Searcher<'a> for CharEqSearcher<'a, C> {
#[inline]
fn haystack(&self) -> &'a str {
self.haystack
}
#[inline]
fn next(&mut self) -> SearchStep {
let s = &mut self.char_indices;
// Compare lengths of the internal byte slice iterator
// to find length of current char
let (pre_len, _) = s.iter.iter.size_hint();
if let Some((i, c)) = s.next() {
let (len, _) = s.iter.iter.size_hint();
let char_len = pre_len - len;
if self.char_eq.matches(c) {
return SearchStep::Match(i, i + char_len);
} else {
return SearchStep::Reject(i, i + char_len);
}
}
SearchStep::Done
}
}
unsafe impl<'a, C: CharEq> ReverseSearcher<'a> for CharEqSearcher<'a, C> {
#[inline]
fn next_back(&mut self) -> SearchStep {
let s = &mut self.char_indices;
// Compare lengths of the internal byte slice iterator
// to find length of current char
let (pre_len, _) = s.iter.iter.size_hint();
if let Some((i, c)) = s.next_back() {
let (len, _) = s.iter.iter.size_hint();
let char_len = pre_len - len;
if self.char_eq.matches(c) {
return SearchStep::Match(i, i + char_len);
} else {
return SearchStep::Reject(i, i + char_len);
}
}
SearchStep::Done
}
}
impl<'a, C: CharEq> DoubleEndedSearcher<'a> for CharEqSearcher<'a, C> {}
/////////////////////////////////////////////////////////////////////////////
macro_rules! pattern_methods {
($t:ty, $pmap:expr, $smap:expr) => {
type Searcher = $t;
#[inline]
fn into_searcher(self, haystack: &'a str) -> $t {
($smap)(($pmap)(self).into_searcher(haystack))
}
#[inline]
fn is_contained_in(self, haystack: &'a str) -> bool {
($pmap)(self).is_contained_in(haystack)
}
#[inline]
fn is_prefix_of(self, haystack: &'a str) -> bool {
($pmap)(self).is_prefix_of(haystack)
}
#[inline]
fn is_suffix_of(self, haystack: &'a str) -> bool
where $t: ReverseSearcher<'a>
{
($pmap)(self).is_suffix_of(haystack)
}
}
}
macro_rules! searcher_methods {
(forward) => {
#[inline]
fn haystack(&self) -> &'a str {
self.0.haystack()
}
#[inline]
fn next(&mut self) -> SearchStep {
self.0.next()
}
#[inline]
fn next_match(&mut self) -> Option<(usize, usize)> {
self.0.next_match()
}
#[inline]
fn next_reject(&mut self) -> Option<(usize, usize)> {
self.0.next_reject()
}
};
(reverse) => {
#[inline]
fn next_back(&mut self) -> SearchStep {
self.0.next_back()
}
#[inline]
fn next_match_back(&mut self) -> Option<(usize, usize)> {
self.0.next_match_back()
}
#[inline]
fn next_reject_back(&mut self) -> Option<(usize, usize)> {
self.0.next_reject_back()
}
}
}
/////////////////////////////////////////////////////////////////////////////
// Impl for char
/////////////////////////////////////////////////////////////////////////////
/// Associated type for `<char as Pattern<'a>>::Searcher`.
#[derive(Clone)]
pub struct CharSearcher<'a>(<CharEqPattern<char> as Pattern<'a>>::Searcher);
unsafe impl<'a> Searcher<'a> for CharSearcher<'a> {
searcher_methods!(forward);
}
unsafe impl<'a> ReverseSearcher<'a> for CharSearcher<'a> {
searcher_methods!(reverse);
}
impl<'a> DoubleEndedSearcher<'a> for CharSearcher<'a> {}
/// Searches for chars that are equal to a given char
impl<'a> Pattern<'a> for char {
pattern_methods!(CharSearcher<'a>, CharEqPattern, CharSearcher);
}
/////////////////////////////////////////////////////////////////////////////
// Impl for &[char]
/////////////////////////////////////////////////////////////////////////////
// Todo: Change / Remove due to ambiguity in meaning.
/// Associated type for `<&[char] as Pattern<'a>>::Searcher`.
#[derive(Clone)]
pub struct CharSliceSearcher<'a, 'b>(<CharEqPattern<&'b [char]> as Pattern<'a>>::Searcher);
unsafe impl<'a, 'b> Searcher<'a> for CharSliceSearcher<'a, 'b> {
searcher_methods!(forward);
}
unsafe impl<'a, 'b> ReverseSearcher<'a> for CharSliceSearcher<'a, 'b> {
searcher_methods!(reverse);
}
impl<'a, 'b> DoubleEndedSearcher<'a> for CharSliceSearcher<'a, 'b> {}
/// Searches for chars that are equal to any of the chars in the array
impl<'a, 'b> Pattern<'a> for &'b [char] {
pattern_methods!(CharSliceSearcher<'a, 'b>, CharEqPattern, CharSliceSearcher);
}
/////////////////////////////////////////////////////////////////////////////
// Impl for F: FnMut(char) -> bool
/////////////////////////////////////////////////////////////////////////////
/// Associated type for `<F as Pattern<'a>>::Searcher`.
#[derive(Clone)]
pub struct CharPredicateSearcher<'a, F>(<CharEqPattern<F> as Pattern<'a>>::Searcher)
where F: FnMut(char) -> bool;
unsafe impl<'a, F> Searcher<'a> for CharPredicateSearcher<'a, F>
where F: FnMut(char) -> bool
{
searcher_methods!(forward);
}
unsafe impl<'a, F> ReverseSearcher<'a> for CharPredicateSearcher<'a, F>
where F: FnMut(char) -> bool
{
searcher_methods!(reverse);
}
impl<'a, F> DoubleEndedSearcher<'a> for CharPredicateSearcher<'a, F>
where F: FnMut(char) -> bool {}
/// Searches for chars that match the given predicate
impl<'a, F> Pattern<'a> for F where F: FnMut(char) -> bool {
pattern_methods!(CharPredicateSearcher<'a, F>, CharEqPattern, CharPredicateSearcher);
}
/////////////////////////////////////////////////////////////////////////////
// Impl for &&str
/////////////////////////////////////////////////////////////////////////////
/// Delegates to the `&str` impl.
impl<'a, 'b> Pattern<'a> for &'b &'b str {
pattern_methods!(StrSearcher<'a, 'b>, |&s| s, |s| s);
}
/////////////////////////////////////////////////////////////////////////////
// Impl for &str
/////////////////////////////////////////////////////////////////////////////
/// Non-allocating substring search.
///
/// Will handle the pattern `""` as returning empty matches at each character
/// boundary.
impl<'a, 'b> Pattern<'a> for &'b str {
type Searcher = StrSearcher<'a, 'b>;
#[inline]
fn into_searcher(self, haystack: &'a str) -> StrSearcher<'a, 'b> {
StrSearcher::new(haystack, self)
}
/// Checks whether the pattern matches at the front of the haystack
#[inline]
fn is_prefix_of(self, haystack: &'a str) -> bool {
// Use `as_bytes` so that we can slice through a character in the haystack.
// Since self is always valid UTF-8, this can't result in a false positive.
self.len() <= haystack.len() &&
self.as_bytes() == &haystack.as_bytes()[..self.len()]
}
/// Checks whether the pattern matches at the back of the haystack
#[inline]
fn is_suffix_of(self, haystack: &'a str) -> bool {
self.len() <= haystack.len() &&
self.as_bytes() == &haystack.as_bytes()[haystack.len() - self.len()..]
}
}
/////////////////////////////////////////////////////////////////////////////
// Two Way substring searcher
/////////////////////////////////////////////////////////////////////////////
#[derive(Clone, Debug)]
/// Associated type for `<&str as Pattern<'a>>::Searcher`.
pub struct StrSearcher<'a, 'b> {
haystack: &'a str,
needle: &'b str,
searcher: StrSearcherImpl,
}
#[derive(Clone, Debug)]
enum StrSearcherImpl {
Empty(EmptyNeedle),
TwoWay(TwoWaySearcher),
}
#[derive(Clone, Debug)]
struct EmptyNeedle {
position: usize,
end: usize,
is_match_fw: bool,
is_match_bw: bool,
}
impl<'a, 'b> StrSearcher<'a, 'b> {
fn new(haystack: &'a str, needle: &'b str) -> StrSearcher<'a, 'b> {
if needle.is_empty() {
StrSearcher {
haystack: haystack,
needle: needle,
searcher: StrSearcherImpl::Empty(EmptyNeedle {
position: 0,
end: haystack.len(),
is_match_fw: true,
is_match_bw: true,
}),
}
} else {
StrSearcher {
haystack: haystack,
needle: needle,
searcher: StrSearcherImpl::TwoWay(
TwoWaySearcher::new(needle.as_bytes(), haystack.len())
),
}
}
}
}
unsafe impl<'a, 'b> Searcher<'a> for StrSearcher<'a, 'b> {
fn haystack(&self) -> &'a str { self.haystack }
#[inline]
fn next(&mut self) -> SearchStep {
match self.searcher {
StrSearcherImpl::Empty(ref mut searcher) => {
// empty needle rejects every char and matches every empty string between them
let is_match = searcher.is_match_fw;
searcher.is_match_fw = !searcher.is_match_fw;
let pos = searcher.position;
match self.haystack[pos..].chars().next() {
_ if is_match => SearchStep::Match(pos, pos),
None => SearchStep::Done,
Some(ch) => {
searcher.position += ch.len_utf8();
SearchStep::Reject(pos, searcher.position)
}
}
}
StrSearcherImpl::TwoWay(ref mut searcher) => {
// TwoWaySearcher produces valid *Match* indices that split at char boundaries
// as long as it does correct matching and that haystack and needle are
// valid UTF-8
// *Rejects* from the algorithm can fall on any indices, but we will walk them
// manually to the next character boundary, so that they are utf-8 safe.
if searcher.position == self.haystack.len() {
return SearchStep::Done;
}
let is_long = searcher.memory == usize::MAX;
match searcher.next::<RejectAndMatch>(self.haystack.as_bytes(),
self.needle.as_bytes(),
is_long)
{
SearchStep::Reject(a, mut b) => {
// skip to next char boundary
while !self.haystack.is_char_boundary(b) {
b += 1;
}
searcher.position = cmp::max(b, searcher.position);
SearchStep::Reject(a, b)
}
otherwise => otherwise,
}
}
}
}
#[inline(always)]
fn next_match(&mut self) -> Option<(usize, usize)> {
match self.searcher {
StrSearcherImpl::Empty(..) => {
loop {
match self.next() {
SearchStep::Match(a, b) => return Some((a, b)),
SearchStep::Done => return None,
SearchStep::Reject(..) => { }
}
}
}
StrSearcherImpl::TwoWay(ref mut searcher) => {
let is_long = searcher.memory == usize::MAX;
if is_long {
searcher.next::<MatchOnly>(self.haystack.as_bytes(),
self.needle.as_bytes(),
true)
} else {
searcher.next::<MatchOnly>(self.haystack.as_bytes(),
self.needle.as_bytes(),
false)
}
}
}
}
}
unsafe impl<'a, 'b> ReverseSearcher<'a> for StrSearcher<'a, 'b> {
#[inline]
fn next_back(&mut self) -> SearchStep {
match self.searcher {
StrSearcherImpl::Empty(ref mut searcher) => {
let is_match = searcher.is_match_bw;
searcher.is_match_bw = !searcher.is_match_bw;
let end = searcher.end;
match self.haystack[..end].chars().next_back() {
_ if is_match => SearchStep::Match(end, end),
None => SearchStep::Done,
Some(ch) => {
searcher.end -= ch.len_utf8();
SearchStep::Reject(searcher.end, end)
}
}
}
StrSearcherImpl::TwoWay(ref mut searcher) => {
if searcher.end == 0 {
return SearchStep::Done;
}
match searcher.next_back::<RejectAndMatch>(self.haystack.as_bytes(),
self.needle.as_bytes())
{
SearchStep::Reject(mut a, b) => {
// skip to next char boundary
while !self.haystack.is_char_boundary(a) {
a -= 1;
}
searcher.end = cmp::min(a, searcher.end);
SearchStep::Reject(a, b)
}
otherwise => otherwise,
}
}
}
}
#[inline]
fn next_match_back(&mut self) -> Option<(usize, usize)> {
match self.searcher {
StrSearcherImpl::Empty(..) => {
loop {
match self.next_back() {
SearchStep::Match(a, b) => return Some((a, b)),
SearchStep::Done => return None,
SearchStep::Reject(..) => { }
}
}
}
StrSearcherImpl::TwoWay(ref mut searcher) => {
searcher.next_back::<MatchOnly>(self.haystack.as_bytes(),
self.needle.as_bytes())
}
}
}
}
/// The internal state of an iterator that searches for matches of a substring
/// within a larger string using two-way search
#[derive(Clone, Debug)]
struct TwoWaySearcher {
// constants
crit_pos: usize,
period: usize,
byteset: u64,
// variables
position: usize,
end: usize,
memory: usize
}
/*
This is the Two-Way search algorithm, which was introduced in the paper:
Crochemore, M., Perrin, D., 1991, Two-way string-matching, Journal of the ACM 38(3):651-675.
Here's some background information.
A *word* is a string of symbols. The *length* of a word should be a familiar
notion, and here we denote it for any word x by |x|.
(We also allow for the possibility of the *empty word*, a word of length zero).
If x is any non-empty word, then an integer p with 0 < p <= |x| is said to be a
*period* for x iff for all i with 0 <= i <= |x| - p - 1, we have x[i] == x[i+p].
For example, both 1 and 2 are periods for the string "aa". As another example,
the only period of the string "abcd" is 4.
We denote by period(x) the *smallest* period of x (provided that x is non-empty).
This is always well-defined since every non-empty word x has at least one period,
|x|. We sometimes call this *the period* of x.
If u, v and x are words such that x = uv, where uv is the concatenation of u and
v, then we say that (u, v) is a *factorization* of x.
Let (u, v) be a factorization for a word x. Then if w is a non-empty word such
that both of the following hold
- either w is a suffix of u or u is a suffix of w
- either w is a prefix of v or v is a prefix of w
then w is said to be a *repetition* for the factorization (u, v).
Just to unpack this, there are four possibilities here. Let w = "abc". Then we
might have:
- w is a suffix of u and w is a prefix of v. ex: ("lolabc", "abcde")
- w is a suffix of u and v is a prefix of w. ex: ("lolabc", "ab")
- u is a suffix of w and w is a prefix of v. ex: ("bc", "abchi")
- u is a suffix of w and v is a prefix of w. ex: ("bc", "a")
Note that the word vu is a repetition for any factorization (u,v) of x = uv,
so every factorization has at least one repetition.
If x is a string and (u, v) is a factorization for x, then a *local period* for
(u, v) is an integer r such that there is some word w such that |w| = r and w is
a repetition for (u, v).
We denote by local_period(u, v) the smallest local period of (u, v). We sometimes
call this *the local period* of (u, v). Provided that x = uv is non-empty, this
is well-defined (because each non-empty word has at least one factorization, as
noted above).
It can be proven that the following is an equivalent definition of a local period
for a factorization (u, v): any positive integer r such that x[i] == x[i+r] for
all i such that |u| - r <= i <= |u| - 1 and such that both x[i] and x[i+r] are
defined. (i.e. i > 0 and i + r < |x|).
Using the above reformulation, it is easy to prove that
1 <= local_period(u, v) <= period(uv)
A factorization (u, v) of x such that local_period(u,v) = period(x) is called a
*critical factorization*.
The algorithm hinges on the following theorem, which is stated without proof:
**Critical Factorization Theorem** Any word x has at least one critical
factorization (u, v) such that |u| < period(x).
The purpose of maximal_suffix is to find such a critical factorization.
*/
impl TwoWaySearcher {
fn new(needle: &[u8], end: usize) -> TwoWaySearcher {
let (crit_pos_false, period_false) = TwoWaySearcher::maximal_suffix(needle, false);
let (crit_pos_true, period_true) = TwoWaySearcher::maximal_suffix(needle, true);
let (crit_pos, period) =
if crit_pos_false > crit_pos_true {
(crit_pos_false, period_false)
} else {
(crit_pos_true, period_true)
};
// This isn't in the original algorithm, as far as I'm aware.
let byteset = needle.iter()
.fold(0, |a, &b| (1 << ((b & 0x3f) as usize)) | a);
// A particularly readable explanation of what's going on here can be found
// in Crochemore and Rytter's book "Text Algorithms", ch 13. Specifically
// see the code for "Algorithm CP" on p. 323.
//
// What's going on is we have some critical factorization (u, v) of the
// needle, and we want to determine whether u is a suffix of
// &v[..period]. If it is, we use "Algorithm CP1". Otherwise we use
// "Algorithm CP2", which is optimized for when the period of the needle
// is large.
if &needle[..crit_pos] == &needle[period.. period + crit_pos] {
// short period case
TwoWaySearcher {
crit_pos: crit_pos,
period: period,
byteset: byteset,
position: 0,
end: end,
memory: 0
}
} else {
// long period case
// we have an approximation to the actual period, and don't use memory.
TwoWaySearcher {
crit_pos: crit_pos,
period: cmp::max(crit_pos, needle.len() - crit_pos) + 1,
byteset: byteset,
position: 0,
end: end,
memory: usize::MAX // Dummy value to signify that the period is long
}
}
}
#[inline(always)]
fn byteset_contains(&self, byte: u8) -> bool {
(self.byteset >> ((byte & 0x3f) as usize)) & 1 != 0
}
// One of the main ideas of Two-Way is that we factorize the needle into
// two halves, (u, v), and begin trying to find v in the haystack by scanning
// left to right. If v matches, we try to match u by scanning right to left.
// How far we can jump when we encounter a mismatch is all based on the fact
// that (u, v) is a critical factorization for the needle.
#[inline(always)]
fn next<S>(&mut self, haystack: &[u8], needle: &[u8], long_period: bool)
-> S::Output
where S: TwoWayStrategy
{
// `next()` uses `self.position` as its cursor
let old_pos = self.position;
'search: loop {
// Check that we have room to search in
if needle.len() > haystack.len() - self.position {
self.position = haystack.len();
return S::rejecting(old_pos, self.position);
}
if S::use_early_reject() && old_pos != self.position {
return S::rejecting(old_pos, self.position);
}
// Quickly skip by large portions unrelated to our substring
if !self.byteset_contains(haystack[self.position + needle.len() - 1]) {
self.position += needle.len();
if !long_period {
self.memory = 0;
}
continue 'search;
}
// See if the right part of the needle matches
let start = if long_period { self.crit_pos }
else { cmp::max(self.crit_pos, self.memory) };
for i in start..needle.len() {
if needle[i] != haystack[self.position + i] {
self.position += i - self.crit_pos + 1;
if !long_period {
self.memory = 0;
}
continue 'search;
}
}
// See if the left part of the needle matches
let start = if long_period { 0 } else { self.memory };
for i in (start..self.crit_pos).rev() {
if needle[i] != haystack[self.position + i] {
self.position += self.period;
if !long_period {
self.memory = needle.len() - self.period;
}
continue 'search;
}
}
// We have found a match!
let match_pos = self.position;
// Note: add self.period instead of needle.len() to have overlapping matches
self.position += needle.len();
if !long_period {
self.memory = 0; // set to needle.len() - self.period for overlapping matches
}
return S::matching(match_pos, match_pos + needle.len());
}
}
// Follows the ideas in `next()`.
//
// All the definitions are completely symmetrical, with period(x) = period(reverse(x))
// and local_period(u, v) = local_period(reverse(v), reverse(u)), so if (u, v)
// is a critical factorization, so is (reverse(v), reverse(u)). Similarly,
// the "period" stored in self.period is the real period if long_period is
// false, and so is still valid for a reversed needle, and if long_period is
// true, all the algorithm requires is that self.period is less than or
// equal to the real period, which must be true for the forward case anyway.
//
// To search in reverse through the haystack, we search forward through
// a reversed haystack with a reversed needle, and the above paragraph shows
// that the precomputed parameters can be left alone.
#[inline]
fn next_back<S>(&mut self, haystack: &[u8], needle: &[u8])
-> S::Output
where S: TwoWayStrategy
{
// `next_back()` uses `self.end` as its cursor -- so that `next()` and `next_back()`
// are independent.
let old_end = self.end;
'search: loop {
// Check that we have room to search in
if needle.len() > self.end {
self.end = 0;
return S::rejecting(0, old_end);
}
if S::use_early_reject() && old_end != self.end {
return S::rejecting(self.end, old_end);
}
// Quickly skip by large portions unrelated to our substring
if !self.byteset_contains(haystack[self.end - needle.len()]) {
self.end -= needle.len();
continue 'search;
}
// See if the left part of the needle matches
for i in (0..self.crit_pos).rev() {
if needle[i] != haystack[self.end - needle.len() + i] {
self.end -= self.crit_pos - i;
continue 'search;
}
}
// See if the right part of the needle matches
for i in self.crit_pos..needle.len() {
if needle[i] != haystack[self.end - needle.len() + i] {
self.end -= self.period;
continue 'search;
}
}
// We have found a match!
let match_pos = self.end - needle.len();
// Note: sub self.period instead of needle.len() to have overlapping matches
self.end -= needle.len();
return S::matching(match_pos, match_pos + needle.len());
}
}
// Computes a critical factorization (u, v) of `arr`.
// Specifically, returns (i, p), where i is the starting index of v in some
// critical factorization (u, v) and p = period(v)
#[inline]
fn maximal_suffix(arr: &[u8], reversed: bool) -> (usize, usize) {
let mut left: usize = !0; // Corresponds to i in the paper
let mut right = 0; // Corresponds to j in the paper
let mut offset = 1; // Corresponds to k in the paper
let mut period = 1; // Corresponds to p in the paper