stable_pattern/

pattern.rs

//! The string Pattern API.
//!
//! The Pattern API provides a generic mechanism for using different pattern
//! types when searching through a string.
//!
//! For more details, see the traits [`Pattern`], [`Searcher`],
//! [`ReverseSearcher`], and [`DoubleEndedSearcher`].
//!
//! Although this API is unstable, it is exposed via stable APIs on the
//! [`str`] type.
//!
//! # Examples
//!
//! [`Pattern`] is [implemented][pattern-impls] in the stable API for
//! [`&str`][`str`], [`char`], slices of [`char`], and functions and closures
//! implementing `FnMut(char) -> bool`.
//!
//! ```
//! let s = "Can you find a needle in a haystack?";
//!
//! // &str pattern
//! assert_eq!(s.find("you"), Some(4));
//! // char pattern
//! assert_eq!(s.find('n'), Some(2));
//! // slice of chars pattern
//! assert_eq!(s.find(&['a', 'e', 'i', 'o', 'u'][..]), Some(1));
//! // closure pattern
//! assert_eq!(s.find(|c: char| c.is_ascii_punctuation()), Some(35));
//! ```
//!
//! [pattern-impls]: Pattern#implementors

use core::cmp;
use core::fmt;

// 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`][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.
///
/// Depending on the type of the pattern, the behaviour of methods like
/// [`str::find`] and [`str::contains`] can change. The table below describes
/// some of those behaviours.
///
/// | Pattern type             | Match condition                           |
/// |--------------------------|-------------------------------------------|
/// | `&str`                   | is substring                              |
/// | `char`                   | is contained in string                    |
/// | `&[char]`                | any char in slice is contained in string  |
/// | `F: FnMut(char) -> bool` | `F` returns `true` for a char in string   |
/// | `&&str`                  | is substring                              |
/// | `&String`                | is substring                              |
///
/// # Examples
///
/// ```
/// // &str
/// assert_eq!("abaaa".find("ba"), Some(1));
/// assert_eq!("abaaa".find("bac"), None);
///
/// // char
/// assert_eq!("abaaa".find('a'), Some(0));
/// assert_eq!("abaaa".find('b'), Some(1));
/// assert_eq!("abaaa".find('c'), None);
///
/// // &[char]
/// assert_eq!("ab".find(&['b', 'a'][..]), Some(0));
/// assert_eq!("abaaa".find(&['a', 'z'][..]), Some(0));
/// assert_eq!("abaaa".find(&['c', 'd'][..]), None);
///
/// // FnMut(char) -> bool
/// assert_eq!("abcdef_z".find(|ch| ch > 'd' && ch < 'y'), Some(4));
/// assert_eq!("abcddd_z".find(|ch| ch > 'd' && ch < 'y'), None);
/// ```
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 {
        matches!(self.into_searcher(haystack).next(), SearchStep::Match(0, _))
    }

    /// 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>,
    {
        matches!(self.into_searcher(haystack).next_back(), SearchStep::Match(_, j) if haystack.len() == j)
    }

    /// Removes the pattern from the front of haystack, if it matches.
    #[inline]
    fn strip_prefix_of(self, haystack: &'a str) -> Option<&'a str> {
        if let SearchStep::Match(start, len) = self.into_searcher(haystack).next() {
            debug_assert_eq!(
                start, 0,
                "The first search step from Searcher \
                 must include the first character"
            );
            // SAFETY: `Searcher` is known to return valid indices.
            unsafe { Some(haystack.get_unchecked(len..)) }
        } else {
            None
        }
    }

    /// Removes the pattern from the back of haystack, if it matches.
    #[inline]
    fn strip_suffix_of(self, haystack: &'a str) -> Option<&'a str>
    where
        Self::Searcher: ReverseSearcher<'a>,
    {
        if let SearchStep::Match(start, end) = self.into_searcher(haystack).next_back() {
            debug_assert_eq!(
                end,
                haystack.len(),
                "The first search step from ReverseSearcher \
                 must include the last character"
            );
            // SAFETY: `Searcher` is known to return valid indices.
            unsafe { Some(haystack.get_unchecked(..start)) }
        } else {
            None
        }
    }
}

// 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 visited, 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()`][Searcher::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 underlying string to be searched in
    ///
    /// Will always return the same [`&str`][str].
    fn haystack(&self) -> &'a str;

    /// Performs the next search step starting from the front.
    ///
    /// - Returns [`Match(a, b)`][SearchStep::Match] if `haystack[a..b]` matches
    ///   the pattern.
    /// - Returns [`Reject(a, b)`][SearchStep::Reject] if `haystack[a..b]` can
    ///   not match the pattern, even partially.
    /// - Returns [`Done`][SearchStep::Done] if every byte of the haystack has
    ///   been visited.
    ///
    /// The stream of [`Match`][SearchStep::Match] and
    /// [`Reject`][SearchStep::Reject] values up to a [`Done`][SearchStep::Done]
    /// will contain index ranges that are adjacent, non-overlapping,
    /// covering the whole haystack, and laying on utf8 boundaries.
    ///
    /// A [`Match`][SearchStep::Match] result needs to contain the whole matched
    /// pattern, however [`Reject`][SearchStep::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;

    /// Finds the next [`Match`][SearchStep::Match] result. See [`next()`][Searcher::next].
    ///
    /// Unlike [`next()`][Searcher::next], there is no guarantee that the returned ranges
    /// of this and [`next_reject`][Searcher::next_reject] will overlap. This will return
    /// `(start_match, end_match)`, where start_match is the index of where
    /// the match begins, and end_match is the index after the end of the match.
    #[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,
            }
        }
    }

    /// Finds the next [`Reject`][SearchStep::Reject] result. See [`next()`][Searcher::next]
    /// and [`next_match()`][Searcher::next_match].
    ///
    /// Unlike [`next()`][Searcher::next], there is no guarantee that the returned ranges
    /// of this and [`next_match`][Searcher::next_match] will overlap.
    #[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)`][SearchStep::Match] if `haystack[a..b]`
    ///   matches the pattern.
    /// - Returns [`Reject(a, b)`][SearchStep::Reject] if `haystack[a..b]`
    ///   can not match the pattern, even partially.
    /// - Returns [`Done`][SearchStep::Done] if every byte of the haystack
    ///   has been visited
    ///
    /// The stream of [`Match`][SearchStep::Match] and
    /// [`Reject`][SearchStep::Reject] values up to a [`Done`][SearchStep::Done]
    /// will contain index ranges that are adjacent, non-overlapping,
    /// covering the whole haystack, and laying on utf8 boundaries.
    ///
    /// A [`Match`][SearchStep::Match] result needs to contain the whole matched
    /// pattern, however [`Reject`][SearchStep::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;

    /// Finds the next [`Match`][SearchStep::Match] result.
    /// See [`next_back()`][ReverseSearcher::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,
            }
        }
    }

    /// Finds the next [`Reject`][SearchStep::Reject] result.
    /// See [`next_back()`][ReverseSearcher::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 char
/////////////////////////////////////////////////////////////////////////////

/// Associated type for `<char as Pattern<'a>>::Searcher`.
#[derive(Clone, Debug)]
pub struct CharSearcher<'a> {
    haystack: &'a str,
    // safety invariant: `finger`/`finger_back` must be a valid utf8 byte index of `haystack`
    // This invariant can be broken *within* next_match and next_match_back, however
    // they must exit with fingers on valid code point boundaries.
    /// `finger` is the current byte index of the forward search.
    /// Imagine that it exists before the byte at its index, i.e.
    /// `haystack[finger]` is the first byte of the slice we must inspect during
    /// forward searching
    finger: usize,
    /// `finger_back` is the current byte index of the reverse search.
    /// Imagine that it exists after the byte at its index, i.e.
    /// haystack[finger_back - 1] is the last byte of the slice we must inspect during
    /// forward searching (and thus the first byte to be inspected when calling next_back()).
    finger_back: usize,
    /// The character being searched for
    needle: char,

    // safety invariant: `utf8_size` must be less than 5
    /// The number of bytes `needle` takes up when encoded in utf8.
    utf8_size: usize,
    /// A utf8 encoded copy of the `needle`
    utf8_encoded: [u8; 4],
}

unsafe impl<'a> Searcher<'a> for CharSearcher<'a> {
    #[inline]
    fn haystack(&self) -> &'a str {
        self.haystack
    }
    #[inline]
    fn next(&mut self) -> SearchStep {
        let old_finger = self.finger;
        // SAFETY: 1-4 guarantee safety of `get_unchecked`
        // 1. `self.finger` and `self.finger_back` are kept on unicode boundaries
        //    (this is invariant)
        // 2. `self.finger >= 0` since it starts at 0 and only increases
        // 3. `self.finger < self.finger_back` because otherwise the char `iter`
        //    would return `SearchStep::Done`
        // 4. `self.finger` comes before the end of the haystack because `self.finger_back`
        //    starts at the end and only decreases
        let slice = unsafe { self.haystack.get_unchecked(old_finger..self.finger_back) };
        let mut iter = slice.chars();
        let old_len = iter.as_str().len();
        if let Some(ch) = iter.next() {
            // add byte offset of current character
            // without re-encoding as utf-8
            self.finger += old_len - iter.as_str().len();
            if ch == self.needle {
                SearchStep::Match(old_finger, self.finger)
            } else {
                SearchStep::Reject(old_finger, self.finger)
            }
        } else {
            SearchStep::Done
        }
    }
    #[inline]
    fn next_match(&mut self) -> Option<(usize, usize)> {
        loop {
            // get the haystack after the last character found
            let bytes = self.haystack.as_bytes().get(self.finger..self.finger_back)?;
            // the last byte of the utf8 encoded needle
            // SAFETY: we have an invariant that `utf8_size < 5`
            let last_byte = unsafe { *self.utf8_encoded.get_unchecked(self.utf8_size - 1) };
            if let Some(index) = memchr::memchr(last_byte, bytes) {
                // The new finger is the index of the byte we found,
                // plus one, since we memchr'd for the last byte of the character.
                //
                // Note that this doesn't always give us a finger on a UTF8 boundary.
                // If we *didn't* find our character
                // we may have indexed to the non-last byte of a 3-byte or 4-byte character.
                // We can't just skip to the next valid starting byte because a character like
                // ꁁ (U+A041 YI SYLLABLE PA), utf-8 `EA 81 81` will have us always find
                // the second byte when searching for the third.
                //
                // However, this is totally okay. While we have the invariant that
                // self.finger is on a UTF8 boundary, this invariant is not relied upon
                // within this method (it is relied upon in CharSearcher::next()).
                //
                // We only exit this method when we reach the end of the string, or if we
                // find something. When we find something the `finger` will be set
                // to a UTF8 boundary.
                self.finger += index + 1;
                if self.finger >= self.utf8_size {
                    let found_char = self.finger - self.utf8_size;
                    if let Some(slice) = self.haystack.as_bytes().get(found_char..self.finger) {
                        if slice == &self.utf8_encoded[0..self.utf8_size] {
                            return Some((found_char, self.finger));
                        }
                    }
                }
            } else {
                // found nothing, exit
                self.finger = self.finger_back;
                return None;
            }
        }
    }

    // let next_reject use the default implementation from the Searcher trait
}

unsafe impl<'a> ReverseSearcher<'a> for CharSearcher<'a> {
    #[inline]
    fn next_back(&mut self) -> SearchStep {
        let old_finger = self.finger_back;
        // SAFETY: see the comment for next() above
        let slice = unsafe { self.haystack.get_unchecked(self.finger..old_finger) };
        let mut iter = slice.chars();
        let old_len = iter.as_str().len();
        if let Some(ch) = iter.next_back() {
            // subtract byte offset of current character
            // without re-encoding as utf-8
            self.finger_back -= old_len - iter.as_str().len();
            if ch == self.needle {
                SearchStep::Match(self.finger_back, old_finger)
            } else {
                SearchStep::Reject(self.finger_back, old_finger)
            }
        } else {
            SearchStep::Done
        }
    }
    #[inline]
    fn next_match_back(&mut self) -> Option<(usize, usize)> {
        let haystack = self.haystack.as_bytes();
        loop {
            // get the haystack up to but not including the last character searched
            let bytes = haystack.get(self.finger..self.finger_back)?;
            // the last byte of the utf8 encoded needle
            // SAFETY: we have an invariant that `utf8_size < 5`
            let last_byte = unsafe { *self.utf8_encoded.get_unchecked(self.utf8_size - 1) };
            if let Some(index) = memchr::memrchr(last_byte, bytes) {
                // we searched a slice that was offset by self.finger,
                // add self.finger to recoup the original index
                let index = self.finger + index;
                // memrchr will return the index of the byte we wish to
                // find. In case of an ASCII character, this is indeed
                // were we wish our new finger to be ("after" the found
                // char in the paradigm of reverse iteration). For
                // multibyte chars we need to skip down by the number of more
                // bytes they have than ASCII
                let shift = self.utf8_size - 1;
                if index >= shift {
                    let found_char = index - shift;
                    if let Some(slice) = haystack.get(found_char..(found_char + self.utf8_size)) {
                        if slice == &self.utf8_encoded[0..self.utf8_size] {
                            // move finger to before the character found (i.e., at its start index)
                            self.finger_back = found_char;
                            return Some((self.finger_back, self.finger_back + self.utf8_size));
                        }
                    }
                }
                // We can't use finger_back = index - size + 1 here. If we found the last char
                // of a different-sized character (or the middle byte of a different character)
                // we need to bump the finger_back down to `index`. This similarly makes
                // `finger_back` have the potential to no longer be on a boundary,
                // but this is OK since we only exit this function on a boundary
                // or when the haystack has been searched completely.
                //
                // Unlike next_match this does not
                // have the problem of repeated bytes in utf-8 because
                // we're searching for the last byte, and we can only have
                // found the last byte when searching in reverse.
                self.finger_back = index;
            } else {
                self.finger_back = self.finger;
                // found nothing, exit
                return None;
            }
        }
    }

    // let next_reject_back use the default implementation from the Searcher trait
}

impl<'a> DoubleEndedSearcher<'a> for CharSearcher<'a> {}

/// Searches for chars that are equal to a given [`char`].
///
/// # Examples
///
/// ```
/// assert_eq!("Hello world".find('o'), Some(4));
/// ```
impl<'a> Pattern<'a> for char {
    type Searcher = CharSearcher<'a>;

    #[inline]
    fn into_searcher(self, haystack: &'a str) -> Self::Searcher {
        let mut utf8_encoded = [0; 4];
        let utf8_size = self.encode_utf8(&mut utf8_encoded).len();
        CharSearcher {
            haystack,
            finger: 0,
            finger_back: haystack.len(),
            needle: self,
            utf8_size,
            utf8_encoded,
        }
    }

    #[inline]
    fn is_contained_in(self, haystack: &'a str) -> bool {
        if (self as u32) < 128 {
            haystack.as_bytes().contains(&(self as u8))
        } else {
            let mut buffer = [0u8; 4];
            self.encode_utf8(&mut buffer).is_contained_in(haystack)
        }
    }

    #[inline]
    fn is_prefix_of(self, haystack: &'a str) -> bool {
        self.encode_utf8(&mut [0u8; 4]).is_prefix_of(haystack)
    }

    #[inline]
    fn strip_prefix_of(self, haystack: &'a str) -> Option<&'a str> {
        self.encode_utf8(&mut [0u8; 4]).strip_prefix_of(haystack)
    }

    #[inline]
    fn is_suffix_of(self, haystack: &'a str) -> bool
    where
        Self::Searcher: ReverseSearcher<'a>,
    {
        self.encode_utf8(&mut [0u8; 4]).is_suffix_of(haystack)
    }

    #[inline]
    fn strip_suffix_of(self, haystack: &'a str) -> Option<&'a str>
    where
        Self::Searcher: ReverseSearcher<'a>,
    {
        self.encode_utf8(&mut [0u8; 4]).strip_suffix_of(haystack)
    }
}

/////////////////////////////////////////////////////////////////////////////
// Impl for a MultiCharEq wrapper
/////////////////////////////////////////////////////////////////////////////

#[doc(hidden)]
trait MultiCharEq {
    fn matches(&mut self, c: char) -> bool;
}

impl<F> MultiCharEq for F
where
    F: FnMut(char) -> bool,
{
    #[inline]
    fn matches(&mut self, c: char) -> bool {
        (*self)(c)
    }
}

impl MultiCharEq for &[char] {
    #[inline]
    fn matches(&mut self, c: char) -> bool {
        self.iter().any(|&m| m == c)
    }
}

struct MultiCharEqPattern<C: MultiCharEq>(C);

#[derive(Clone, Debug)]
struct MultiCharEqSearcher<'a, C: MultiCharEq> {
    char_eq: C,
    haystack: &'a str,
    char_indices: core::str::CharIndices<'a>,
}

impl<'a, C: MultiCharEq> Pattern<'a> for MultiCharEqPattern<C> {
    type Searcher = MultiCharEqSearcher<'a, C>;

    #[inline]
    fn into_searcher(self, haystack: &'a str) -> MultiCharEqSearcher<'a, C> {
        MultiCharEqSearcher { haystack, char_eq: self.0, char_indices: haystack.char_indices() }
    }
}

unsafe impl<'a, C: MultiCharEq> Searcher<'a> for MultiCharEqSearcher<'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.as_str().len();
        if let Some((i, c)) = s.next() {
            let len = s.as_str().len();
            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: MultiCharEq> ReverseSearcher<'a> for MultiCharEqSearcher<'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.as_str().len();
        if let Some((i, c)) = s.next_back() {
            let len = s.as_str().len();
            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: MultiCharEq> DoubleEndedSearcher<'a> for MultiCharEqSearcher<'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 strip_prefix_of(self, haystack: &'a str) -> Option<&'a str> {
            ($pmap)(self).strip_prefix_of(haystack)
        }

        #[inline]
        fn is_suffix_of(self, haystack: &'a str) -> bool
        where
            $t: ReverseSearcher<'a>,
        {
            ($pmap)(self).is_suffix_of(haystack)
        }

        #[inline]
        fn strip_suffix_of(self, haystack: &'a str) -> Option<&'a str>
        where
            $t: ReverseSearcher<'a>,
        {
            ($pmap)(self).strip_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]
/////////////////////////////////////////////////////////////////////////////

// Todo: Change / Remove due to ambiguity in meaning.

/// Associated type for `<&[char] as Pattern<'a>>::Searcher`.
#[derive(Clone, Debug)]
pub struct CharSliceSearcher<'a, 'b>(<MultiCharEqPattern<&'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 [`char`]s in the slice.
///
/// # Examples
///
/// ```
/// assert_eq!("Hello world".find(&['l', 'l'] as &[_]), Some(2));
/// assert_eq!("Hello world".find(&['l', 'l'][..]), Some(2));
/// ```
impl<'a, 'b> Pattern<'a> for &'b [char] {
    pattern_methods!(CharSliceSearcher<'a, 'b>, MultiCharEqPattern, CharSliceSearcher);
}

/////////////////////////////////////////////////////////////////////////////
// Impl for F: FnMut(char) -> bool
/////////////////////////////////////////////////////////////////////////////

/// Associated type for `<F as Pattern<'a>>::Searcher`.
#[derive(Clone)]
pub struct CharPredicateSearcher<'a, F>(<MultiCharEqPattern<F> as Pattern<'a>>::Searcher)
where
    F: FnMut(char) -> bool;

impl<F> fmt::Debug for CharPredicateSearcher<'_, F>
where
    F: FnMut(char) -> bool,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_struct("CharPredicateSearcher")
            .field("haystack", &self.0.haystack)
            .field("char_indices", &self.0.char_indices)
            .finish()
    }
}
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 [`char`]s that match the given predicate.
///
/// # Examples
///
/// ```
/// assert_eq!("Hello world".find(char::is_uppercase), Some(0));
/// assert_eq!("Hello world".find(|c| "aeiou".contains(c)), Some(1));
/// ```
impl<'a, F> Pattern<'a> for F
where
    F: FnMut(char) -> bool,
{
    pattern_methods!(CharPredicateSearcher<'a, F>, MultiCharEqPattern, CharPredicateSearcher);
}

/////////////////////////////////////////////////////////////////////////////
// Impl for &&str
/////////////////////////////////////////////////////////////////////////////

/// Delegates to the `&str` impl.
impl<'a, 'b, 'c> Pattern<'a> for &'c &'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.
///
/// # Examples
///
/// ```
/// assert_eq!("Hello world".find("world"), Some(6));
/// ```
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 {
        haystack.as_bytes().starts_with(self.as_bytes())
    }

    /// Removes the pattern from the front of haystack, if it matches.
    #[inline]
    fn strip_prefix_of(self, haystack: &'a str) -> Option<&'a str> {
        if self.is_prefix_of(haystack) {
            // SAFETY: prefix was just verified to exist.
            unsafe { Some(haystack.get_unchecked(self.as_bytes().len()..)) }
        } else {
            None
        }
    }

    /// Checks whether the pattern matches at the back of the haystack.
    #[inline]
    fn is_suffix_of(self, haystack: &'a str) -> bool {
        haystack.as_bytes().ends_with(self.as_bytes())
    }

    /// Removes the pattern from the back of haystack, if it matches.
    #[inline]
    fn strip_suffix_of(self, haystack: &'a str) -> Option<&'a str> {
        if self.is_suffix_of(haystack) {
            let i = haystack.len() - self.as_bytes().len();
            // SAFETY: suffix was just verified to exist.
            unsafe { Some(haystack.get_unchecked(..i)) }
        } else {
            None
        }
    }
}

/////////////////////////////////////////////////////////////////////////////
// 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,
                needle,
                searcher: StrSearcherImpl::Empty(EmptyNeedle {
                    position: 0,
                    end: haystack.len(),
                    is_match_fw: true,
                    is_match_bw: true,
                }),
            }
        } else {
            StrSearcher {
                haystack,
                needle,
                searcher: StrSearcherImpl::TwoWay(TwoWaySearcher::new(
                    needle.as_bytes(),
                    haystack.len(),
                )),
            }
        }
    }
}

unsafe impl<'a, 'b> Searcher<'a> for StrSearcher<'a, 'b> {
    #[inline]
    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]
    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;
                // write out `true` and `false` cases to encourage the compiler
                // to specialize the two cases separately.
                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;
                }
                let is_long = searcher.memory == usize::MAX;
                match searcher.next_back::<RejectAndMatch>(
                    self.haystack.as_bytes(),
                    self.needle.as_bytes(),
                    is_long,
                ) {
                    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) => {
                let is_long = searcher.memory == usize::MAX;
                // write out `true` and `false`, like `next_match`
                if is_long {
                    searcher.next_back::<MatchOnly>(
                        self.haystack.as_bytes(),
                        self.needle.as_bytes(),
                        true,
                    )
                } else {
                    searcher.next_back::<MatchOnly>(
                        self.haystack.as_bytes(),
                        self.needle.as_bytes(),
                        false,
                    )
                }
            }
        }
    }
}

/// The internal state of the two-way substring search algorithm.
#[derive(Clone, Debug)]
struct TwoWaySearcher {
    // constants
    /// critical factorization index
    crit_pos: usize,
    /// critical factorization index for reversed needle
    crit_pos_back: usize,
    period: usize,
    /// `byteset` is an extension (not part of the two way algorithm);
    /// it's a 64-bit "fingerprint" where each set bit `j` corresponds
    /// to a (byte & 63) == j present in the needle.
    byteset: u64,

    // variables
    position: usize,
    end: usize,
    /// index into needle before which we have already matched
    memory: usize,
    /// index into needle after which we have already matched
    memory_back: 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.

    If the period is short, compute another factorization x = u' v' to use
    for reverse search, chosen instead so that |v'| < period(x).

*/
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)
        };

        // 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 -- the period is exact
            // compute a separate critical factorization for the reversed needle
            // x = u' v' where |v'| < period(x).
            //
            // This is sped up by the period being known already.
            // Note that a case like x = "acba" may be factored exactly forwards
            // (crit_pos = 1, period = 3) while being factored with approximate
            // period in reverse (crit_pos = 2, period = 2). We use the given
            // reverse factorization but keep the exact period.
            let crit_pos_back = needle.len()
                - cmp::max(
                    TwoWaySearcher::reverse_maximal_suffix(needle, period, false),
                    TwoWaySearcher::reverse_maximal_suffix(needle, period, true),
                );

            TwoWaySearcher {
                crit_pos,
                crit_pos_back,
                period,
                byteset: Self::byteset_create(&needle[..period]),

                position: 0,
                end,
                memory: 0,
                memory_back: needle.len(),
            }
        } else {
            // long period case -- we have an approximation to the actual period,
            // and don't use memorization.
            //
            // Approximate the period by lower bound max(|u|, |v|) + 1.
            // The critical factorization is efficient to use for both forward and
            // reverse search.

            TwoWaySearcher {
                crit_pos,
                crit_pos_back: crit_pos,
                period: cmp::max(crit_pos, needle.len() - crit_pos) + 1,
                byteset: Self::byteset_create(needle),

                position: 0,
                end,
                memory: usize::MAX, // Dummy value to signify that the period is long
                memory_back: usize::MAX,
            }
        }
    }

    #[inline]
    fn byteset_create(bytes: &[u8]) -> u64 {
        bytes.iter().fold(0, |a, &b| (1 << (b & 0x3f)) | a)
    }

    #[inline]
    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]
    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;
        let needle_last = needle.len() - 1;
        'search: loop {
            // Check that we have room to search in
            // position + needle_last can not overflow if we assume slices
            // are bounded by isize's range.
            let tail_byte = match haystack.get(self.position + needle_last) {
                Some(&b) => b,
                None => {
                    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(tail_byte) {
                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()`.
    //
    // The definitions are 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)).
    //
    // For the reverse case we have computed a critical factorization x = u' v'
    // (field `crit_pos_back`). We need |u| < period(x) for the forward case and
    // thus |v'| < period(x) for the reverse.
    //
    // To search in reverse through the haystack, we search forward through
    // a reversed haystack with a reversed needle, matching first u' and then v'.
    #[inline]
    fn next_back<S>(&mut self, haystack: &[u8], needle: &[u8], long_period: bool) -> 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
            // end - needle.len() will wrap around when there is no more room,
            // but due to slice length limits it can never wrap all the way back
            // into the length of haystack.
            let front_byte = match haystack.get(self.end.wrapping_sub(needle.len())) {
                Some(&b) => b,
                None => {
                    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(front_byte) {
                self.end -= needle.len();
                if !long_period {
                    self.memory_back = needle.len();
                }
                continue 'search;
            }

            // See if the left part of the needle matches
            let crit = if long_period {
                self.crit_pos_back
            } else {
                cmp::min(self.crit_pos_back, self.memory_back)
            };
            for i in (0..crit).rev() {
                if needle[i] != haystack[self.end - needle.len() + i] {
                    self.end -= self.crit_pos_back - i;
                    if !long_period {
                        self.memory_back = needle.len();
                    }
                    continue 'search;
                }
            }

            // See if the right part of the needle matches
            let needle_end = if long_period { needle.len() } else { self.memory_back };
            for i in self.crit_pos_back..needle_end {
                if needle[i] != haystack[self.end - needle.len() + i] {
                    self.end -= self.period;
                    if !long_period {
                        self.memory_back = 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();
            if !long_period {
                self.memory_back = needle.len();
            }

            return S::matching(match_pos, match_pos + needle.len());
        }
    }

    // Compute the maximal suffix of `arr`.
    //
    // The maximal suffix is a possible critical factorization (u, v) of `arr`.
    //
    // Returns (`i`, `p`) where `i` is the starting index of v and `p` is the
    // period of v.
    //
    // `order_greater` determines if lexical order is `<` or `>`. Both
    // orders must be computed -- the ordering with the largest `i` gives
    // a critical factorization.
    //
    // For long period cases, the resulting period is not exact (it is too short).
    #[inline]
    fn maximal_suffix(arr: &[u8], order_greater: bool) -> (usize, usize) {
        let mut left = 0; // Corresponds to i in the paper
        let mut right = 1; // Corresponds to j in the paper
        let mut offset = 0; // Corresponds to k in the paper, but starting at 0
        // to match 0-based indexing.
        let mut period = 1; // Corresponds to p in the paper

        while let Some(&a) = arr.get(right + offset) {
            // `left` will be inbounds when `right` is.
            let b = arr[left + offset];
            if (a < b && !order_greater) || (a > b && order_greater) {
                // Suffix is smaller, period is entire prefix so far.
                right += offset + 1;
                offset = 0;
                period = right - left;
            } else if a == b {
                // Advance through repetition of the current period.
                if offset + 1 == period {
                    right += offset + 1;
                    offset = 0;
                } else {
                    offset += 1;
                }
            } else {
                // Suffix is larger, start over from current location.
                left = right;
                right += 1;
                offset = 0;
                period = 1;
            }
        }
        (left, period)
    }

    // Compute the maximal suffix of the reverse of `arr`.
    //
    // The maximal suffix is a possible critical factorization (u', v') of `arr`.
    //
    // Returns `i` where `i` is the starting index of v', from the back;
    // returns immediately when a period of `known_period` is reached.
    //
    // `order_greater` determines if lexical order is `<` or `>`. Both
    // orders must be computed -- the ordering with the largest `i` gives
    // a critical factorization.
    //
    // For long period cases, the resulting period is not exact (it is too short).
    fn reverse_maximal_suffix(arr: &[u8], known_period: usize, order_greater: bool) -> usize {
        let mut left = 0; // Corresponds to i in the paper
        let mut right = 1; // Corresponds to j in the paper
        let mut offset = 0; // Corresponds to k in the paper, but starting at 0
        // to match 0-based indexing.
        let mut period = 1; // Corresponds to p in the paper
        let n = arr.len();

        while right + offset < n {
            let a = arr[n - (1 + right + offset)];
            let b = arr[n - (1 + left + offset)];
            if (a < b && !order_greater) || (a > b && order_greater) {
                // Suffix is smaller, period is entire prefix so far.
                right += offset + 1;
                offset = 0;
                period = right - left;
            } else if a == b {
                // Advance through repetition of the current period.
                if offset + 1 == period {
                    right += offset + 1;
                    offset = 0;
                } else {
                    offset += 1;
                }
            } else {
                // Suffix is larger, start over from current location.
                left = right;
                right += 1;
                offset = 0;
                period = 1;
            }
            if period == known_period {
                break;
            }
        }
        debug_assert!(period <= known_period);
        left
    }
}

// TwoWayStrategy allows the algorithm to either skip non-matches as quickly
// as possible, or to work in a mode where it emits Rejects relatively quickly.
trait TwoWayStrategy {
    type Output;
    fn use_early_reject() -> bool;
    fn rejecting(a: usize, b: usize) -> Self::Output;
    fn matching(a: usize, b: usize) -> Self::Output;
}

/// Skip to match intervals as quickly as possible
enum MatchOnly {}

impl TwoWayStrategy for MatchOnly {
    type Output = Option<(usize, usize)>;

    #[inline]
    fn use_early_reject() -> bool {
        false
    }
    #[inline]
    fn rejecting(_a: usize, _b: usize) -> Self::Output {
        None
    }
    #[inline]
    fn matching(a: usize, b: usize) -> Self::Output {
        Some((a, b))
    }
}

/// Emit Rejects regularly
enum RejectAndMatch {}

impl TwoWayStrategy for RejectAndMatch {
    type Output = SearchStep;

    #[inline]
    fn use_early_reject() -> bool {
        true
    }
    #[inline]
    fn rejecting(a: usize, b: usize) -> Self::Output {
        SearchStep::Reject(a, b)
    }
    #[inline]
    fn matching(a: usize, b: usize) -> Self::Output {
        SearchStep::Match(a, b)
    }
}