regex_automata/nfa/thompson/

backtrack.rs

/*!
An NFA backed bounded backtracker for executing regex searches with capturing
groups.

This module provides a [`BoundedBacktracker`] that works by simulating an NFA
using the classical backtracking algorithm with a twist: it avoids redoing
work that it has done before and thereby avoids worst case exponential time.
In exchange, it can only be used on "short" haystacks. Its advantage is that
is can be faster than the [`PikeVM`](thompson::pikevm::PikeVM) in many cases
because it does less book-keeping.
*/

use alloc::{vec, vec::Vec};

use crate::{
    nfa::thompson::{self, BuildError, State, NFA},
    util::{
        captures::Captures,
        empty, iter,
        prefilter::Prefilter,
        primitives::{NonMaxUsize, PatternID, SmallIndex, StateID},
        search::{Anchored, HalfMatch, Input, Match, MatchError, Span},
    },
};

/// Returns the minimum visited capacity for the given haystack.
///
/// This function can be used as the argument to [`Config::visited_capacity`]
/// in order to guarantee that a backtracking search for the given `input`
/// won't return an error when using a [`BoundedBacktracker`] built from the
/// given `NFA`.
///
/// This routine exists primarily as a way to test that the bounded backtracker
/// works correctly when its capacity is set to the smallest possible amount.
/// Still, it may be useful in cases where you know you want to use the bounded
/// backtracker for a specific input, and just need to know what visited
/// capacity to provide to make it work.
///
/// Be warned that this number could be quite large as it is multiplicative in
/// the size the given NFA and haystack.
pub fn min_visited_capacity(nfa: &NFA, input: &Input<'_>) -> usize {
    div_ceil(nfa.states().len() * (input.get_span().len() + 1), 8)
}

/// The configuration used for building a bounded backtracker.
///
/// A bounded backtracker configuration is a simple data object that is
/// typically used with [`Builder::configure`].
#[derive(Clone, Debug, Default)]
pub struct Config {
    pre: Option<Option<Prefilter>>,
    visited_capacity: Option<usize>,
}

impl Config {
    /// Return a new default regex configuration.
    pub fn new() -> Config {
        Config::default()
    }

    /// Set a prefilter to be used whenever a start state is entered.
    ///
    /// A [`Prefilter`] in this context is meant to accelerate searches by
    /// looking for literal prefixes that every match for the corresponding
    /// pattern (or patterns) must start with. Once a prefilter produces a
    /// match, the underlying search routine continues on to try and confirm
    /// the match.
    ///
    /// Be warned that setting a prefilter does not guarantee that the search
    /// will be faster. While it's usually a good bet, if the prefilter
    /// produces a lot of false positive candidates (i.e., positions matched
    /// by the prefilter but not by the regex), then the overall result can
    /// be slower than if you had just executed the regex engine without any
    /// prefilters.
    ///
    /// By default no prefilter is set.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     util::prefilter::Prefilter,
    ///     Input, Match, MatchKind,
    /// };
    ///
    /// let pre = Prefilter::new(MatchKind::LeftmostFirst, &["foo", "bar"]);
    /// let re = BoundedBacktracker::builder()
    ///     .configure(BoundedBacktracker::config().prefilter(pre))
    ///     .build(r"(foo|bar)[a-z]+")?;
    /// let mut cache = re.create_cache();
    /// let input = Input::new("foo1 barfox bar");
    /// assert_eq!(
    ///     Some(Match::must(0, 5..11)),
    ///     re.try_find(&mut cache, input)?,
    /// );
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// Be warned though that an incorrect prefilter can lead to incorrect
    /// results!
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     util::prefilter::Prefilter,
    ///     Input, HalfMatch, MatchKind,
    /// };
    ///
    /// let pre = Prefilter::new(MatchKind::LeftmostFirst, &["foo", "car"]);
    /// let re = BoundedBacktracker::builder()
    ///     .configure(BoundedBacktracker::config().prefilter(pre))
    ///     .build(r"(foo|bar)[a-z]+")?;
    /// let mut cache = re.create_cache();
    /// let input = Input::new("foo1 barfox bar");
    /// // No match reported even though there clearly is one!
    /// assert_eq!(None, re.try_find(&mut cache, input)?);
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn prefilter(mut self, pre: Option<Prefilter>) -> Config {
        self.pre = Some(pre);
        self
    }

    /// Set the visited capacity used to bound backtracking.
    ///
    /// The visited capacity represents the amount of heap memory (in bytes) to
    /// allocate toward tracking which parts of the backtracking search have
    /// been done before. The heap memory needed for any particular search is
    /// proportional to `haystack.len() * nfa.states().len()`, which an be
    /// quite large. Therefore, the bounded backtracker is typically only able
    /// to run on shorter haystacks.
    ///
    /// For a given regex, increasing the visited capacity means that the
    /// maximum haystack length that can be searched is increased. The
    /// [`BoundedBacktracker::max_haystack_len`] method returns that maximum.
    ///
    /// The default capacity is a reasonable but empirically chosen size.
    ///
    /// # Example
    ///
    /// As with other regex engines, Unicode is what tends to make the bounded
    /// backtracker less useful by making the maximum haystack length quite
    /// small. If necessary, increasing the visited capacity using this routine
    /// will increase the maximum haystack length at the cost of using more
    /// memory.
    ///
    /// Note though that the specific maximum values here are not an API
    /// guarantee. The default visited capacity is subject to change and not
    /// covered by semver.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::nfa::thompson::backtrack::BoundedBacktracker;
    ///
    /// // Unicode inflates the size of the underlying NFA quite a bit, and
    /// // thus means that the backtracker can only handle smaller haystacks,
    /// // assuming that the visited capacity remains unchanged.
    /// let re = BoundedBacktracker::new(r"\w+")?;
    /// assert!(re.max_haystack_len() <= 7_000);
    /// // But we can increase the visited capacity to handle bigger haystacks!
    /// let re = BoundedBacktracker::builder()
    ///     .configure(BoundedBacktracker::config().visited_capacity(1<<20))
    ///     .build(r"\w+")?;
    /// assert!(re.max_haystack_len() >= 25_000);
    /// assert!(re.max_haystack_len() <= 28_000);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn visited_capacity(mut self, capacity: usize) -> Config {
        self.visited_capacity = Some(capacity);
        self
    }

    /// Returns the prefilter set in this configuration, if one at all.
    pub fn get_prefilter(&self) -> Option<&Prefilter> {
        self.pre.as_ref().unwrap_or(&None).as_ref()
    }

    /// Returns the configured visited capacity.
    ///
    /// Note that the actual capacity used may be slightly bigger than the
    /// configured capacity.
    pub fn get_visited_capacity(&self) -> usize {
        const DEFAULT: usize = 256 * (1 << 10); // 256 KB
        self.visited_capacity.unwrap_or(DEFAULT)
    }

    /// Overwrite the default configuration such that the options in `o` are
    /// always used. If an option in `o` is not set, then the corresponding
    /// option in `self` is used. If it's not set in `self` either, then it
    /// remains not set.
    pub(crate) fn overwrite(&self, o: Config) -> Config {
        Config {
            pre: o.pre.or_else(|| self.pre.clone()),
            visited_capacity: o.visited_capacity.or(self.visited_capacity),
        }
    }
}

/// A builder for a bounded backtracker.
///
/// This builder permits configuring options for the syntax of a pattern, the
/// NFA construction and the `BoundedBacktracker` construction. This builder
/// is different from a general purpose regex builder in that it permits fine
/// grain configuration of the construction process. The trade off for this is
/// complexity, and the possibility of setting a configuration that might not
/// make sense. For example, there are two different UTF-8 modes:
///
/// * [`syntax::Config::utf8`](crate::util::syntax::Config::utf8) controls
/// whether the pattern itself can contain sub-expressions that match invalid
/// UTF-8.
/// * [`thompson::Config::utf8`] controls how the regex iterators themselves
/// advance the starting position of the next search when a match with zero
/// length is found.
///
/// Generally speaking, callers will want to either enable all of these or
/// disable all of these.
///
/// # Example
///
/// This example shows how to disable UTF-8 mode in the syntax and the regex
/// itself. This is generally what you want for matching on arbitrary bytes.
///
/// ```
/// use regex_automata::{
///     nfa::thompson::{self, backtrack::BoundedBacktracker},
///     util::syntax,
///     Match,
/// };
///
/// let re = BoundedBacktracker::builder()
///     .syntax(syntax::Config::new().utf8(false))
///     .thompson(thompson::Config::new().utf8(false))
///     .build(r"foo(?-u:[^b])ar.*")?;
/// let mut cache = re.create_cache();
///
/// let haystack = b"\xFEfoo\xFFarzz\xE2\x98\xFF\n";
/// let expected = Some(Ok(Match::must(0, 1..9)));
/// let got = re.try_find_iter(&mut cache, haystack).next();
/// assert_eq!(expected, got);
/// // Notice that `(?-u:[^b])` matches invalid UTF-8,
/// // but the subsequent `.*` does not! Disabling UTF-8
/// // on the syntax permits this.
/// //
/// // N.B. This example does not show the impact of
/// // disabling UTF-8 mode on a BoundedBacktracker Config, since that
/// // only impacts regexes that can produce matches of
/// // length 0.
/// assert_eq!(b"foo\xFFarzz", &haystack[got.unwrap()?.range()]);
///
/// # Ok::<(), Box<dyn std::error::Error>>(())
/// ```
#[derive(Clone, Debug)]
pub struct Builder {
    config: Config,
    #[cfg(feature = "syntax")]
    thompson: thompson::Compiler,
}

impl Builder {
    /// Create a new BoundedBacktracker builder with its default configuration.
    pub fn new() -> Builder {
        Builder {
            config: Config::default(),
            #[cfg(feature = "syntax")]
            thompson: thompson::Compiler::new(),
        }
    }

    /// Build a `BoundedBacktracker` from the given pattern.
    ///
    /// If there was a problem parsing or compiling the pattern, then an error
    /// is returned.
    #[cfg(feature = "syntax")]
    pub fn build(
        &self,
        pattern: &str,
    ) -> Result<BoundedBacktracker, BuildError> {
        self.build_many(&[pattern])
    }

    /// Build a `BoundedBacktracker` from the given patterns.
    #[cfg(feature = "syntax")]
    pub fn build_many<P: AsRef<str>>(
        &self,
        patterns: &[P],
    ) -> Result<BoundedBacktracker, BuildError> {
        let nfa = self.thompson.build_many(patterns)?;
        self.build_from_nfa(nfa)
    }

    /// Build a `BoundedBacktracker` directly from its NFA.
    ///
    /// Note that when using this method, any configuration that applies to the
    /// construction of the NFA itself will of course be ignored, since the NFA
    /// given here is already built.
    pub fn build_from_nfa(
        &self,
        nfa: NFA,
    ) -> Result<BoundedBacktracker, BuildError> {
        nfa.look_set_any().available().map_err(BuildError::word)?;
        Ok(BoundedBacktracker { config: self.config.clone(), nfa })
    }

    /// Apply the given `BoundedBacktracker` configuration options to this
    /// builder.
    pub fn configure(&mut self, config: Config) -> &mut Builder {
        self.config = self.config.overwrite(config);
        self
    }

    /// Set the syntax configuration for this builder using
    /// [`syntax::Config`](crate::util::syntax::Config).
    ///
    /// This permits setting things like case insensitivity, Unicode and multi
    /// line mode.
    ///
    /// These settings only apply when constructing a `BoundedBacktracker`
    /// directly from a pattern.
    #[cfg(feature = "syntax")]
    pub fn syntax(
        &mut self,
        config: crate::util::syntax::Config,
    ) -> &mut Builder {
        self.thompson.syntax(config);
        self
    }

    /// Set the Thompson NFA configuration for this builder using
    /// [`nfa::thompson::Config`](crate::nfa::thompson::Config).
    ///
    /// This permits setting things like if additional time should be spent
    /// shrinking the size of the NFA.
    ///
    /// These settings only apply when constructing a `BoundedBacktracker`
    /// directly from a pattern.
    #[cfg(feature = "syntax")]
    pub fn thompson(&mut self, config: thompson::Config) -> &mut Builder {
        self.thompson.configure(config);
        self
    }
}

/// A backtracking regex engine that bounds its execution to avoid exponential
/// blow-up.
///
/// This regex engine only implements leftmost-first match semantics and
/// only supports leftmost searches. It effectively does the same thing as a
/// [`PikeVM`](thompson::pikevm::PikeVM), but typically does it faster because
/// it doesn't have to worry about copying capturing group spans for most NFA
/// states. Instead, the backtracker can maintain one set of captures (provided
/// by the caller) and never needs to copy them. In exchange, the backtracker
/// bounds itself to ensure it doesn't exhibit worst case exponential time.
/// This results in the backtracker only being able to handle short haystacks
/// given reasonable memory usage.
///
/// # Searches may return an error!
///
/// By design, this backtracking regex engine is bounded. This bound is
/// implemented by not visiting any combination of NFA state ID and position
/// in a haystack more than once. Thus, the total memory required to bound
/// backtracking is proportional to `haystack.len() * nfa.states().len()`.
/// This can obviously get quite large, since large haystacks aren't terribly
/// uncommon. To avoid using exorbitant memory, the capacity is bounded by
/// a fixed limit set via [`Config::visited_capacity`]. Thus, if the total
/// capacity required for a particular regex and a haystack exceeds this
/// capacity, then the search routine will return an error.
///
/// Unlike other regex engines that may return an error at search time (like
/// the DFA or the hybrid NFA/DFA), there is no way to guarantee that a bounded
/// backtracker will work for every haystack. Therefore, this regex engine
/// _only_ exposes fallible search routines to avoid the footgun of panicking
/// when running a search on a haystack that is too big.
///
/// If one wants to use the fallible search APIs without handling the
/// error, the only way to guarantee an error won't occur from the
/// haystack length is to ensure the haystack length does not exceed
/// [`BoundedBacktracker::max_haystack_len`].
///
/// # Example: Unicode word boundaries
///
/// This example shows that the bounded backtracker implements Unicode word
/// boundaries correctly by default.
///
/// ```
/// # if cfg!(miri) { return Ok(()); } // miri takes too long
/// use regex_automata::{nfa::thompson::backtrack::BoundedBacktracker, Match};
///
/// let re = BoundedBacktracker::new(r"\b\w+\b")?;
/// let mut cache = re.create_cache();
///
/// let mut it = re.try_find_iter(&mut cache, "Шерлок Холмс");
/// assert_eq!(Some(Ok(Match::must(0, 0..12))), it.next());
/// assert_eq!(Some(Ok(Match::must(0, 13..23))), it.next());
/// assert_eq!(None, it.next());
/// # Ok::<(), Box<dyn std::error::Error>>(())
/// ```
///
/// # Example: multiple regex patterns
///
/// The bounded backtracker supports searching for multiple patterns
/// simultaneously, just like other regex engines. Note though that because it
/// uses a backtracking strategy, this regex engine is unlikely to scale well
/// as more patterns are added. But then again, as more patterns are added, the
/// maximum haystack length allowed will also shorten (assuming the visited
/// capacity remains invariant).
///
/// ```
/// use regex_automata::{nfa::thompson::backtrack::BoundedBacktracker, Match};
///
/// let re = BoundedBacktracker::new_many(&["[a-z]+", "[0-9]+"])?;
/// let mut cache = re.create_cache();
///
/// let mut it = re.try_find_iter(&mut cache, "abc 1 foo 4567 0 quux");
/// assert_eq!(Some(Ok(Match::must(0, 0..3))), it.next());
/// assert_eq!(Some(Ok(Match::must(1, 4..5))), it.next());
/// assert_eq!(Some(Ok(Match::must(0, 6..9))), it.next());
/// assert_eq!(Some(Ok(Match::must(1, 10..14))), it.next());
/// assert_eq!(Some(Ok(Match::must(1, 15..16))), it.next());
/// assert_eq!(Some(Ok(Match::must(0, 17..21))), it.next());
/// assert_eq!(None, it.next());
/// # Ok::<(), Box<dyn std::error::Error>>(())
/// ```
#[derive(Clone, Debug)]
pub struct BoundedBacktracker {
    config: Config,
    nfa: NFA,
}

impl BoundedBacktracker {
    /// Parse the given regular expression using the default configuration and
    /// return the corresponding `BoundedBacktracker`.
    ///
    /// If you want a non-default configuration, then use the [`Builder`] to
    /// set your own configuration.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match,
    /// };
    ///
    /// let re = BoundedBacktracker::new("foo[0-9]+bar")?;
    /// let mut cache = re.create_cache();
    /// assert_eq!(
    ///     Some(Ok(Match::must(0, 3..14))),
    ///     re.try_find_iter(&mut cache, "zzzfoo12345barzzz").next(),
    /// );
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[cfg(feature = "syntax")]
    pub fn new(pattern: &str) -> Result<BoundedBacktracker, BuildError> {
        BoundedBacktracker::builder().build(pattern)
    }

    /// Like `new`, but parses multiple patterns into a single "multi regex."
    /// This similarly uses the default regex configuration.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match,
    /// };
    ///
    /// let re = BoundedBacktracker::new_many(&["[a-z]+", "[0-9]+"])?;
    /// let mut cache = re.create_cache();
    ///
    /// let mut it = re.try_find_iter(&mut cache, "abc 1 foo 4567 0 quux");
    /// assert_eq!(Some(Ok(Match::must(0, 0..3))), it.next());
    /// assert_eq!(Some(Ok(Match::must(1, 4..5))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 6..9))), it.next());
    /// assert_eq!(Some(Ok(Match::must(1, 10..14))), it.next());
    /// assert_eq!(Some(Ok(Match::must(1, 15..16))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 17..21))), it.next());
    /// assert_eq!(None, it.next());
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[cfg(feature = "syntax")]
    pub fn new_many<P: AsRef<str>>(
        patterns: &[P],
    ) -> Result<BoundedBacktracker, BuildError> {
        BoundedBacktracker::builder().build_many(patterns)
    }

    /// # Example
    ///
    /// This shows how to hand assemble a regular expression via its HIR,
    /// compile an NFA from it and build a BoundedBacktracker from the NFA.
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::{NFA, backtrack::BoundedBacktracker},
    ///     Match,
    /// };
    /// use regex_syntax::hir::{Hir, Class, ClassBytes, ClassBytesRange};
    ///
    /// let hir = Hir::class(Class::Bytes(ClassBytes::new(vec![
    ///     ClassBytesRange::new(b'0', b'9'),
    ///     ClassBytesRange::new(b'A', b'Z'),
    ///     ClassBytesRange::new(b'_', b'_'),
    ///     ClassBytesRange::new(b'a', b'z'),
    /// ])));
    ///
    /// let config = NFA::config().nfa_size_limit(Some(1_000));
    /// let nfa = NFA::compiler().configure(config).build_from_hir(&hir)?;
    ///
    /// let re = BoundedBacktracker::new_from_nfa(nfa)?;
    /// let (mut cache, mut caps) = (re.create_cache(), re.create_captures());
    /// let expected = Some(Match::must(0, 3..4));
    /// re.try_captures(&mut cache, "!@#A#@!", &mut caps)?;
    /// assert_eq!(expected, caps.get_match());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn new_from_nfa(nfa: NFA) -> Result<BoundedBacktracker, BuildError> {
        BoundedBacktracker::builder().build_from_nfa(nfa)
    }

    /// Create a new `BoundedBacktracker` that matches every input.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match,
    /// };
    ///
    /// let re = BoundedBacktracker::always_match()?;
    /// let mut cache = re.create_cache();
    ///
    /// let expected = Some(Ok(Match::must(0, 0..0)));
    /// assert_eq!(expected, re.try_find_iter(&mut cache, "").next());
    /// assert_eq!(expected, re.try_find_iter(&mut cache, "foo").next());
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn always_match() -> Result<BoundedBacktracker, BuildError> {
        let nfa = thompson::NFA::always_match();
        BoundedBacktracker::new_from_nfa(nfa)
    }

    /// Create a new `BoundedBacktracker` that never matches any input.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::nfa::thompson::backtrack::BoundedBacktracker;
    ///
    /// let re = BoundedBacktracker::never_match()?;
    /// let mut cache = re.create_cache();
    ///
    /// assert_eq!(None, re.try_find_iter(&mut cache, "").next());
    /// assert_eq!(None, re.try_find_iter(&mut cache, "foo").next());
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn never_match() -> Result<BoundedBacktracker, BuildError> {
        let nfa = thompson::NFA::never_match();
        BoundedBacktracker::new_from_nfa(nfa)
    }

    /// Return a default configuration for a `BoundedBacktracker`.
    ///
    /// This is a convenience routine to avoid needing to import the `Config`
    /// type when customizing the construction of a `BoundedBacktracker`.
    ///
    /// # Example
    ///
    /// This example shows how to disable UTF-8 mode. When UTF-8 mode is
    /// disabled, zero-width matches that split a codepoint are allowed.
    /// Otherwise they are never reported.
    ///
    /// In the code below, notice that `""` is permitted to match positions
    /// that split the encoding of a codepoint.
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::{self, backtrack::BoundedBacktracker},
    ///     Match,
    /// };
    ///
    /// let re = BoundedBacktracker::builder()
    ///     .thompson(thompson::Config::new().utf8(false))
    ///     .build(r"")?;
    /// let mut cache = re.create_cache();
    ///
    /// let haystack = "a☃z";
    /// let mut it = re.try_find_iter(&mut cache, haystack);
    /// assert_eq!(Some(Ok(Match::must(0, 0..0))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 1..1))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 2..2))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 3..3))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 4..4))), it.next());
    /// assert_eq!(Some(Ok(Match::must(0, 5..5))), it.next());
    /// assert_eq!(None, it.next());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn config() -> Config {
        Config::new()
    }

    /// Return a builder for configuring the construction of a
    /// `BoundedBacktracker`.
    ///
    /// This is a convenience routine to avoid needing to import the
    /// [`Builder`] type in common cases.
    ///
    /// # Example
    ///
    /// This example shows how to use the builder to disable UTF-8 mode
    /// everywhere.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::{
    ///     nfa::thompson::{self, backtrack::BoundedBacktracker},
    ///     util::syntax,
    ///     Match,
    /// };
    ///
    /// let re = BoundedBacktracker::builder()
    ///     .syntax(syntax::Config::new().utf8(false))
    ///     .thompson(thompson::Config::new().utf8(false))
    ///     .build(r"foo(?-u:[^b])ar.*")?;
    /// let (mut cache, mut caps) = (re.create_cache(), re.create_captures());
    ///
    /// let haystack = b"\xFEfoo\xFFarzz\xE2\x98\xFF\n";
    /// let expected = Some(Match::must(0, 1..9));
    /// re.try_captures(&mut cache, haystack, &mut caps)?;
    /// assert_eq!(expected, caps.get_match());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn builder() -> Builder {
        Builder::new()
    }

    /// Create a new cache for this regex.
    ///
    /// The cache returned should only be used for searches for this
    /// regex. If you want to reuse the cache for another regex, then you
    /// must call [`Cache::reset`] with that regex (or, equivalently,
    /// [`BoundedBacktracker::reset_cache`]).
    pub fn create_cache(&self) -> Cache {
        Cache::new(self)
    }

    /// Create a new empty set of capturing groups that is guaranteed to be
    /// valid for the search APIs on this `BoundedBacktracker`.
    ///
    /// A `Captures` value created for a specific `BoundedBacktracker` cannot
    /// be used with any other `BoundedBacktracker`.
    ///
    /// This is a convenience function for [`Captures::all`]. See the
    /// [`Captures`] documentation for an explanation of its alternative
    /// constructors that permit the `BoundedBacktracker` to do less work
    /// during a search, and thus might make it faster.
    pub fn create_captures(&self) -> Captures {
        Captures::all(self.get_nfa().group_info().clone())
    }

    /// Reset the given cache such that it can be used for searching with the
    /// this `BoundedBacktracker` (and only this `BoundedBacktracker`).
    ///
    /// A cache reset permits reusing memory already allocated in this cache
    /// with a different `BoundedBacktracker`.
    ///
    /// # Example
    ///
    /// This shows how to re-purpose a cache for use with a different
    /// `BoundedBacktracker`.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match,
    /// };
    ///
    /// let re1 = BoundedBacktracker::new(r"\w")?;
    /// let re2 = BoundedBacktracker::new(r"\W")?;
    ///
    /// let mut cache = re1.create_cache();
    /// assert_eq!(
    ///     Some(Ok(Match::must(0, 0..2))),
    ///     re1.try_find_iter(&mut cache, "Δ").next(),
    /// );
    ///
    /// // Using 'cache' with re2 is not allowed. It may result in panics or
    /// // incorrect results. In order to re-purpose the cache, we must reset
    /// // it with the BoundedBacktracker we'd like to use it with.
    /// //
    /// // Similarly, after this reset, using the cache with 're1' is also not
    /// // allowed.
    /// cache.reset(&re2);
    /// assert_eq!(
    ///     Some(Ok(Match::must(0, 0..3))),
    ///     re2.try_find_iter(&mut cache, "☃").next(),
    /// );
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn reset_cache(&self, cache: &mut Cache) {
        cache.reset(self);
    }

    /// Returns the total number of patterns compiled into this
    /// `BoundedBacktracker`.
    ///
    /// In the case of a `BoundedBacktracker` that contains no patterns, this
    /// returns `0`.
    ///
    /// # Example
    ///
    /// This example shows the pattern length for a `BoundedBacktracker` that
    /// never matches:
    ///
    /// ```
    /// use regex_automata::nfa::thompson::backtrack::BoundedBacktracker;
    ///
    /// let re = BoundedBacktracker::never_match()?;
    /// assert_eq!(re.pattern_len(), 0);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// And another example for a `BoundedBacktracker` that matches at every
    /// position:
    ///
    /// ```
    /// use regex_automata::nfa::thompson::backtrack::BoundedBacktracker;
    ///
    /// let re = BoundedBacktracker::always_match()?;
    /// assert_eq!(re.pattern_len(), 1);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// And finally, a `BoundedBacktracker` that was constructed from multiple
    /// patterns:
    ///
    /// ```
    /// use regex_automata::nfa::thompson::backtrack::BoundedBacktracker;
    ///
    /// let re = BoundedBacktracker::new_many(&["[0-9]+", "[a-z]+", "[A-Z]+"])?;
    /// assert_eq!(re.pattern_len(), 3);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn pattern_len(&self) -> usize {
        self.nfa.pattern_len()
    }

    /// Return the config for this `BoundedBacktracker`.
    #[inline]
    pub fn get_config(&self) -> &Config {
        &self.config
    }

    /// Returns a reference to the underlying NFA.
    #[inline]
    pub fn get_nfa(&self) -> &NFA {
        &self.nfa
    }

    /// Returns the maximum haystack length supported by this backtracker.
    ///
    /// This routine is a function of both [`Config::visited_capacity`] and the
    /// internal size of the backtracker's NFA.
    ///
    /// # Example
    ///
    /// This example shows how the maximum haystack length can vary depending
    /// on the size of the regex itself. Note though that the specific maximum
    /// values here are not an API guarantee. The default visited capacity is
    /// subject to change and not covered by semver.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match, MatchError,
    /// };
    ///
    /// // If you're only using ASCII, you get a big budget.
    /// let re = BoundedBacktracker::new(r"(?-u)\w+")?;
    /// let mut cache = re.create_cache();
    /// assert_eq!(re.max_haystack_len(), 299_592);
    /// // Things work up to the max.
    /// let mut haystack = "a".repeat(299_592);
    /// let expected = Some(Ok(Match::must(0, 0..299_592)));
    /// assert_eq!(expected, re.try_find_iter(&mut cache, &haystack).next());
    /// // But you'll get an error if you provide a haystack that's too big.
    /// // Notice that we use the 'try_find_iter' routine instead, which
    /// // yields Result<Match, MatchError> instead of Match.
    /// haystack.push('a');
    /// let expected = Some(Err(MatchError::haystack_too_long(299_593)));
    /// assert_eq!(expected, re.try_find_iter(&mut cache, &haystack).next());
    ///
    /// // Unicode inflates the size of the underlying NFA quite a bit, and
    /// // thus means that the backtracker can only handle smaller haystacks,
    /// // assuming that the visited capacity remains unchanged.
    /// let re = BoundedBacktracker::new(r"\w+")?;
    /// assert!(re.max_haystack_len() <= 7_000);
    /// // But we can increase the visited capacity to handle bigger haystacks!
    /// let re = BoundedBacktracker::builder()
    ///     .configure(BoundedBacktracker::config().visited_capacity(1<<20))
    ///     .build(r"\w+")?;
    /// assert!(re.max_haystack_len() >= 25_000);
    /// assert!(re.max_haystack_len() <= 28_000);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn max_haystack_len(&self) -> usize {
        // The capacity given in the config is "bytes of heap memory," but the
        // capacity we use here is "number of bits." So convert the capacity in
        // bytes to the capacity in bits.
        let capacity = 8 * self.get_config().get_visited_capacity();
        let blocks = div_ceil(capacity, Visited::BLOCK_SIZE);
        let real_capacity = blocks.saturating_mul(Visited::BLOCK_SIZE);
        // It's possible for `real_capacity` to be smaller than the number of
        // NFA states for particularly large regexes, so we saturate towards
        // zero.
        (real_capacity / self.nfa.states().len()).saturating_sub(1)
    }
}

impl BoundedBacktracker {
    /// Returns true if and only if this regex matches the given haystack.
    ///
    /// In the case of a backtracking regex engine, and unlike most other
    /// regex engines in this crate, short circuiting isn't practical. However,
    /// this routine may still be faster because it instructs backtracking to
    /// not keep track of any capturing groups.
    ///
    /// # Errors
    ///
    /// This routine only errors if the search could not complete. For this
    /// backtracking regex engine, this only occurs when the haystack length
    /// exceeds [`BoundedBacktracker::max_haystack_len`].
    ///
    /// When a search cannot complete, callers cannot know whether a match
    /// exists or not.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::nfa::thompson::backtrack::BoundedBacktracker;
    ///
    /// let re = BoundedBacktracker::new("foo[0-9]+bar")?;
    /// let mut cache = re.create_cache();
    ///
    /// assert!(re.try_is_match(&mut cache, "foo12345bar")?);
    /// assert!(!re.try_is_match(&mut cache, "foobar")?);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// # Example: consistency with search APIs
    ///
    /// `is_match` is guaranteed to return `true` whenever `find` returns a
    /// match. This includes searches that are executed entirely within a
    /// codepoint:
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Input,
    /// };
    ///
    /// let re = BoundedBacktracker::new("a*")?;
    /// let mut cache = re.create_cache();
    ///
    /// assert!(!re.try_is_match(&mut cache, Input::new("☃").span(1..2))?);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// Notice that when UTF-8 mode is disabled, then the above reports a
    /// match because the restriction against zero-width matches that split a
    /// codepoint has been lifted:
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::{backtrack::BoundedBacktracker, NFA},
    ///     Input,
    /// };
    ///
    /// let re = BoundedBacktracker::builder()
    ///     .thompson(NFA::config().utf8(false))
    ///     .build("a*")?;
    /// let mut cache = re.create_cache();
    ///
    /// assert!(re.try_is_match(&mut cache, Input::new("☃").span(1..2))?);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_is_match<'h, I: Into<Input<'h>>>(
        &self,
        cache: &mut Cache,
        input: I,
    ) -> Result<bool, MatchError> {
        let input = input.into().earliest(true);
        self.try_search_slots(cache, &input, &mut []).map(|pid| pid.is_some())
    }

    /// Executes a leftmost forward search and returns a `Match` if one exists.
    ///
    /// This routine only includes the overall match span. To get
    /// access to the individual spans of each capturing group, use
    /// [`BoundedBacktracker::try_captures`].
    ///
    /// # Errors
    ///
    /// This routine only errors if the search could not complete. For this
    /// backtracking regex engine, this only occurs when the haystack length
    /// exceeds [`BoundedBacktracker::max_haystack_len`].
    ///
    /// When a search cannot complete, callers cannot know whether a match
    /// exists or not.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match,
    /// };
    ///
    /// let re = BoundedBacktracker::new("foo[0-9]+")?;
    /// let mut cache = re.create_cache();
    /// let expected = Match::must(0, 0..8);
    /// assert_eq!(Some(expected), re.try_find(&mut cache, "foo12345")?);
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_find<'h, I: Into<Input<'h>>>(
        &self,
        cache: &mut Cache,
        input: I,
    ) -> Result<Option<Match>, MatchError> {
        let input = input.into();
        if self.get_nfa().pattern_len() == 1 {
            let mut slots = [None, None];
            let pid = match self.try_search_slots(cache, &input, &mut slots)? {
                None => return Ok(None),
                Some(pid) => pid,
            };
            let start = match slots[0] {
                None => return Ok(None),
                Some(s) => s.get(),
            };
            let end = match slots[1] {
                None => return Ok(None),
                Some(s) => s.get(),
            };
            return Ok(Some(Match::new(pid, Span { start, end })));
        }
        let ginfo = self.get_nfa().group_info();
        let slots_len = ginfo.implicit_slot_len();
        let mut slots = vec![None; slots_len];
        let pid = match self.try_search_slots(cache, &input, &mut slots)? {
            None => return Ok(None),
            Some(pid) => pid,
        };
        let start = match slots[pid.as_usize() * 2] {
            None => return Ok(None),
            Some(s) => s.get(),
        };
        let end = match slots[pid.as_usize() * 2 + 1] {
            None => return Ok(None),
            Some(s) => s.get(),
        };
        Ok(Some(Match::new(pid, Span { start, end })))
    }

    /// Executes a leftmost forward search and writes the spans of capturing
    /// groups that participated in a match into the provided [`Captures`]
    /// value. If no match was found, then [`Captures::is_match`] is guaranteed
    /// to return `false`.
    ///
    /// # Errors
    ///
    /// This routine only errors if the search could not complete. For this
    /// backtracking regex engine, this only occurs when the haystack length
    /// exceeds [`BoundedBacktracker::max_haystack_len`].
    ///
    /// When a search cannot complete, callers cannot know whether a match
    /// exists or not.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Span,
    /// };
    ///
    /// let re = BoundedBacktracker::new(
    ///     r"^([0-9]{4})-([0-9]{2})-([0-9]{2})$",
    /// )?;
    /// let (mut cache, mut caps) = (re.create_cache(), re.create_captures());
    ///
    /// re.try_captures(&mut cache, "2010-03-14", &mut caps)?;
    /// assert!(caps.is_match());
    /// assert_eq!(Some(Span::from(0..4)), caps.get_group(1));
    /// assert_eq!(Some(Span::from(5..7)), caps.get_group(2));
    /// assert_eq!(Some(Span::from(8..10)), caps.get_group(3));
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_captures<'h, I: Into<Input<'h>>>(
        &self,
        cache: &mut Cache,
        input: I,
        caps: &mut Captures,
    ) -> Result<(), MatchError> {
        self.try_search(cache, &input.into(), caps)
    }

    /// Returns an iterator over all non-overlapping leftmost matches in the
    /// given bytes. If no match exists, then the iterator yields no elements.
    ///
    /// If the regex engine returns an error at any point, then the iterator
    /// will yield that error.
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match, MatchError,
    /// };
    ///
    /// let re = BoundedBacktracker::new("foo[0-9]+")?;
    /// let mut cache = re.create_cache();
    ///
    /// let text = "foo1 foo12 foo123";
    /// let result: Result<Vec<Match>, MatchError> = re
    ///     .try_find_iter(&mut cache, text)
    ///     .collect();
    /// let matches = result?;
    /// assert_eq!(matches, vec![
    ///     Match::must(0, 0..4),
    ///     Match::must(0, 5..10),
    ///     Match::must(0, 11..17),
    /// ]);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_find_iter<'r, 'c, 'h, I: Into<Input<'h>>>(
        &'r self,
        cache: &'c mut Cache,
        input: I,
    ) -> TryFindMatches<'r, 'c, 'h> {
        let caps = Captures::matches(self.get_nfa().group_info().clone());
        let it = iter::Searcher::new(input.into());
        TryFindMatches { re: self, cache, caps, it }
    }

    /// Returns an iterator over all non-overlapping `Captures` values. If no
    /// match exists, then the iterator yields no elements.
    ///
    /// This yields the same matches as [`BoundedBacktracker::try_find_iter`],
    /// but it includes the spans of all capturing groups that participate in
    /// each match.
    ///
    /// If the regex engine returns an error at any point, then the iterator
    /// will yield that error.
    ///
    /// **Tip:** See [`util::iter::Searcher`](crate::util::iter::Searcher) for
    /// how to correctly iterate over all matches in a haystack while avoiding
    /// the creation of a new `Captures` value for every match. (Which you are
    /// forced to do with an `Iterator`.)
    ///
    /// # Example
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Span,
    /// };
    ///
    /// let re = BoundedBacktracker::new("foo(?P<numbers>[0-9]+)")?;
    /// let mut cache = re.create_cache();
    ///
    /// let text = "foo1 foo12 foo123";
    /// let mut spans = vec![];
    /// for result in re.try_captures_iter(&mut cache, text) {
    ///     let caps = result?;
    ///     // The unwrap is OK since 'numbers' matches if the pattern matches.
    ///     spans.push(caps.get_group_by_name("numbers").unwrap());
    /// }
    /// assert_eq!(spans, vec![
    ///     Span::from(3..4),
    ///     Span::from(8..10),
    ///     Span::from(14..17),
    /// ]);
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_captures_iter<'r, 'c, 'h, I: Into<Input<'h>>>(
        &'r self,
        cache: &'c mut Cache,
        input: I,
    ) -> TryCapturesMatches<'r, 'c, 'h> {
        let caps = self.create_captures();
        let it = iter::Searcher::new(input.into());
        TryCapturesMatches { re: self, cache, caps, it }
    }
}

impl BoundedBacktracker {
    /// Executes a leftmost forward search and writes the spans of capturing
    /// groups that participated in a match into the provided [`Captures`]
    /// value. If no match was found, then [`Captures::is_match`] is guaranteed
    /// to return `false`.
    ///
    /// This is like [`BoundedBacktracker::try_captures`], but it accepts a
    /// concrete `&Input` instead of an `Into<Input>`.
    ///
    /// # Errors
    ///
    /// This routine only errors if the search could not complete. For this
    /// backtracking regex engine, this only occurs when the haystack length
    /// exceeds [`BoundedBacktracker::max_haystack_len`].
    ///
    /// When a search cannot complete, callers cannot know whether a match
    /// exists or not.
    ///
    /// # Example: specific pattern search
    ///
    /// This example shows how to build a multi bounded backtracker that
    /// permits searching for specific patterns.
    ///
    /// ```
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Anchored, Input, Match, PatternID,
    /// };
    ///
    /// let re = BoundedBacktracker::new_many(&[
    ///     "[a-z0-9]{6}",
    ///     "[a-z][a-z0-9]{5}",
    /// ])?;
    /// let (mut cache, mut caps) = (re.create_cache(), re.create_captures());
    /// let haystack = "foo123";
    ///
    /// // Since we are using the default leftmost-first match and both
    /// // patterns match at the same starting position, only the first pattern
    /// // will be returned in this case when doing a search for any of the
    /// // patterns.
    /// let expected = Some(Match::must(0, 0..6));
    /// re.try_search(&mut cache, &Input::new(haystack), &mut caps)?;
    /// assert_eq!(expected, caps.get_match());
    ///
    /// // But if we want to check whether some other pattern matches, then we
    /// // can provide its pattern ID.
    /// let expected = Some(Match::must(1, 0..6));
    /// let input = Input::new(haystack)
    ///     .anchored(Anchored::Pattern(PatternID::must(1)));
    /// re.try_search(&mut cache, &input, &mut caps)?;
    /// assert_eq!(expected, caps.get_match());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// # Example: specifying the bounds of a search
    ///
    /// This example shows how providing the bounds of a search can produce
    /// different results than simply sub-slicing the haystack.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match, Input,
    /// };
    ///
    /// let re = BoundedBacktracker::new(r"\b[0-9]{3}\b")?;
    /// let (mut cache, mut caps) = (re.create_cache(), re.create_captures());
    /// let haystack = "foo123bar";
    ///
    /// // Since we sub-slice the haystack, the search doesn't know about
    /// // the larger context and assumes that `123` is surrounded by word
    /// // boundaries. And of course, the match position is reported relative
    /// // to the sub-slice as well, which means we get `0..3` instead of
    /// // `3..6`.
    /// let expected = Some(Match::must(0, 0..3));
    /// re.try_search(&mut cache, &Input::new(&haystack[3..6]), &mut caps)?;
    /// assert_eq!(expected, caps.get_match());
    ///
    /// // But if we provide the bounds of the search within the context of the
    /// // entire haystack, then the search can take the surrounding context
    /// // into account. (And if we did find a match, it would be reported
    /// // as a valid offset into `haystack` instead of its sub-slice.)
    /// let expected = None;
    /// re.try_search(
    ///     &mut cache, &Input::new(haystack).range(3..6), &mut caps,
    /// )?;
    /// assert_eq!(expected, caps.get_match());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_search(
        &self,
        cache: &mut Cache,
        input: &Input<'_>,
        caps: &mut Captures,
    ) -> Result<(), MatchError> {
        caps.set_pattern(None);
        let pid = self.try_search_slots(cache, input, caps.slots_mut())?;
        caps.set_pattern(pid);
        Ok(())
    }

    /// Executes a leftmost forward search and writes the spans of capturing
    /// groups that participated in a match into the provided `slots`, and
    /// returns the matching pattern ID. The contents of the slots for patterns
    /// other than the matching pattern are unspecified. If no match was found,
    /// then `None` is returned and the contents of all `slots` is unspecified.
    ///
    /// This is like [`BoundedBacktracker::try_search`], but it accepts a raw
    /// slots slice instead of a `Captures` value. This is useful in contexts
    /// where you don't want or need to allocate a `Captures`.
    ///
    /// It is legal to pass _any_ number of slots to this routine. If the regex
    /// engine would otherwise write a slot offset that doesn't fit in the
    /// provided slice, then it is simply skipped. In general though, there are
    /// usually three slice lengths you might want to use:
    ///
    /// * An empty slice, if you only care about which pattern matched.
    /// * A slice with
    /// [`pattern_len() * 2`](crate::nfa::thompson::NFA::pattern_len)
    /// slots, if you only care about the overall match spans for each matching
    /// pattern.
    /// * A slice with
    /// [`slot_len()`](crate::util::captures::GroupInfo::slot_len) slots, which
    /// permits recording match offsets for every capturing group in every
    /// pattern.
    ///
    /// # Errors
    ///
    /// This routine only errors if the search could not complete. For this
    /// backtracking regex engine, this only occurs when the haystack length
    /// exceeds [`BoundedBacktracker::max_haystack_len`].
    ///
    /// When a search cannot complete, callers cannot know whether a match
    /// exists or not.
    ///
    /// # Example
    ///
    /// This example shows how to find the overall match offsets in a
    /// multi-pattern search without allocating a `Captures` value. Indeed, we
    /// can put our slots right on the stack.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     PatternID, Input,
    /// };
    ///
    /// let re = BoundedBacktracker::new_many(&[
    ///     r"\pL+",
    ///     r"\d+",
    /// ])?;
    /// let mut cache = re.create_cache();
    /// let input = Input::new("!@#123");
    ///
    /// // We only care about the overall match offsets here, so we just
    /// // allocate two slots for each pattern. Each slot records the start
    /// // and end of the match.
    /// let mut slots = [None; 4];
    /// let pid = re.try_search_slots(&mut cache, &input, &mut slots)?;
    /// assert_eq!(Some(PatternID::must(1)), pid);
    ///
    /// // The overall match offsets are always at 'pid * 2' and 'pid * 2 + 1'.
    /// // See 'GroupInfo' for more details on the mapping between groups and
    /// // slot indices.
    /// let slot_start = pid.unwrap().as_usize() * 2;
    /// let slot_end = slot_start + 1;
    /// assert_eq!(Some(3), slots[slot_start].map(|s| s.get()));
    /// assert_eq!(Some(6), slots[slot_end].map(|s| s.get()));
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn try_search_slots(
        &self,
        cache: &mut Cache,
        input: &Input<'_>,
        slots: &mut [Option<NonMaxUsize>],
    ) -> Result<Option<PatternID>, MatchError> {
        let utf8empty = self.get_nfa().has_empty() && self.get_nfa().is_utf8();
        if !utf8empty {
            let maybe_hm = self.try_search_slots_imp(cache, input, slots)?;
            return Ok(maybe_hm.map(|hm| hm.pattern()));
        }
        // See PikeVM::try_search_slots for why we do this.
        let min = self.get_nfa().group_info().implicit_slot_len();
        if slots.len() >= min {
            let maybe_hm = self.try_search_slots_imp(cache, input, slots)?;
            return Ok(maybe_hm.map(|hm| hm.pattern()));
        }
        if self.get_nfa().pattern_len() == 1 {
            let mut enough = [None, None];
            let got = self.try_search_slots_imp(cache, input, &mut enough)?;
            // This is OK because we know `enough_slots` is strictly bigger
            // than `slots`, otherwise this special case isn't reached.
            slots.copy_from_slice(&enough[..slots.len()]);
            return Ok(got.map(|hm| hm.pattern()));
        }
        let mut enough = vec![None; min];
        let got = self.try_search_slots_imp(cache, input, &mut enough)?;
        // This is OK because we know `enough_slots` is strictly bigger than
        // `slots`, otherwise this special case isn't reached.
        slots.copy_from_slice(&enough[..slots.len()]);
        Ok(got.map(|hm| hm.pattern()))
    }

    /// This is the actual implementation of `try_search_slots_imp` that
    /// doesn't account for the special case when 1) the NFA has UTF-8 mode
    /// enabled, 2) the NFA can match the empty string and 3) the caller has
    /// provided an insufficient number of slots to record match offsets.
    #[inline(never)]
    fn try_search_slots_imp(
        &self,
        cache: &mut Cache,
        input: &Input<'_>,
        slots: &mut [Option<NonMaxUsize>],
    ) -> Result<Option<HalfMatch>, MatchError> {
        let utf8empty = self.get_nfa().has_empty() && self.get_nfa().is_utf8();
        let hm = match self.search_imp(cache, input, slots)? {
            None => return Ok(None),
            Some(hm) if !utf8empty => return Ok(Some(hm)),
            Some(hm) => hm,
        };
        empty::skip_splits_fwd(input, hm, hm.offset(), |input| {
            Ok(self
                .search_imp(cache, input, slots)?
                .map(|hm| (hm, hm.offset())))
        })
    }

    /// The implementation of standard leftmost backtracking search.
    ///
    /// Capturing group spans are written to 'caps', but only if requested.
    /// 'caps' can be one of three things: 1) totally empty, in which case, we
    /// only report the pattern that matched or 2) only has slots for recording
    /// the overall match offsets for any pattern or 3) has all slots available
    /// for recording the spans of any groups participating in a match.
    fn search_imp(
        &self,
        cache: &mut Cache,
        input: &Input<'_>,
        slots: &mut [Option<NonMaxUsize>],
    ) -> Result<Option<HalfMatch>, MatchError> {
        // Unlike in the PikeVM, we write our capturing group spans directly
        // into the caller's captures groups. So we have to make sure we're
        // starting with a blank slate first. In the PikeVM, we avoid this
        // by construction: the spans that are copied to every slot in the
        // 'Captures' value already account for presence/absence. In this
        // backtracker, we write directly into the caller provided slots, where
        // as in the PikeVM, we write into scratch space first and only copy
        // them to the caller provided slots when a match is found.
        for slot in slots.iter_mut() {
            *slot = None;
        }
        cache.setup_search(&self, input)?;
        if input.is_done() {
            return Ok(None);
        }
        let (anchored, start_id) = match input.get_anchored() {
            // Only way we're unanchored is if both the caller asked for an
            // unanchored search *and* the pattern is itself not anchored.
            Anchored::No => (
                self.nfa.is_always_start_anchored(),
                // We always use the anchored starting state here, even if
                // doing an unanchored search. The "unanchored" part of it is
                // implemented in the loop below, by simply trying the next
                // byte offset if the previous backtracking exploration failed.
                self.nfa.start_anchored(),
            ),
            Anchored::Yes => (true, self.nfa.start_anchored()),
            Anchored::Pattern(pid) => match self.nfa.start_pattern(pid) {
                None => return Ok(None),
                Some(sid) => (true, sid),
            },
        };
        if anchored {
            let at = input.start();
            return Ok(self.backtrack(cache, input, at, start_id, slots));
        }
        let pre = self.get_config().get_prefilter();
        let mut at = input.start();
        while at <= input.end() {
            if let Some(ref pre) = pre {
                let span = Span::from(at..input.end());
                match pre.find(input.haystack(), span) {
                    None => break,
                    Some(ref span) => at = span.start,
                }
            }
            if let Some(hm) = self.backtrack(cache, input, at, start_id, slots)
            {
                return Ok(Some(hm));
            }
            at += 1;
        }
        Ok(None)
    }

    /// Look for a match starting at `at` in `input` and write the matching
    /// pattern ID and group spans to `caps`. The search uses `start_id` as its
    /// starting state in the underlying NFA.
    ///
    /// If no match was found, then the caller should increment `at` and try
    /// at the next position.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn backtrack(
        &self,
        cache: &mut Cache,
        input: &Input<'_>,
        at: usize,
        start_id: StateID,
        slots: &mut [Option<NonMaxUsize>],
    ) -> Option<HalfMatch> {
        cache.stack.push(Frame::Step { sid: start_id, at });
        while let Some(frame) = cache.stack.pop() {
            match frame {
                Frame::Step { sid, at } => {
                    if let Some(hm) = self.step(cache, input, sid, at, slots) {
                        return Some(hm);
                    }
                }
                Frame::RestoreCapture { slot, offset } => {
                    slots[slot] = offset;
                }
            }
        }
        None
    }

    // LAMENTATION: The actual backtracking search is implemented in about
    // 75 lines below. Yet this file is over 2,000 lines long. What have I
    // done?

    /// Execute a "step" in the backtracing algorithm.
    ///
    /// A "step" is somewhat of a misnomer, because this routine keeps going
    /// until it either runs out of things to try or fins a match. In the
    /// former case, it may have pushed some things on to the backtracking
    /// stack, in which case, those will be tried next as part of the
    /// 'backtrack' routine above.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn step(
        &self,
        cache: &mut Cache,
        input: &Input<'_>,
        mut sid: StateID,
        mut at: usize,
        slots: &mut [Option<NonMaxUsize>],
    ) -> Option<HalfMatch> {
        loop {
            if !cache.visited.insert(sid, at - input.start()) {
                return None;
            }
            match *self.nfa.state(sid) {
                State::ByteRange { ref trans } => {
                    // Why do we need this? Unlike other regex engines in this
                    // crate, the backtracker can steam roll ahead in the
                    // haystack outside of the main loop over the bytes in the
                    // haystack. While 'trans.matches()' below handles the case
                    // of 'at' being out of bounds of 'input.haystack()', we
                    // also need to handle the case of 'at' going out of bounds
                    // of the span the caller asked to search.
                    //
                    // We should perhaps make the 'trans.matches()' API accept
                    // an '&Input' instead of a '&[u8]'. Or at least, add a new
                    // API that does it.
                    if at >= input.end() {
                        return None;
                    }
                    if !trans.matches(input.haystack(), at) {
                        return None;
                    }
                    sid = trans.next;
                    at += 1;
                }
                State::Sparse(ref sparse) => {
                    if at >= input.end() {
                        return None;
                    }
                    sid = sparse.matches(input.haystack(), at)?;
                    at += 1;
                }
                State::Dense(ref dense) => {
                    if at >= input.end() {
                        return None;
                    }
                    sid = dense.matches(input.haystack(), at)?;
                    at += 1;
                }
                State::Look { look, next } => {
                    // OK because we don't permit building a searcher with a
                    // Unicode word boundary if the requisite Unicode data is
                    // unavailable.
                    if !self.nfa.look_matcher().matches_inline(
                        look,
                        input.haystack(),
                        at,
                    ) {
                        return None;
                    }
                    sid = next;
                }
                State::Union { ref alternates } => {
                    sid = match alternates.get(0) {
                        None => return None,
                        Some(&sid) => sid,
                    };
                    cache.stack.extend(
                        alternates[1..]
                            .iter()
                            .copied()
                            .rev()
                            .map(|sid| Frame::Step { sid, at }),
                    );
                }
                State::BinaryUnion { alt1, alt2 } => {
                    sid = alt1;
                    cache.stack.push(Frame::Step { sid: alt2, at });
                }
                State::Capture { next, slot, .. } => {
                    if slot.as_usize() < slots.len() {
                        cache.stack.push(Frame::RestoreCapture {
                            slot,
                            offset: slots[slot],
                        });
                        slots[slot] = NonMaxUsize::new(at);
                    }
                    sid = next;
                }
                State::Fail => return None,
                State::Match { pattern_id } => {
                    return Some(HalfMatch::new(pattern_id, at));
                }
            }
        }
    }
}

/// An iterator over all non-overlapping matches for a fallible search.
///
/// The iterator yields a `Result<Match, MatchError` value until no more
/// matches could be found.
///
/// The lifetime parameters are as follows:
///
/// * `'r` represents the lifetime of the BoundedBacktracker.
/// * `'c` represents the lifetime of the BoundedBacktracker's cache.
/// * `'h` represents the lifetime of the haystack being searched.
///
/// This iterator can be created with the [`BoundedBacktracker::try_find_iter`]
/// method.
#[derive(Debug)]
pub struct TryFindMatches<'r, 'c, 'h> {
    re: &'r BoundedBacktracker,
    cache: &'c mut Cache,
    caps: Captures,
    it: iter::Searcher<'h>,
}

impl<'r, 'c, 'h> Iterator for TryFindMatches<'r, 'c, 'h> {
    type Item = Result<Match, MatchError>;

    #[inline]
    fn next(&mut self) -> Option<Result<Match, MatchError>> {
        // Splitting 'self' apart seems necessary to appease borrowck.
        let TryFindMatches { re, ref mut cache, ref mut caps, ref mut it } =
            *self;
        it.try_advance(|input| {
            re.try_search(cache, input, caps)?;
            Ok(caps.get_match())
        })
        .transpose()
    }
}

/// An iterator over all non-overlapping leftmost matches, with their capturing
/// groups, for a fallible search.
///
/// The iterator yields a `Result<Captures, MatchError>` value until no more
/// matches could be found.
///
/// The lifetime parameters are as follows:
///
/// * `'r` represents the lifetime of the BoundedBacktracker.
/// * `'c` represents the lifetime of the BoundedBacktracker's cache.
/// * `'h` represents the lifetime of the haystack being searched.
///
/// This iterator can be created with the
/// [`BoundedBacktracker::try_captures_iter`] method.
#[derive(Debug)]
pub struct TryCapturesMatches<'r, 'c, 'h> {
    re: &'r BoundedBacktracker,
    cache: &'c mut Cache,
    caps: Captures,
    it: iter::Searcher<'h>,
}

impl<'r, 'c, 'h> Iterator for TryCapturesMatches<'r, 'c, 'h> {
    type Item = Result<Captures, MatchError>;

    #[inline]
    fn next(&mut self) -> Option<Result<Captures, MatchError>> {
        // Splitting 'self' apart seems necessary to appease borrowck.
        let TryCapturesMatches { re, ref mut cache, ref mut caps, ref mut it } =
            *self;
        let _ = it
            .try_advance(|input| {
                re.try_search(cache, input, caps)?;
                Ok(caps.get_match())
            })
            .transpose()?;
        if caps.is_match() {
            Some(Ok(caps.clone()))
        } else {
            None
        }
    }
}

/// A cache represents mutable state that a [`BoundedBacktracker`] requires
/// during a search.
///
/// For a given [`BoundedBacktracker`], its corresponding cache may be created
/// either via [`BoundedBacktracker::create_cache`], or via [`Cache::new`].
/// They are equivalent in every way, except the former does not require
/// explicitly importing `Cache`.
///
/// A particular `Cache` is coupled with the [`BoundedBacktracker`] from which
/// it was created. It may only be used with that `BoundedBacktracker`. A cache
/// and its allocations may be re-purposed via [`Cache::reset`], in which case,
/// it can only be used with the new `BoundedBacktracker` (and not the old
/// one).
#[derive(Clone, Debug)]
pub struct Cache {
    /// Stack used on the heap for doing backtracking instead of the
    /// traditional recursive approach. We don't want recursion because then
    /// we're likely to hit a stack overflow for bigger regexes.
    stack: Vec<Frame>,
    /// The set of (StateID, HaystackOffset) pairs that have been visited
    /// by the backtracker within a single search. If such a pair has been
    /// visited, then we avoid doing the work for that pair again. This is
    /// what "bounds" the backtracking and prevents it from having worst case
    /// exponential time.
    visited: Visited,
}

impl Cache {
    /// Create a new [`BoundedBacktracker`] cache.
    ///
    /// A potentially more convenient routine to create a cache is
    /// [`BoundedBacktracker::create_cache`], as it does not require also
    /// importing the `Cache` type.
    ///
    /// If you want to reuse the returned `Cache` with some other
    /// `BoundedBacktracker`, then you must call [`Cache::reset`] with the
    /// desired `BoundedBacktracker`.
    pub fn new(re: &BoundedBacktracker) -> Cache {
        Cache { stack: vec![], visited: Visited::new(re) }
    }

    /// Reset this cache such that it can be used for searching with different
    /// [`BoundedBacktracker`].
    ///
    /// A cache reset permits reusing memory already allocated in this cache
    /// with a different `BoundedBacktracker`.
    ///
    /// # Example
    ///
    /// This shows how to re-purpose a cache for use with a different
    /// `BoundedBacktracker`.
    ///
    /// ```
    /// # if cfg!(miri) { return Ok(()); } // miri takes too long
    /// use regex_automata::{
    ///     nfa::thompson::backtrack::BoundedBacktracker,
    ///     Match,
    /// };
    ///
    /// let re1 = BoundedBacktracker::new(r"\w")?;
    /// let re2 = BoundedBacktracker::new(r"\W")?;
    ///
    /// let mut cache = re1.create_cache();
    /// assert_eq!(
    ///     Some(Ok(Match::must(0, 0..2))),
    ///     re1.try_find_iter(&mut cache, "Δ").next(),
    /// );
    ///
    /// // Using 'cache' with re2 is not allowed. It may result in panics or
    /// // incorrect results. In order to re-purpose the cache, we must reset
    /// // it with the BoundedBacktracker we'd like to use it with.
    /// //
    /// // Similarly, after this reset, using the cache with 're1' is also not
    /// // allowed.
    /// cache.reset(&re2);
    /// assert_eq!(
    ///     Some(Ok(Match::must(0, 0..3))),
    ///     re2.try_find_iter(&mut cache, "☃").next(),
    /// );
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn reset(&mut self, re: &BoundedBacktracker) {
        self.visited.reset(re);
    }

    /// Returns the heap memory usage, in bytes, of this cache.
    ///
    /// This does **not** include the stack size used up by this cache. To
    /// compute that, use `std::mem::size_of::<Cache>()`.
    pub fn memory_usage(&self) -> usize {
        self.stack.len() * core::mem::size_of::<Frame>()
            + self.visited.memory_usage()
    }

    /// Clears this cache. This should be called at the start of every search
    /// to ensure we start with a clean slate.
    ///
    /// This also sets the length of the capturing groups used in the current
    /// search. This permits an optimization where by 'SlotTable::for_state'
    /// only returns the number of slots equivalent to the number of slots
    /// given in the 'Captures' value. This may be less than the total number
    /// of possible slots, e.g., when one only wants to track overall match
    /// offsets. This in turn permits less copying of capturing group spans
    /// in the BoundedBacktracker.
    fn setup_search(
        &mut self,
        re: &BoundedBacktracker,
        input: &Input<'_>,
    ) -> Result<(), MatchError> {
        self.stack.clear();
        self.visited.setup_search(re, input)?;
        Ok(())
    }
}

/// Represents a stack frame on the heap while doing backtracking.
///
/// Instead of using explicit recursion for backtracking, we use a stack on
/// the heap to keep track of things that we want to explore if the current
/// backtracking branch turns out to not lead to a match.
#[derive(Clone, Debug)]
enum Frame {
    /// Look for a match starting at `sid` and the given position in the
    /// haystack.
    Step { sid: StateID, at: usize },
    /// Reset the given `slot` to the given `offset` (which might be `None`).
    /// This effectively gives a "scope" to capturing groups, such that an
    /// offset for a particular group only gets returned if the match goes
    /// through that capturing group. If backtracking ends up going down a
    /// different branch that results in a different offset (or perhaps none at
    /// all), then this "restore capture" frame will cause the offset to get
    /// reset.
    RestoreCapture { slot: SmallIndex, offset: Option<NonMaxUsize> },
}

/// A bitset that keeps track of whether a particular (StateID, offset) has
/// been considered during backtracking. If it has already been visited, then
/// backtracking skips it. This is what gives backtracking its "bound."
#[derive(Clone, Debug)]
struct Visited {
    /// The actual underlying bitset. Each element in the bitset corresponds
    /// to a particular (StateID, offset) pair. States correspond to the rows
    /// and the offsets correspond to the columns.
    ///
    /// If our underlying NFA has N states and the haystack we're searching
    /// has M bytes, then we have N*(M+1) entries in our bitset table. The
    /// M+1 occurs because our matches are delayed by one byte (to support
    /// look-around), and so we need to handle the end position itself rather
    /// than stopping just before the end. (If there is no end position, then
    /// it's treated as "end-of-input," which is matched by things like '$'.)
    ///
    /// Given BITS=N*(M+1), we wind up with div_ceil(BITS, sizeof(usize))
    /// blocks.
    ///
    /// We use 'usize' to represent our blocks because it makes some of the
    /// arithmetic in 'insert' a bit nicer. For example, if we used 'u32' for
    /// our block, we'd either need to cast u32s to usizes or usizes to u32s.
    bitset: Vec<usize>,
    /// The stride represents one plus length of the haystack we're searching
    /// (as described above). The stride must be initialized for each search.
    stride: usize,
}

impl Visited {
    /// The size of each block, in bits.
    const BLOCK_SIZE: usize = 8 * core::mem::size_of::<usize>();

    /// Create a new visited set for the given backtracker.
    ///
    /// The set is ready to use, but must be setup at the beginning of each
    /// search by calling `setup_search`.
    fn new(re: &BoundedBacktracker) -> Visited {
        let mut visited = Visited { bitset: vec![], stride: 0 };
        visited.reset(re);
        visited
    }

    /// Insert the given (StateID, offset) pair into this set. If it already
    /// exists, then this is a no-op and it returns false. Otherwise this
    /// returns true.
    fn insert(&mut self, sid: StateID, at: usize) -> bool {
        let table_index = sid.as_usize() * self.stride + at;
        let block_index = table_index / Visited::BLOCK_SIZE;
        let bit = table_index % Visited::BLOCK_SIZE;
        let block_with_bit = 1 << bit;
        if self.bitset[block_index] & block_with_bit != 0 {
            return false;
        }
        self.bitset[block_index] |= block_with_bit;
        true
    }

    /// Reset this visited set to work with the given bounded backtracker.
    fn reset(&mut self, _: &BoundedBacktracker) {
        self.bitset.truncate(0);
    }

    /// Setup this visited set to work for a search using the given NFA
    /// and input configuration. The NFA must be the same NFA used by the
    /// BoundedBacktracker given to Visited::reset. Failing to call this might
    /// result in panics or silently incorrect search behavior.
    fn setup_search(
        &mut self,
        re: &BoundedBacktracker,
        input: &Input<'_>,
    ) -> Result<(), MatchError> {
        // Our haystack length is only the length of the span of the entire
        // haystack that we'll be searching.
        let haylen = input.get_span().len();
        let err = || MatchError::haystack_too_long(haylen);
        // Our stride is one more than the length of the input because our main
        // search loop includes the position at input.end(). (And it does this
        // because matches are delayed by one byte to account for look-around.)
        self.stride = haylen + 1;
        let needed_capacity =
            match re.get_nfa().states().len().checked_mul(self.stride) {
                None => return Err(err()),
                Some(capacity) => capacity,
            };
        let max_capacity = 8 * re.get_config().get_visited_capacity();
        if needed_capacity > max_capacity {
            return Err(err());
        }
        let needed_blocks = div_ceil(needed_capacity, Visited::BLOCK_SIZE);
        self.bitset.truncate(needed_blocks);
        for block in self.bitset.iter_mut() {
            *block = 0;
        }
        if needed_blocks > self.bitset.len() {
            self.bitset.resize(needed_blocks, 0);
        }
        Ok(())
    }

    /// Return the heap memory usage, in bytes, of this visited set.
    fn memory_usage(&self) -> usize {
        self.bitset.len() * core::mem::size_of::<usize>()
    }
}

/// Integer division, but rounds up instead of down.
fn div_ceil(lhs: usize, rhs: usize) -> usize {
    if lhs % rhs == 0 {
        lhs / rhs
    } else {
        (lhs / rhs) + 1
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    // This is a regression test for the maximum haystack length computation.
    // Previously, it assumed that the total capacity of the backtracker's
    // bitset would always be greater than the number of NFA states. But there
    // is of course no guarantee that this is true. This regression test
    // ensures that not only does `max_haystack_len` not panic, but that it
    // should return `0`.
    #[cfg(feature = "syntax")]
    #[test]
    fn max_haystack_len_overflow() {
        let re = BoundedBacktracker::builder()
            .configure(BoundedBacktracker::config().visited_capacity(10))
            .build(r"[0-9A-Za-z]{100}")
            .unwrap();
        assert_eq!(0, re.max_haystack_len());
    }
}