regex_automata/dfa/

determinize.rs

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

use crate::{
    dfa::{
        dense::{self, BuildError},
        DEAD,
    },
    nfa::thompson,
    util::{
        self,
        alphabet::{self, ByteSet},
        determinize::{State, StateBuilderEmpty, StateBuilderNFA},
        primitives::{PatternID, StateID},
        search::{Anchored, MatchKind},
        sparse_set::SparseSets,
        start::Start,
    },
};

/// A builder for configuring and running a DFA determinizer.
#[derive(Clone, Debug)]
pub(crate) struct Config {
    match_kind: MatchKind,
    quit: ByteSet,
    dfa_size_limit: Option<usize>,
    determinize_size_limit: Option<usize>,
}

impl Config {
    /// Create a new default config for a determinizer. The determinizer may be
    /// configured before calling `run`.
    pub fn new() -> Config {
        Config {
            match_kind: MatchKind::LeftmostFirst,
            quit: ByteSet::empty(),
            dfa_size_limit: None,
            determinize_size_limit: None,
        }
    }

    /// Run determinization on the given NFA and write the resulting DFA into
    /// the one given. The DFA given should be initialized but otherwise empty.
    /// "Initialized" means that it is setup to handle the NFA's byte classes,
    /// number of patterns and whether to build start states for each pattern.
    pub fn run(
        &self,
        nfa: &thompson::NFA,
        dfa: &mut dense::OwnedDFA,
    ) -> Result<(), BuildError> {
        let dead = State::dead();
        let quit = State::dead();
        let mut cache = StateMap::default();
        // We only insert the dead state here since its representation is
        // identical to the quit state. And we never want anything pointing
        // to the quit state other than specific transitions derived from the
        // determinizer's configured "quit" bytes.
        //
        // We do put the quit state into 'builder_states' below. This ensures
        // that a proper DFA state ID is allocated for it, and that no other
        // DFA state uses the "location after the DEAD state." That is, it
        // is assumed that the quit state is always the state immediately
        // following the DEAD state.
        cache.insert(dead.clone(), DEAD);

        let runner = Runner {
            config: self.clone(),
            nfa,
            dfa,
            builder_states: alloc::vec![dead, quit],
            cache,
            memory_usage_state: 0,
            sparses: SparseSets::new(nfa.states().len()),
            stack: alloc::vec![],
            scratch_state_builder: StateBuilderEmpty::new(),
        };
        runner.run()
    }

    /// The match semantics to use for determinization.
    ///
    /// MatchKind::All corresponds to the standard textbook construction.
    /// All possible match states are represented in the DFA.
    /// MatchKind::LeftmostFirst permits greediness and otherwise tries to
    /// simulate the match semantics of backtracking regex engines. Namely,
    /// only a subset of match states are built, and dead states are used to
    /// stop searches with an unanchored prefix.
    ///
    /// The default is MatchKind::LeftmostFirst.
    pub fn match_kind(&mut self, kind: MatchKind) -> &mut Config {
        self.match_kind = kind;
        self
    }

    /// The set of bytes to use that will cause the DFA to enter a quit state,
    /// stop searching and return an error. By default, this is empty.
    pub fn quit(&mut self, set: ByteSet) -> &mut Config {
        self.quit = set;
        self
    }

    /// The limit, in bytes of the heap, that the DFA is permitted to use. This
    /// does not include the auxiliary heap storage used by determinization.
    pub fn dfa_size_limit(&mut self, bytes: Option<usize>) -> &mut Config {
        self.dfa_size_limit = bytes;
        self
    }

    /// The limit, in bytes of the heap, that determinization itself is allowed
    /// to use. This does not include the size of the DFA being built.
    pub fn determinize_size_limit(
        &mut self,
        bytes: Option<usize>,
    ) -> &mut Config {
        self.determinize_size_limit = bytes;
        self
    }
}

/// The actual implementation of determinization that converts an NFA to a DFA
/// through powerset construction.
///
/// This determinizer roughly follows the typical powerset construction, where
/// each DFA state is comprised of one or more NFA states. In the worst case,
/// there is one DFA state for every possible combination of NFA states. In
/// practice, this only happens in certain conditions, typically when there are
/// bounded repetitions.
///
/// The main differences between this implementation and typical deteminization
/// are that this implementation delays matches by one state and hackily makes
/// look-around work. Comments below attempt to explain this.
///
/// The lifetime variable `'a` refers to the lifetime of the NFA or DFA,
/// whichever is shorter.
#[derive(Debug)]
struct Runner<'a> {
    /// The configuration used to initialize determinization.
    config: Config,
    /// The NFA we're converting into a DFA.
    nfa: &'a thompson::NFA,
    /// The DFA we're building.
    dfa: &'a mut dense::OwnedDFA,
    /// Each DFA state being built is defined as an *ordered* set of NFA
    /// states, along with some meta facts about the ordered set of NFA states.
    ///
    /// This is never empty. The first state is always a dummy state such that
    /// a state id == 0 corresponds to a dead state. The second state is always
    /// the quit state.
    ///
    /// Why do we have states in both a `Vec` and in a cache map below?
    /// Well, they serve two different roles based on access patterns.
    /// `builder_states` is the canonical home of each state, and provides
    /// constant random access by a DFA state's ID. The cache map below, on
    /// the other hand, provides a quick way of searching for identical DFA
    /// states by using the DFA state as a key in the map. Of course, we use
    /// reference counting to avoid actually duplicating the state's data
    /// itself. (Although this has never been benchmarked.) Note that the cache
    /// map does not give us full minimization; it just lets us avoid some very
    /// obvious redundant states.
    ///
    /// Note that the index into this Vec isn't quite the DFA's state ID.
    /// Rather, it's just an index. To get the state ID, you have to multiply
    /// it by the DFA's stride. That's done by self.dfa.from_index. And the
    /// inverse is self.dfa.to_index.
    ///
    /// Moreover, DFA states don't usually retain the IDs assigned to them
    /// by their position in this Vec. After determinization completes,
    /// states are shuffled around to support other optimizations. See the
    /// sibling 'special' module for more details on that. (The reason for
    /// mentioning this is that if you print out the DFA for debugging during
    /// determinization, and then print out the final DFA after it is fully
    /// built, then the state IDs likely won't match up.)
    builder_states: Vec<State>,
    /// A cache of DFA states that already exist and can be easily looked up
    /// via ordered sets of NFA states.
    ///
    /// See `builder_states` docs for why we store states in two different
    /// ways.
    cache: StateMap,
    /// The memory usage, in bytes, used by builder_states and cache. We track
    /// this as new states are added since states use a variable amount of
    /// heap. Tracking this as we add states makes it possible to compute the
    /// total amount of memory used by the determinizer in constant time.
    memory_usage_state: usize,
    /// A pair of sparse sets for tracking ordered sets of NFA state IDs.
    /// These are reused throughout determinization. A bounded sparse set
    /// gives us constant time insertion, membership testing and clearing.
    sparses: SparseSets,
    /// Scratch space for a stack of NFA states to visit, for depth first
    /// visiting without recursion.
    stack: Vec<StateID>,
    /// Scratch space for storing an ordered sequence of NFA states, for
    /// amortizing allocation. This is principally useful for when we avoid
    /// adding a new DFA state since it already exists. In order to detect this
    /// case though, we still need an ordered set of NFA state IDs. So we use
    /// this space to stage that ordered set before we know whether we need to
    /// create a new DFA state or not.
    scratch_state_builder: StateBuilderEmpty,
}

/// A map from states to state identifiers. When using std, we use a standard
/// hashmap, since it's a bit faster for this use case. (Other maps, like
/// one's based on FNV, have not yet been benchmarked.)
///
/// The main purpose of this map is to reuse states where possible. This won't
/// fully minimize the DFA, but it works well in a lot of cases.
#[cfg(feature = "std")]
type StateMap = std::collections::HashMap<State, StateID>;
#[cfg(not(feature = "std"))]
type StateMap = BTreeMap<State, StateID>;

impl<'a> Runner<'a> {
    /// Build the DFA. If there was a problem constructing the DFA (e.g., if
    /// the chosen state identifier representation is too small), then an error
    /// is returned.
    fn run(mut self) -> Result<(), BuildError> {
        if self.nfa.look_set_any().contains_word_unicode()
            && !self.config.quit.contains_range(0x80, 0xFF)
        {
            return Err(BuildError::unsupported_dfa_word_boundary_unicode());
        }

        // A sequence of "representative" bytes drawn from each equivalence
        // class. These representative bytes are fed to the NFA to compute
        // state transitions. This allows us to avoid re-computing state
        // transitions for bytes that are guaranteed to produce identical
        // results. Since computing the representatives needs to do a little
        // work, we do it once here because we'll be iterating over them a lot.
        let representatives: Vec<alphabet::Unit> =
            self.dfa.byte_classes().representatives(..).collect();
        // The set of all DFA state IDs that still need to have their
        // transitions set. We start by seeding this with all starting states.
        let mut uncompiled = alloc::vec![];
        self.add_all_starts(&mut uncompiled)?;
        while let Some(dfa_id) = uncompiled.pop() {
            for &unit in &representatives {
                if unit.as_u8().map_or(false, |b| self.config.quit.contains(b))
                {
                    continue;
                }
                // In many cases, the state we transition to has already been
                // computed. 'cached_state' will do the minimal amount of work
                // to check this, and if it exists, immediately return an
                // already existing state ID.
                let (next_dfa_id, is_new) = self.cached_state(dfa_id, unit)?;
                self.dfa.set_transition(dfa_id, unit, next_dfa_id);
                // If the state ID we got back is newly created, then we need
                // to compile it, so add it to our uncompiled frontier.
                if is_new {
                    uncompiled.push(next_dfa_id);
                }
            }
        }
        debug!(
            "determinization complete, memory usage: {}, \
             dense DFA size: {}, \
             is reverse? {}",
            self.memory_usage(),
            self.dfa.memory_usage(),
            self.nfa.is_reverse(),
        );

        // A map from DFA state ID to one or more NFA match IDs. Each NFA match
        // ID corresponds to a distinct regex pattern that matches in the state
        // corresponding to the key.
        let mut matches: BTreeMap<StateID, Vec<PatternID>> = BTreeMap::new();
        self.cache.clear();
        #[cfg(feature = "logging")]
        let mut total_pat_len = 0;
        for (i, state) in self.builder_states.into_iter().enumerate() {
            if let Some(pat_ids) = state.match_pattern_ids() {
                let id = self.dfa.to_state_id(i);
                log! {
                    total_pat_len += pat_ids.len();
                }
                matches.insert(id, pat_ids);
            }
        }
        log! {
            use core::mem::size_of;
            let per_elem = size_of::<StateID>() + size_of::<Vec<PatternID>>();
            let pats = total_pat_len * size_of::<PatternID>();
            let mem = (matches.len() * per_elem) + pats;
            log::debug!("matches map built, memory usage: {}", mem);
        }
        // At this point, we shuffle the "special" states in the final DFA.
        // This permits a DFA's match loop to detect a match condition (among
        // other things) by merely inspecting the current state's identifier,
        // and avoids the need for any additional auxiliary storage.
        self.dfa.shuffle(matches)?;
        Ok(())
    }

    /// Return the identifier for the next DFA state given an existing DFA
    /// state and an input byte. If the next DFA state already exists, then
    /// return its identifier from the cache. Otherwise, build the state, cache
    /// it and return its identifier.
    ///
    /// This routine returns a boolean indicating whether a new state was
    /// built. If a new state is built, then the caller needs to add it to its
    /// frontier of uncompiled DFA states to compute transitions for.
    fn cached_state(
        &mut self,
        dfa_id: StateID,
        unit: alphabet::Unit,
    ) -> Result<(StateID, bool), BuildError> {
        // Compute the set of all reachable NFA states, including epsilons.
        let empty_builder = self.get_state_builder();
        let builder = util::determinize::next(
            self.nfa,
            self.config.match_kind,
            &mut self.sparses,
            &mut self.stack,
            &self.builder_states[self.dfa.to_index(dfa_id)],
            unit,
            empty_builder,
        );
        self.maybe_add_state(builder)
    }

    /// Compute the set of DFA start states and add their identifiers in
    /// 'dfa_state_ids' (no duplicates are added).
    fn add_all_starts(
        &mut self,
        dfa_state_ids: &mut Vec<StateID>,
    ) -> Result<(), BuildError> {
        // These should be the first states added.
        assert!(dfa_state_ids.is_empty());
        // We only want to add (un)anchored starting states that is consistent
        // with our DFA's configuration. Unconditionally adding both (although
        // it is the default) can make DFAs quite a bit bigger.
        if self.dfa.start_kind().has_unanchored() {
            self.add_start_group(Anchored::No, dfa_state_ids)?;
        }
        if self.dfa.start_kind().has_anchored() {
            self.add_start_group(Anchored::Yes, dfa_state_ids)?;
        }
        // I previously has an 'assert' here checking that either
        // 'dfa_state_ids' was non-empty, or the NFA had zero patterns. But it
        // turns out this isn't always true. For example, the NFA might have
        // one or more patterns but where all such patterns are just 'fail'
        // states. These will ultimately just compile down to DFA dead states,
        // and since the dead state was added earlier, no new DFA states are
        // added. And thus, it is valid and okay for 'dfa_state_ids' to be
        // empty even if there are a non-zero number of patterns in the NFA.

        // We only need to compute anchored start states for each pattern if it
        // was requested to do so.
        if self.dfa.starts_for_each_pattern() {
            for pid in self.nfa.patterns() {
                self.add_start_group(Anchored::Pattern(pid), dfa_state_ids)?;
            }
        }
        Ok(())
    }

    /// Add a group of start states for the given match pattern ID. Any new
    /// DFA states added are pushed on to 'dfa_state_ids'. (No duplicates are
    /// pushed.)
    ///
    /// When pattern_id is None, then this will compile a group of unanchored
    /// start states (if the DFA is unanchored). When the pattern_id is
    /// present, then this will compile a group of anchored start states that
    /// only match the given pattern.
    ///
    /// This panics if `anchored` corresponds to an invalid pattern ID.
    fn add_start_group(
        &mut self,
        anchored: Anchored,
        dfa_state_ids: &mut Vec<StateID>,
    ) -> Result<(), BuildError> {
        let nfa_start = match anchored {
            Anchored::No => self.nfa.start_unanchored(),
            Anchored::Yes => self.nfa.start_anchored(),
            Anchored::Pattern(pid) => {
                self.nfa.start_pattern(pid).expect("valid pattern ID")
            }
        };

        // When compiling start states, we're careful not to build additional
        // states that aren't necessary. For example, if the NFA has no word
        // boundary assertion, then there's no reason to have distinct start
        // states for 'NonWordByte' and 'WordByte' starting configurations.
        // Instead, the 'WordByte' starting configuration can just point
        // directly to the start state for the 'NonWordByte' config.
        //
        // Note though that we only need to care about assertions in the prefix
        // of an NFA since this only concerns the starting states. (Actually,
        // the most precisely thing we could do it is look at the prefix
        // assertions of each pattern when 'anchored == Anchored::Pattern',
        // and then only compile extra states if the prefix is non-empty.) But
        // we settle for simplicity here instead of absolute minimalism. It is
        // somewhat rare, after all, for multiple patterns in the same regex to
        // have different prefix look-arounds.

        let (id, is_new) =
            self.add_one_start(nfa_start, Start::NonWordByte)?;
        self.dfa.set_start_state(anchored, Start::NonWordByte, id);
        if is_new {
            dfa_state_ids.push(id);
        }

        if !self.nfa.look_set_prefix_any().contains_word() {
            self.dfa.set_start_state(anchored, Start::WordByte, id);
        } else {
            let (id, is_new) =
                self.add_one_start(nfa_start, Start::WordByte)?;
            self.dfa.set_start_state(anchored, Start::WordByte, id);
            if is_new {
                dfa_state_ids.push(id);
            }
        }
        if !self.nfa.look_set_prefix_any().contains_anchor() {
            self.dfa.set_start_state(anchored, Start::Text, id);
            self.dfa.set_start_state(anchored, Start::LineLF, id);
            self.dfa.set_start_state(anchored, Start::LineCR, id);
            self.dfa.set_start_state(
                anchored,
                Start::CustomLineTerminator,
                id,
            );
        } else {
            let (id, is_new) = self.add_one_start(nfa_start, Start::Text)?;
            self.dfa.set_start_state(anchored, Start::Text, id);
            if is_new {
                dfa_state_ids.push(id);
            }

            let (id, is_new) = self.add_one_start(nfa_start, Start::LineLF)?;
            self.dfa.set_start_state(anchored, Start::LineLF, id);
            if is_new {
                dfa_state_ids.push(id);
            }

            let (id, is_new) = self.add_one_start(nfa_start, Start::LineCR)?;
            self.dfa.set_start_state(anchored, Start::LineCR, id);
            if is_new {
                dfa_state_ids.push(id);
            }

            let (id, is_new) =
                self.add_one_start(nfa_start, Start::CustomLineTerminator)?;
            self.dfa.set_start_state(
                anchored,
                Start::CustomLineTerminator,
                id,
            );
            if is_new {
                dfa_state_ids.push(id);
            }
        }

        Ok(())
    }

    /// Add a new DFA start state corresponding to the given starting NFA
    /// state, and the starting search configuration. (The starting search
    /// configuration essentially tells us which look-behind assertions are
    /// true for this particular state.)
    ///
    /// The boolean returned indicates whether the state ID returned is a newly
    /// created state, or a previously cached state.
    fn add_one_start(
        &mut self,
        nfa_start: StateID,
        start: Start,
    ) -> Result<(StateID, bool), BuildError> {
        // Compute the look-behind assertions that are true in this starting
        // configuration, and the determine the epsilon closure. While
        // computing the epsilon closure, we only follow condiional epsilon
        // transitions that satisfy the look-behind assertions in 'look_have'.
        let mut builder_matches = self.get_state_builder().into_matches();
        util::determinize::set_lookbehind_from_start(
            self.nfa,
            &start,
            &mut builder_matches,
        );
        self.sparses.set1.clear();
        util::determinize::epsilon_closure(
            self.nfa,
            nfa_start,
            builder_matches.look_have(),
            &mut self.stack,
            &mut self.sparses.set1,
        );
        let mut builder = builder_matches.into_nfa();
        util::determinize::add_nfa_states(
            &self.nfa,
            &self.sparses.set1,
            &mut builder,
        );
        self.maybe_add_state(builder)
    }

    /// Adds the given state to the DFA being built depending on whether it
    /// already exists in this determinizer's cache.
    ///
    /// If it does exist, then the memory used by 'state' is put back into the
    /// determinizer and the previously created state's ID is returned. (Along
    /// with 'false', indicating that no new state was added.)
    ///
    /// If it does not exist, then the state is added to the DFA being built
    /// and a fresh ID is allocated (if ID allocation fails, then an error is
    /// returned) and returned. (Along with 'true', indicating that a new state
    /// was added.)
    fn maybe_add_state(
        &mut self,
        builder: StateBuilderNFA,
    ) -> Result<(StateID, bool), BuildError> {
        if let Some(&cached_id) = self.cache.get(builder.as_bytes()) {
            // Since we have a cached state, put the constructed state's
            // memory back into our scratch space, so that it can be reused.
            self.put_state_builder(builder);
            return Ok((cached_id, false));
        }
        self.add_state(builder).map(|sid| (sid, true))
    }

    /// Add the given state to the DFA and make it available in the cache.
    ///
    /// The state initially has no transitions. That is, it transitions to the
    /// dead state for all possible inputs, and transitions to the quit state
    /// for all quit bytes.
    ///
    /// If adding the state would exceed the maximum value for StateID, then an
    /// error is returned.
    fn add_state(
        &mut self,
        builder: StateBuilderNFA,
    ) -> Result<StateID, BuildError> {
        let id = self.dfa.add_empty_state()?;
        if !self.config.quit.is_empty() {
            for b in self.config.quit.iter() {
                self.dfa.set_transition(
                    id,
                    alphabet::Unit::u8(b),
                    self.dfa.quit_id(),
                );
            }
        }
        let state = builder.to_state();
        // States use reference counting internally, so we only need to count
        // their memory usage once.
        self.memory_usage_state += state.memory_usage();
        self.builder_states.push(state.clone());
        self.cache.insert(state, id);
        self.put_state_builder(builder);
        if let Some(limit) = self.config.dfa_size_limit {
            if self.dfa.memory_usage() > limit {
                return Err(BuildError::dfa_exceeded_size_limit(limit));
            }
        }
        if let Some(limit) = self.config.determinize_size_limit {
            if self.memory_usage() > limit {
                return Err(BuildError::determinize_exceeded_size_limit(
                    limit,
                ));
            }
        }
        Ok(id)
    }

    /// Returns a state builder from this determinizer that might have existing
    /// capacity. This helps avoid allocs in cases where a state is built that
    /// turns out to already be cached.
    ///
    /// Callers must put the state builder back with 'put_state_builder',
    /// otherwise the allocation reuse won't work.
    fn get_state_builder(&mut self) -> StateBuilderEmpty {
        core::mem::replace(
            &mut self.scratch_state_builder,
            StateBuilderEmpty::new(),
        )
    }

    /// Puts the given state builder back into this determinizer for reuse.
    ///
    /// Note that building a 'State' from a builder always creates a new
    /// alloc, so callers should always put the builder back.
    fn put_state_builder(&mut self, builder: StateBuilderNFA) {
        let _ = core::mem::replace(
            &mut self.scratch_state_builder,
            builder.clear(),
        );
    }

    /// Return the memory usage, in bytes, of this determinizer at the current
    /// point in time. This does not include memory used by the NFA or the
    /// dense DFA itself.
    fn memory_usage(&self) -> usize {
        use core::mem::size_of;

        self.builder_states.len() * size_of::<State>()
        // Maps likely use more memory than this, but it's probably close.
        + self.cache.len() * (size_of::<State>() + size_of::<StateID>())
        + self.memory_usage_state
        + self.stack.capacity() * size_of::<StateID>()
        + self.scratch_state_builder.capacity()
    }
}