xref: /external/rust/crates/regex/src/dfa.rs

/*!
The DFA matching engine.

A DFA provides faster matching because the engine is in exactly one state at
any point in time. In the NFA, there may be multiple active states, and
considerable CPU cycles are spent shuffling them around. In finite automata
speak, the DFA follows epsilon transitions in the regex far less than the NFA.

A DFA is a classic trade off between time and space. The NFA is slower, but
its memory requirements are typically small and predictable. The DFA is faster,
but given the right regex and the right input, the number of states in the
DFA can grow exponentially. To mitigate this space problem, we do two things:

1. We implement an *online* DFA. That is, the DFA is constructed from the NFA
   during a search. When a new state is computed, it is stored in a cache so
   that it may be reused. An important consequence of this implementation
   is that states that are never reached for a particular input are never
   computed. (This is impossible in an "offline" DFA which needs to compute
   all possible states up front.)
2. If the cache gets too big, we wipe it and continue matching.

In pathological cases, a new state can be created for every byte of input.
(e.g., The regex `(a|b)*a(a|b){20}` on a long sequence of a's and b's.)
In this case, performance regresses to slightly slower than the full NFA
simulation, in large part because the cache becomes useless. If the cache
is wiped too frequently, the DFA quits and control falls back to one of the
NFA simulations.

Because of the "lazy" nature of this DFA, the inner matching loop is
considerably more complex than one might expect out of a DFA. A number of
tricks are employed to make it fast. Tread carefully.

N.B. While this implementation is heavily commented, Russ Cox's series of
articles on regexes is strongly recommended: https://swtch.com/~rsc/regexp/
(As is the DFA implementation in RE2, which heavily influenced this
implementation.)
*/

use std::collections::HashMap;
use std::fmt;
use std::iter::repeat;
use std::mem;
use std::sync::Arc;

use exec::ProgramCache;
use prog::{Inst, Program};
use sparse::SparseSet;

/// Return true if and only if the given program can be executed by a DFA.
///
/// Generally, a DFA is always possible. A pathological case where it is not
/// possible is if the number of NFA states exceeds `u32::MAX`, in which case,
/// this function will return false.
///
/// This function will also return false if the given program has any Unicode
/// instructions (Char or Ranges) since the DFA operates on bytes only.
pub fn can_exec(insts: &Program) -> bool {
    use prog::Inst::*;
    // If for some reason we manage to allocate a regex program with more
    // than i32::MAX instructions, then we can't execute the DFA because we
    // use 32 bit instruction pointer deltas for memory savings.
    // If i32::MAX is the largest positive delta,
    // then -i32::MAX == i32::MIN + 1 is the largest negative delta,
    // and we are OK to use 32 bits.
    if insts.dfa_size_limit == 0 || insts.len() > ::std::i32::MAX as usize {
        return false;
    }
    for inst in insts {
        match *inst {
            Char(_) | Ranges(_) => return false,
            EmptyLook(_) | Match(_) | Save(_) | Split(_) | Bytes(_) => {}
        }
    }
    true
}

/// A reusable cache of DFA states.
///
/// This cache is reused between multiple invocations of the same regex
/// program. (It is not shared simultaneously between threads. If there is
/// contention, then new caches are created.)
#[derive(Debug)]
pub struct Cache {
    /// Group persistent DFA related cache state together. The sparse sets
    /// listed below are used as scratch space while computing uncached states.
    inner: CacheInner,
    /// qcur and qnext are ordered sets with constant time
    /// addition/membership/clearing-whole-set and linear time iteration. They
    /// are used to manage the sets of NFA states in DFA states when computing
    /// cached DFA states. In particular, the order of the NFA states matters
    /// for leftmost-first style matching. Namely, when computing a cached
    /// state, the set of NFA states stops growing as soon as the first Match
    /// instruction is observed.
    qcur: SparseSet,
    qnext: SparseSet,
}

/// `CacheInner` is logically just a part of Cache, but groups together fields
/// that aren't passed as function parameters throughout search. (This split
/// is mostly an artifact of the borrow checker. It is happily paid.)
#[derive(Debug)]
struct CacheInner {
    /// A cache of pre-compiled DFA states, keyed by the set of NFA states
    /// and the set of empty-width flags set at the byte in the input when the
    /// state was observed.
    ///
    /// A StatePtr is effectively a `*State`, but to avoid various inconvenient
    /// things, we just pass indexes around manually. The performance impact of
    /// this is probably an instruction or two in the inner loop. However, on
    /// 64 bit, each StatePtr is half the size of a *State.
    compiled: StateMap,
    /// The transition table.
    ///
    /// The transition table is laid out in row-major order, where states are
    /// rows and the transitions for each state are columns. At a high level,
    /// given state `s` and byte `b`, the next state can be found at index
    /// `s * 256 + b`.
    ///
    /// This is, of course, a lie. A StatePtr is actually a pointer to the
    /// *start* of a row in this table. When indexing in the DFA's inner loop,
    /// this removes the need to multiply the StatePtr by the stride. Yes, it
    /// matters. This reduces the number of states we can store, but: the
    /// stride is rarely 256 since we define transitions in terms of
    /// *equivalence classes* of bytes. Each class corresponds to a set of
    /// bytes that never discriminate a distinct path through the DFA from each
    /// other.
    trans: Transitions,
    /// A set of cached start states, which are limited to the number of
    /// permutations of flags set just before the initial byte of input. (The
    /// index into this vec is a `EmptyFlags`.)
    ///
    /// N.B. A start state can be "dead" (i.e., no possible match), so we
    /// represent it with a StatePtr.
    start_states: Vec<StatePtr>,
    /// Stack scratch space used to follow epsilon transitions in the NFA.
    /// (This permits us to avoid recursion.)
    ///
    /// The maximum stack size is the number of NFA states.
    stack: Vec<InstPtr>,
    /// The total number of times this cache has been flushed by the DFA
    /// because of space constraints.
    flush_count: u64,
    /// The total heap size of the DFA's cache. We use this to determine when
    /// we should flush the cache.
    size: usize,
    /// Scratch space used when building instruction pointer lists for new
    /// states. This helps amortize allocation.
    insts_scratch_space: Vec<u8>,
}

/// The transition table.
///
/// It is laid out in row-major order, with states as rows and byte class
/// transitions as columns.
///
/// The transition table is responsible for producing valid `StatePtrs`. A
/// `StatePtr` points to the start of a particular row in this table. When
/// indexing to find the next state this allows us to avoid a multiplication
/// when computing an index into the table.
#[derive(Clone)]
struct Transitions {
    /// The table.
    table: Vec<StatePtr>,
    /// The stride.
    num_byte_classes: usize,
}

/// Fsm encapsulates the actual execution of the DFA.
#[derive(Debug)]
pub struct Fsm<'a> {
    /// prog contains the NFA instruction opcodes. DFA execution uses either
    /// the `dfa` instructions or the `dfa_reverse` instructions from
    /// `exec::ExecReadOnly`. (It never uses `ExecReadOnly.nfa`, which may have
    /// Unicode opcodes that cannot be executed by the DFA.)
    prog: &'a Program,
    /// The start state. We record it here because the pointer may change
    /// when the cache is wiped.
    start: StatePtr,
    /// The current position in the input.
    at: usize,
    /// Should we quit after seeing the first match? e.g., When the caller
    /// uses `is_match` or `shortest_match`.
    quit_after_match: bool,
    /// The last state that matched.
    ///
    /// When no match has occurred, this is set to STATE_UNKNOWN.
    ///
    /// This is only useful when matching regex sets. The last match state
    /// is useful because it contains all of the match instructions seen,
    /// thereby allowing us to enumerate which regexes in the set matched.
    last_match_si: StatePtr,
    /// The input position of the last cache flush. We use this to determine
    /// if we're thrashing in the cache too often. If so, the DFA quits so
    /// that we can fall back to the NFA algorithm.
    last_cache_flush: usize,
    /// All cached DFA information that is persisted between searches.
    cache: &'a mut CacheInner,
}

/// The result of running the DFA.
///
/// Generally, the result is either a match or not a match, but sometimes the
/// DFA runs too slowly because the cache size is too small. In that case, it
/// gives up with the intent of falling back to the NFA algorithm.
///
/// The DFA can also give up if it runs out of room to create new states, or if
/// it sees non-ASCII bytes in the presence of a Unicode word boundary.
#[derive(Clone, Debug)]
pub enum Result<T> {
    Match(T),
    NoMatch(usize),
    Quit,
}

impl<T> Result<T> {
    /// Returns true if this result corresponds to a match.
    pub fn is_match(&self) -> bool {
        match *self {
            Result::Match(_) => true,
            Result::NoMatch(_) | Result::Quit => false,
        }
    }

    /// Maps the given function onto T and returns the result.
    ///
    /// If this isn't a match, then this is a no-op.
    #[cfg(feature = "perf-literal")]
    pub fn map<U, F: FnMut(T) -> U>(self, mut f: F) -> Result<U> {
        match self {
            Result::Match(t) => Result::Match(f(t)),
            Result::NoMatch(x) => Result::NoMatch(x),
            Result::Quit => Result::Quit,
        }
    }

    /// Sets the non-match position.
    ///
    /// If this isn't a non-match, then this is a no-op.
    fn set_non_match(self, at: usize) -> Result<T> {
        match self {
            Result::NoMatch(_) => Result::NoMatch(at),
            r => r,
        }
    }
}

/// `State` is a DFA state. It contains an ordered set of NFA states (not
/// necessarily complete) and a smattering of flags.
///
/// The flags are packed into the first byte of data.
///
/// States don't carry their transitions. Instead, transitions are stored in
/// a single row-major table.
///
/// Delta encoding is used to store the instruction pointers.
/// The first instruction pointer is stored directly starting
/// at data[1], and each following pointer is stored as an offset
/// to the previous one. If a delta is in the range -127..127,
/// it is packed into a single byte; Otherwise the byte 128 (-128 as an i8)
/// is coded as a flag, followed by 4 bytes encoding the delta.
#[derive(Clone, Eq, Hash, PartialEq)]
struct State {
    data: Arc<[u8]>,
}

/// `InstPtr` is a 32 bit pointer into a sequence of opcodes (i.e., it indexes
/// an NFA state).
///
/// Throughout this library, this is usually set to `usize`, but we force a
/// `u32` here for the DFA to save on space.
type InstPtr = u32;

/// Adds ip to data using delta encoding with respect to prev.
///
/// After completion, `data` will contain `ip` and `prev` will be set to `ip`.
fn push_inst_ptr(data: &mut Vec<u8>, prev: &mut InstPtr, ip: InstPtr) {
    let delta = (ip as i32) - (*prev as i32);
    write_vari32(data, delta);
    *prev = ip;
}

struct InstPtrs<'a> {
    base: usize,
    data: &'a [u8],
}

impl<'a> Iterator for InstPtrs<'a> {
    type Item = usize;

    fn next(&mut self) -> Option<usize> {
        if self.data.is_empty() {
            return None;
        }
        let (delta, nread) = read_vari32(self.data);
        let base = self.base as i32 + delta;
        debug_assert!(base >= 0);
        debug_assert!(nread > 0);
        self.data = &self.data[nread..];
        self.base = base as usize;
        Some(self.base)
    }
}

impl State {
    fn flags(&self) -> StateFlags {
        StateFlags(self.data[0])
    }

    fn inst_ptrs(&self) -> InstPtrs {
        InstPtrs { base: 0, data: &self.data[1..] }
    }
}

/// `StatePtr` is a 32 bit pointer to the start of a row in the transition
/// table.
///
/// It has many special values. There are two types of special values:
/// sentinels and flags.
///
/// Sentinels corresponds to special states that carry some kind of
/// significance. There are three such states: unknown, dead and quit states.
///
/// Unknown states are states that haven't been computed yet. They indicate
/// that a transition should be filled in that points to either an existing
/// cached state or a new state altogether. In general, an unknown state means
/// "follow the NFA's epsilon transitions."
///
/// Dead states are states that can never lead to a match, no matter what
/// subsequent input is observed. This means that the DFA should quit
/// immediately and return the longest match it has found thus far.
///
/// Quit states are states that imply the DFA is not capable of matching the
/// regex correctly. Currently, this is only used when a Unicode word boundary
/// exists in the regex *and* a non-ASCII byte is observed.
///
/// The other type of state pointer is a state pointer with special flag bits.
/// There are two flags: a start flag and a match flag. The lower bits of both
/// kinds always contain a "valid" `StatePtr` (indicated by the `STATE_MAX`
/// mask).
///
/// The start flag means that the state is a start state, and therefore may be
/// subject to special prefix scanning optimizations.
///
/// The match flag means that the state is a match state, and therefore the
/// current position in the input (while searching) should be recorded.
///
/// The above exists mostly in the service of making the inner loop fast.
/// In particular, the inner *inner* loop looks something like this:
///
/// ```ignore
/// while state <= STATE_MAX and i < len(text):
///     state = state.next[i]
/// ```
///
/// This is nice because it lets us execute a lazy DFA as if it were an
/// entirely offline DFA (i.e., with very few instructions). The loop will
/// quit only when we need to examine a case that needs special attention.
type StatePtr = u32;

/// An unknown state means that the state has not been computed yet, and that
/// the only way to progress is to compute it.
const STATE_UNKNOWN: StatePtr = 1 << 31;

/// A dead state means that the state has been computed and it is known that
/// once it is entered, no future match can ever occur.
const STATE_DEAD: StatePtr = STATE_UNKNOWN + 1;

/// A quit state means that the DFA came across some input that it doesn't
/// know how to process correctly. The DFA should quit and another matching
/// engine should be run in its place.
const STATE_QUIT: StatePtr = STATE_DEAD + 1;

/// A start state is a state that the DFA can start in.
///
/// Note that start states have their lower bits set to a state pointer.
const STATE_START: StatePtr = 1 << 30;

/// A match state means that the regex has successfully matched.
///
/// Note that match states have their lower bits set to a state pointer.
const STATE_MATCH: StatePtr = 1 << 29;

/// The maximum state pointer. This is useful to mask out the "valid" state
/// pointer from a state with the "start" or "match" bits set.
///
/// It doesn't make sense to use this with unknown, dead or quit state
/// pointers, since those pointers are sentinels and never have their lower
/// bits set to anything meaningful.
const STATE_MAX: StatePtr = STATE_MATCH - 1;

/// Byte is a u8 in spirit, but a u16 in practice so that we can represent the
/// special EOF sentinel value.
#[derive(Copy, Clone, Debug)]
struct Byte(u16);

/// A set of flags for zero-width assertions.
#[derive(Clone, Copy, Eq, Debug, Default, Hash, PartialEq)]
struct EmptyFlags {
    start: bool,
    end: bool,
    start_line: bool,
    end_line: bool,
    word_boundary: bool,
    not_word_boundary: bool,
}

/// A set of flags describing various configurations of a DFA state. This is
/// represented by a `u8` so that it is compact.
#[derive(Clone, Copy, Eq, Default, Hash, PartialEq)]
struct StateFlags(u8);

impl Cache {
    /// Create new empty cache for the DFA engine.
    pub fn new(prog: &Program) -> Self {
        // We add 1 to account for the special EOF byte.
        let num_byte_classes = (prog.byte_classes[255] as usize + 1) + 1;
        let starts = vec![STATE_UNKNOWN; 256];
        let mut cache = Cache {
            inner: CacheInner {
                compiled: StateMap::new(num_byte_classes),
                trans: Transitions::new(num_byte_classes),
                start_states: starts,
                stack: vec![],
                flush_count: 0,
                size: 0,
                insts_scratch_space: vec![],
            },
            qcur: SparseSet::new(prog.insts.len()),
            qnext: SparseSet::new(prog.insts.len()),
        };
        cache.inner.reset_size();
        cache
    }
}

impl CacheInner {
    /// Resets the cache size to account for fixed costs, such as the program
    /// and stack sizes.
    fn reset_size(&mut self) {
        self.size = (self.start_states.len() * mem::size_of::<StatePtr>())
            + (self.stack.len() * mem::size_of::<InstPtr>());
    }
}

impl<'a> Fsm<'a> {
    #[cfg_attr(feature = "perf-inline", inline(always))]
    pub fn forward(
        prog: &'a Program,
        cache: &ProgramCache,
        quit_after_match: bool,
        text: &[u8],
        at: usize,
    ) -> Result<usize> {
        let mut cache = cache.borrow_mut();
        let cache = &mut cache.dfa;
        let mut dfa = Fsm {
            prog: prog,
            start: 0, // filled in below
            at: at,
            quit_after_match: quit_after_match,
            last_match_si: STATE_UNKNOWN,
            last_cache_flush: at,
            cache: &mut cache.inner,
        };
        let (empty_flags, state_flags) = dfa.start_flags(text, at);
        dfa.start =
            match dfa.start_state(&mut cache.qcur, empty_flags, state_flags) {
                None => return Result::Quit,
                Some(STATE_DEAD) => return Result::NoMatch(at),
                Some(si) => si,
            };
        debug_assert!(dfa.start != STATE_UNKNOWN);
        dfa.exec_at(&mut cache.qcur, &mut cache.qnext, text)
    }

    #[cfg_attr(feature = "perf-inline", inline(always))]
    pub fn reverse(
        prog: &'a Program,
        cache: &ProgramCache,
        quit_after_match: bool,
        text: &[u8],
        at: usize,
    ) -> Result<usize> {
        let mut cache = cache.borrow_mut();
        let cache = &mut cache.dfa_reverse;
        let mut dfa = Fsm {
            prog: prog,
            start: 0, // filled in below
            at: at,
            quit_after_match: quit_after_match,
            last_match_si: STATE_UNKNOWN,
            last_cache_flush: at,
            cache: &mut cache.inner,
        };
        let (empty_flags, state_flags) = dfa.start_flags_reverse(text, at);
        dfa.start =
            match dfa.start_state(&mut cache.qcur, empty_flags, state_flags) {
                None => return Result::Quit,
                Some(STATE_DEAD) => return Result::NoMatch(at),
                Some(si) => si,
            };
        debug_assert!(dfa.start != STATE_UNKNOWN);
        dfa.exec_at_reverse(&mut cache.qcur, &mut cache.qnext, text)
    }

    #[cfg_attr(feature = "perf-inline", inline(always))]
    pub fn forward_many(
        prog: &'a Program,
        cache: &ProgramCache,
        matches: &mut [bool],
        text: &[u8],
        at: usize,
    ) -> Result<usize> {
        debug_assert!(matches.len() == prog.matches.len());
        let mut cache = cache.borrow_mut();
        let cache = &mut cache.dfa;
        let mut dfa = Fsm {
            prog: prog,
            start: 0, // filled in below
            at: at,
            quit_after_match: false,
            last_match_si: STATE_UNKNOWN,
            last_cache_flush: at,
            cache: &mut cache.inner,
        };
        let (empty_flags, state_flags) = dfa.start_flags(text, at);
        dfa.start =
            match dfa.start_state(&mut cache.qcur, empty_flags, state_flags) {
                None => return Result::Quit,
                Some(STATE_DEAD) => return Result::NoMatch(at),
                Some(si) => si,
            };
        debug_assert!(dfa.start != STATE_UNKNOWN);
        let result = dfa.exec_at(&mut cache.qcur, &mut cache.qnext, text);
        if result.is_match() {
            if matches.len() == 1 {
                matches[0] = true;
            } else {
                debug_assert!(dfa.last_match_si != STATE_UNKNOWN);
                debug_assert!(dfa.last_match_si != STATE_DEAD);
                for ip in dfa.state(dfa.last_match_si).inst_ptrs() {
                    if let Inst::Match(slot) = dfa.prog[ip] {
                        matches[slot] = true;
                    }
                }
            }
        }
        result
    }

    /// Executes the DFA on a forward NFA.
    ///
    /// {qcur,qnext} are scratch ordered sets which may be non-empty.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn exec_at(
        &mut self,
        qcur: &mut SparseSet,
        qnext: &mut SparseSet,
        text: &[u8],
    ) -> Result<usize> {
        // For the most part, the DFA is basically:
        //
        //   last_match = null
        //   while current_byte != EOF:
        //     si = current_state.next[current_byte]
        //     if si is match
        //       last_match = si
        //   return last_match
        //
        // However, we need to deal with a few things:
        //
        //   1. This is an *online* DFA, so the current state's next list
        //      may not point to anywhere yet, so we must go out and compute
        //      them. (They are then cached into the current state's next list
        //      to avoid re-computation.)
        //   2. If we come across a state that is known to be dead (i.e., never
        //      leads to a match), then we can quit early.
        //   3. If the caller just wants to know if a match occurs, then we
        //      can quit as soon as we know we have a match. (Full leftmost
        //      first semantics require continuing on.)
        //   4. If we're in the start state, then we can use a pre-computed set
        //      of prefix literals to skip quickly along the input.
        //   5. After the input is exhausted, we run the DFA on one symbol
        //      that stands for EOF. This is useful for handling empty width
        //      assertions.
        //   6. We can't actually do state.next[byte]. Instead, we have to do
        //      state.next[byte_classes[byte]], which permits us to keep the
        //      'next' list very small.
        //
        // Since there's a bunch of extra stuff we need to consider, we do some
        // pretty hairy tricks to get the inner loop to run as fast as
        // possible.
        debug_assert!(!self.prog.is_reverse);

        // The last match is the currently known ending match position. It is
        // reported as an index to the most recent byte that resulted in a
        // transition to a match state and is always stored in capture slot `1`
        // when searching forwards. Its maximum value is `text.len()`.
        let mut result = Result::NoMatch(self.at);
        let (mut prev_si, mut next_si) = (self.start, self.start);
        let mut at = self.at;
        while at < text.len() {
            // This is the real inner loop. We take advantage of special bits
            // set in the state pointer to determine whether a state is in the
            // "common" case or not. Specifically, the common case is a
            // non-match non-start non-dead state that has already been
            // computed. So long as we remain in the common case, this inner
            // loop will chew through the input.
            //
            // We also unroll the loop 4 times to amortize the cost of checking
            // whether we've consumed the entire input. We are also careful
            // to make sure that `prev_si` always represents the previous state
            // and `next_si` always represents the next state after the loop
            // exits, even if it isn't always true inside the loop.
            while next_si <= STATE_MAX && at < text.len() {
                // Argument for safety is in the definition of next_si.
                prev_si = unsafe { self.next_si(next_si, text, at) };
                at += 1;
                if prev_si > STATE_MAX || at + 2 >= text.len() {
                    mem::swap(&mut prev_si, &mut next_si);
                    break;
                }
                next_si = unsafe { self.next_si(prev_si, text, at) };
                at += 1;
                if next_si > STATE_MAX {
                    break;
                }
                prev_si = unsafe { self.next_si(next_si, text, at) };
                at += 1;
                if prev_si > STATE_MAX {
                    mem::swap(&mut prev_si, &mut next_si);
                    break;
                }
                next_si = unsafe { self.next_si(prev_si, text, at) };
                at += 1;
            }
            if next_si & STATE_MATCH > 0 {
                // A match state is outside of the common case because it needs
                // special case analysis. In particular, we need to record the
                // last position as having matched and possibly quit the DFA if
                // we don't need to keep matching.
                next_si &= !STATE_MATCH;
                result = Result::Match(at - 1);
                if self.quit_after_match {
                    return result;
                }
                self.last_match_si = next_si;
                prev_si = next_si;

                // This permits short-circuiting when matching a regex set.
                // In particular, if this DFA state contains only match states,
                // then it's impossible to extend the set of matches since
                // match states are final. Therefore, we can quit.
                if self.prog.matches.len() > 1 {
                    let state = self.state(next_si);
                    let just_matches =
                        state.inst_ptrs().all(|ip| self.prog[ip].is_match());
                    if just_matches {
                        return result;
                    }
                }

                // Another inner loop! If the DFA stays in this particular
                // match state, then we can rip through all of the input
                // very quickly, and only recording the match location once
                // we've left this particular state.
                let cur = at;
                while (next_si & !STATE_MATCH) == prev_si
                    && at + 2 < text.len()
                {
                    // Argument for safety is in the definition of next_si.
                    next_si = unsafe {
                        self.next_si(next_si & !STATE_MATCH, text, at)
                    };
                    at += 1;
                }
                if at > cur {
                    result = Result::Match(at - 2);
                }
            } else if next_si & STATE_START > 0 {
                // A start state isn't in the common case because we may
                // want to do quick prefix scanning. If the program doesn't
                // have a detected prefix, then start states are actually
                // considered common and this case is never reached.
                debug_assert!(self.has_prefix());
                next_si &= !STATE_START;
                prev_si = next_si;
                at = match self.prefix_at(text, at) {
                    None => return Result::NoMatch(text.len()),
                    Some(i) => i,
                };
            } else if next_si >= STATE_UNKNOWN {
                if next_si == STATE_QUIT {
                    return Result::Quit;
                }
                // Finally, this corresponds to the case where the transition
                // entered a state that can never lead to a match or a state
                // that hasn't been computed yet. The latter being the "slow"
                // path.
                let byte = Byte::byte(text[at - 1]);
                // We no longer care about the special bits in the state
                // pointer.
                prev_si &= STATE_MAX;
                // Record where we are. This is used to track progress for
                // determining whether we should quit if we've flushed the
                // cache too much.
                self.at = at;
                next_si = match self.next_state(qcur, qnext, prev_si, byte) {
                    None => return Result::Quit,
                    Some(STATE_DEAD) => return result.set_non_match(at),
                    Some(si) => si,
                };
                debug_assert!(next_si != STATE_UNKNOWN);
                if next_si & STATE_MATCH > 0 {
                    next_si &= !STATE_MATCH;
                    result = Result::Match(at - 1);
                    if self.quit_after_match {
                        return result;
                    }
                    self.last_match_si = next_si;
                }
                prev_si = next_si;
            } else {
                prev_si = next_si;
            }
        }

        // Run the DFA once more on the special EOF sentinel value.
        // We don't care about the special bits in the state pointer any more,
        // so get rid of them.
        prev_si &= STATE_MAX;
        prev_si = match self.next_state(qcur, qnext, prev_si, Byte::eof()) {
            None => return Result::Quit,
            Some(STATE_DEAD) => return result.set_non_match(text.len()),
            Some(si) => si & !STATE_START,
        };
        debug_assert!(prev_si != STATE_UNKNOWN);
        if prev_si & STATE_MATCH > 0 {
            prev_si &= !STATE_MATCH;
            self.last_match_si = prev_si;
            result = Result::Match(text.len());
        }
        result
    }

    /// Executes the DFA on a reverse NFA.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn exec_at_reverse(
        &mut self,
        qcur: &mut SparseSet,
        qnext: &mut SparseSet,
        text: &[u8],
    ) -> Result<usize> {
        // The comments in `exec_at` above mostly apply here too. The main
        // difference is that we move backwards over the input and we look for
        // the longest possible match instead of the leftmost-first match.
        //
        // N.B. The code duplication here is regrettable. Efforts to improve
        // it without sacrificing performance are welcome. ---AG
        debug_assert!(self.prog.is_reverse);
        let mut result = Result::NoMatch(self.at);
        let (mut prev_si, mut next_si) = (self.start, self.start);
        let mut at = self.at;
        while at > 0 {
            while next_si <= STATE_MAX && at > 0 {
                // Argument for safety is in the definition of next_si.
                at -= 1;
                prev_si = unsafe { self.next_si(next_si, text, at) };
                if prev_si > STATE_MAX || at <= 4 {
                    mem::swap(&mut prev_si, &mut next_si);
                    break;
                }
                at -= 1;
                next_si = unsafe { self.next_si(prev_si, text, at) };
                if next_si > STATE_MAX {
                    break;
                }
                at -= 1;
                prev_si = unsafe { self.next_si(next_si, text, at) };
                if prev_si > STATE_MAX {
                    mem::swap(&mut prev_si, &mut next_si);
                    break;
                }
                at -= 1;
                next_si = unsafe { self.next_si(prev_si, text, at) };
            }
            if next_si & STATE_MATCH > 0 {
                next_si &= !STATE_MATCH;
                result = Result::Match(at + 1);
                if self.quit_after_match {
                    return result;
                }
                self.last_match_si = next_si;
                prev_si = next_si;
                let cur = at;
                while (next_si & !STATE_MATCH) == prev_si && at >= 2 {
                    // Argument for safety is in the definition of next_si.
                    at -= 1;
                    next_si = unsafe {
                        self.next_si(next_si & !STATE_MATCH, text, at)
                    };
                }
                if at < cur {
                    result = Result::Match(at + 2);
                }
            } else if next_si >= STATE_UNKNOWN {
                if next_si == STATE_QUIT {
                    return Result::Quit;
                }
                let byte = Byte::byte(text[at]);
                prev_si &= STATE_MAX;
                self.at = at;
                next_si = match self.next_state(qcur, qnext, prev_si, byte) {
                    None => return Result::Quit,
                    Some(STATE_DEAD) => return result.set_non_match(at),
                    Some(si) => si,
                };
                debug_assert!(next_si != STATE_UNKNOWN);
                if next_si & STATE_MATCH > 0 {
                    next_si &= !STATE_MATCH;
                    result = Result::Match(at + 1);
                    if self.quit_after_match {
                        return result;
                    }
                    self.last_match_si = next_si;
                }
                prev_si = next_si;
            } else {
                prev_si = next_si;
            }
        }

        // Run the DFA once more on the special EOF sentinel value.
        prev_si = match self.next_state(qcur, qnext, prev_si, Byte::eof()) {
            None => return Result::Quit,
            Some(STATE_DEAD) => return result.set_non_match(0),
            Some(si) => si,
        };
        debug_assert!(prev_si != STATE_UNKNOWN);
        if prev_si & STATE_MATCH > 0 {
            prev_si &= !STATE_MATCH;
            self.last_match_si = prev_si;
            result = Result::Match(0);
        }
        result
    }

    /// next_si transitions to the next state, where the transition input
    /// corresponds to text[i].
    ///
    /// This elides bounds checks, and is therefore not safe.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    unsafe fn next_si(&self, si: StatePtr, text: &[u8], i: usize) -> StatePtr {
        // What is the argument for safety here?
        // We have three unchecked accesses that could possibly violate safety:
        //
        //   1. The given byte of input (`text[i]`).
        //   2. The class of the byte of input (`classes[text[i]]`).
        //   3. The transition for the class (`trans[si + cls]`).
        //
        // (1) is only safe when calling next_si is guarded by
        // `i < text.len()`.
        //
        // (2) is the easiest case to guarantee since `text[i]` is always a
        // `u8` and `self.prog.byte_classes` always has length `u8::MAX`.
        // (See `ByteClassSet.byte_classes` in `compile.rs`.)
        //
        // (3) is only safe if (1)+(2) are safe. Namely, the transitions
        // of every state are defined to have length equal to the number of
        // byte classes in the program. Therefore, a valid class leads to a
        // valid transition. (All possible transitions are valid lookups, even
        // if it points to a state that hasn't been computed yet.) (3) also
        // relies on `si` being correct, but StatePtrs should only ever be
        // retrieved from the transition table, which ensures they are correct.
        debug_assert!(i < text.len());
        let b = *text.get_unchecked(i);
        debug_assert!((b as usize) < self.prog.byte_classes.len());
        let cls = *self.prog.byte_classes.get_unchecked(b as usize);
        self.cache.trans.next_unchecked(si, cls as usize)
    }

    /// Computes the next state given the current state and the current input
    /// byte (which may be EOF).
    ///
    /// If STATE_DEAD is returned, then there is no valid state transition.
    /// This implies that no permutation of future input can lead to a match
    /// state.
    ///
    /// STATE_UNKNOWN can never be returned.
    fn exec_byte(
        &mut self,
        qcur: &mut SparseSet,
        qnext: &mut SparseSet,
        mut si: StatePtr,
        b: Byte,
    ) -> Option<StatePtr> {
        use prog::Inst::*;

        // Initialize a queue with the current DFA state's NFA states.
        qcur.clear();
        for ip in self.state(si).inst_ptrs() {
            qcur.insert(ip);
        }

        // Before inspecting the current byte, we may need to also inspect
        // whether the position immediately preceding the current byte
        // satisfies the empty assertions found in the current state.
        //
        // We only need to do this step if there are any empty assertions in
        // the current state.
        let is_word_last = self.state(si).flags().is_word();
        let is_word = b.is_ascii_word();
        if self.state(si).flags().has_empty() {
            // Compute the flags immediately preceding the current byte.
            // This means we only care about the "end" or "end line" flags.
            // (The "start" flags are computed immediately following the
            // current byte and are handled below.)
            let mut flags = EmptyFlags::default();
            if b.is_eof() {
                flags.end = true;
                flags.end_line = true;
            } else if b.as_byte().map_or(false, |b| b == b'\n') {
                flags.end_line = true;
            }
            if is_word_last == is_word {
                flags.not_word_boundary = true;
            } else {
                flags.word_boundary = true;
            }
            // Now follow epsilon transitions from every NFA state, but make
            // sure we only follow transitions that satisfy our flags.
            qnext.clear();
            for &ip in &*qcur {
                self.follow_epsilons(usize_to_u32(ip), qnext, flags);
            }
            mem::swap(qcur, qnext);
        }

        // Now we set flags for immediately after the current byte. Since start
        // states are processed separately, and are the only states that can
        // have the StartText flag set, we therefore only need to worry about
        // the StartLine flag here.
        //
        // We do also keep track of whether this DFA state contains a NFA state
        // that is a matching state. This is precisely how we delay the DFA
        // matching by one byte in order to process the special EOF sentinel
        // byte. Namely, if this DFA state containing a matching NFA state,
        // then it is the *next* DFA state that is marked as a match.
        let mut empty_flags = EmptyFlags::default();
        let mut state_flags = StateFlags::default();
        empty_flags.start_line = b.as_byte().map_or(false, |b| b == b'\n');
        if b.is_ascii_word() {
            state_flags.set_word();
        }
        // Now follow all epsilon transitions again, but only after consuming
        // the current byte.
        qnext.clear();
        for &ip in &*qcur {
            match self.prog[ip as usize] {
                // These states never happen in a byte-based program.
                Char(_) | Ranges(_) => unreachable!(),
                // These states are handled when following epsilon transitions.
                Save(_) | Split(_) | EmptyLook(_) => {}
                Match(_) => {
                    state_flags.set_match();
                    if !self.continue_past_first_match() {
                        break;
                    } else if self.prog.matches.len() > 1
                        && !qnext.contains(ip as usize)
                    {
                        // If we are continuing on to find other matches,
                        // then keep a record of the match states we've seen.
                        qnext.insert(ip);
                    }
                }
                Bytes(ref inst) => {
                    if b.as_byte().map_or(false, |b| inst.matches(b)) {
                        self.follow_epsilons(
                            inst.goto as InstPtr,
                            qnext,
                            empty_flags,
                        );
                    }
                }
            }
        }

        let cache = if b.is_eof() && self.prog.matches.len() > 1 {
            // If we're processing the last byte of the input and we're
            // matching a regex set, then make the next state contain the
            // previous states transitions. We do this so that the main
            // matching loop can extract all of the match instructions.
            mem::swap(qcur, qnext);
            // And don't cache this state because it's totally bunk.
            false
        } else {
            true
        };

        // We've now built up the set of NFA states that ought to comprise the
        // next DFA state, so try to find it in the cache, and if it doesn't
        // exist, cache it.
        //
        // N.B. We pass `&mut si` here because the cache may clear itself if
        // it has gotten too full. When that happens, the location of the
        // current state may change.
        let mut next =
            match self.cached_state(qnext, state_flags, Some(&mut si)) {
                None => return None,
                Some(next) => next,
            };
        if (self.start & !STATE_START) == next {
            // Start states can never be match states since all matches are
            // delayed by one byte.
            debug_assert!(!self.state(next).flags().is_match());
            next = self.start_ptr(next);
        }
        if next <= STATE_MAX && self.state(next).flags().is_match() {
            next |= STATE_MATCH;
        }
        debug_assert!(next != STATE_UNKNOWN);
        // And now store our state in the current state's next list.
        if cache {
            let cls = self.byte_class(b);
            self.cache.trans.set_next(si, cls, next);
        }
        Some(next)
    }

    /// Follows the epsilon transitions starting at (and including) `ip`. The
    /// resulting states are inserted into the ordered set `q`.
    ///
    /// Conditional epsilon transitions (i.e., empty width assertions) are only
    /// followed if they are satisfied by the given flags, which should
    /// represent the flags set at the current location in the input.
    ///
    /// If the current location corresponds to the empty string, then only the
    /// end line and/or end text flags may be set. If the current location
    /// corresponds to a real byte in the input, then only the start line
    /// and/or start text flags may be set.
    ///
    /// As an exception to the above, when finding the initial state, any of
    /// the above flags may be set:
    ///
    /// If matching starts at the beginning of the input, then start text and
    /// start line should be set. If the input is empty, then end text and end
    /// line should also be set.
    ///
    /// If matching starts after the beginning of the input, then only start
    /// line should be set if the preceding byte is `\n`. End line should never
    /// be set in this case. (Even if the following byte is a `\n`, it will
    /// be handled in a subsequent DFA state.)
    fn follow_epsilons(
        &mut self,
        ip: InstPtr,
        q: &mut SparseSet,
        flags: EmptyFlags,
    ) {
        use prog::EmptyLook::*;
        use prog::Inst::*;

        // We need to traverse the NFA to follow epsilon transitions, so avoid
        // recursion with an explicit stack.
        self.cache.stack.push(ip);
        while let Some(mut ip) = self.cache.stack.pop() {
            // Try to munch through as many states as possible without
            // pushes/pops to the stack.
            loop {
                // Don't visit states we've already added.
                if q.contains(ip as usize) {
                    break;
                }
                q.insert(ip as usize);
                match self.prog[ip as usize] {
                    Char(_) | Ranges(_) => unreachable!(),
                    Match(_) | Bytes(_) => {
                        break;
                    }
                    EmptyLook(ref inst) => {
                        // Only follow empty assertion states if our flags
                        // satisfy the assertion.
                        match inst.look {
                            StartLine if flags.start_line => {
                                ip = inst.goto as InstPtr;
                            }
                            EndLine if flags.end_line => {
                                ip = inst.goto as InstPtr;
                            }
                            StartText if flags.start => {
                                ip = inst.goto as InstPtr;
                            }
                            EndText if flags.end => {
                                ip = inst.goto as InstPtr;
                            }
                            WordBoundaryAscii if flags.word_boundary => {
                                ip = inst.goto as InstPtr;
                            }
                            NotWordBoundaryAscii
                                if flags.not_word_boundary =>
                            {
                                ip = inst.goto as InstPtr;
                            }
                            WordBoundary if flags.word_boundary => {
                                ip = inst.goto as InstPtr;
                            }
                            NotWordBoundary if flags.not_word_boundary => {
                                ip = inst.goto as InstPtr;
                            }
                            StartLine | EndLine | StartText | EndText
                            | WordBoundaryAscii | NotWordBoundaryAscii
                            | WordBoundary | NotWordBoundary => {
                                break;
                            }
                        }
                    }
                    Save(ref inst) => {
                        ip = inst.goto as InstPtr;
                    }
                    Split(ref inst) => {
                        self.cache.stack.push(inst.goto2 as InstPtr);
                        ip = inst.goto1 as InstPtr;
                    }
                }
            }
        }
    }

    /// Find a previously computed state matching the given set of instructions
    /// and is_match bool.
    ///
    /// The given set of instructions should represent a single state in the
    /// NFA along with all states reachable without consuming any input.
    ///
    /// The is_match bool should be true if and only if the preceding DFA state
    /// contains an NFA matching state. The cached state produced here will
    /// then signify a match. (This enables us to delay a match by one byte,
    /// in order to account for the EOF sentinel byte.)
    ///
    /// If the cache is full, then it is wiped before caching a new state.
    ///
    /// The current state should be specified if it exists, since it will need
    /// to be preserved if the cache clears itself. (Start states are
    /// always saved, so they should not be passed here.) It takes a mutable
    /// pointer to the index because if the cache is cleared, the state's
    /// location may change.
    fn cached_state(
        &mut self,
        q: &SparseSet,
        mut state_flags: StateFlags,
        current_state: Option<&mut StatePtr>,
    ) -> Option<StatePtr> {
        // If we couldn't come up with a non-empty key to represent this state,
        // then it is dead and can never lead to a match.
        //
        // Note that inst_flags represent the set of empty width assertions
        // in q. We use this as an optimization in exec_byte to determine when
        // we should follow epsilon transitions at the empty string preceding
        // the current byte.
        let key = match self.cached_state_key(q, &mut state_flags) {
            None => return Some(STATE_DEAD),
            Some(v) => v,
        };
        // In the cache? Cool. Done.
        if let Some(si) = self.cache.compiled.get_ptr(&key) {
            return Some(si);
        }
        // If the cache has gotten too big, wipe it.
        if self.approximate_size() > self.prog.dfa_size_limit
            && !self.clear_cache_and_save(current_state)
        {
            // Ooops. DFA is giving up.
            return None;
        }
        // Allocate room for our state and add it.
        self.add_state(key)
    }

    /// Produces a key suitable for describing a state in the DFA cache.
    ///
    /// The key invariant here is that equivalent keys are produced for any two
    /// sets of ordered NFA states (and toggling of whether the previous NFA
    /// states contain a match state) that do not discriminate a match for any
    /// input.
    ///
    /// Specifically, q should be an ordered set of NFA states and is_match
    /// should be true if and only if the previous NFA states contained a match
    /// state.
    fn cached_state_key(
        &mut self,
        q: &SparseSet,
        state_flags: &mut StateFlags,
    ) -> Option<State> {
        use prog::Inst::*;

        // We need to build up enough information to recognize pre-built states
        // in the DFA. Generally speaking, this includes every instruction
        // except for those which are purely epsilon transitions, e.g., the
        // Save and Split instructions.
        //
        // Empty width assertions are also epsilon transitions, but since they
        // are conditional, we need to make them part of a state's key in the
        // cache.

        let mut insts =
            mem::replace(&mut self.cache.insts_scratch_space, vec![]);
        insts.clear();
        // Reserve 1 byte for flags.
        insts.push(0);

        let mut prev = 0;
        for &ip in q {
            let ip = usize_to_u32(ip);
            match self.prog[ip as usize] {
                Char(_) | Ranges(_) => unreachable!(),
                Save(_) | Split(_) => {}
                Bytes(_) => push_inst_ptr(&mut insts, &mut prev, ip),
                EmptyLook(_) => {
                    state_flags.set_empty();
                    push_inst_ptr(&mut insts, &mut prev, ip)
                }
                Match(_) => {
                    push_inst_ptr(&mut insts, &mut prev, ip);
                    if !self.continue_past_first_match() {
                        break;
                    }
                }
            }
        }
        // If we couldn't transition to any other instructions and we didn't
        // see a match when expanding NFA states previously, then this is a
        // dead state and no amount of additional input can transition out
        // of this state.
        let opt_state = if insts.len() == 1 && !state_flags.is_match() {
            None
        } else {
            let StateFlags(f) = *state_flags;
            insts[0] = f;
            Some(State { data: Arc::from(&*insts) })
        };
        self.cache.insts_scratch_space = insts;
        opt_state
    }

    /// Clears the cache, but saves and restores current_state if it is not
    /// none.
    ///
    /// The current state must be provided here in case its location in the
    /// cache changes.
    ///
    /// This returns false if the cache is not cleared and the DFA should
    /// give up.
    fn clear_cache_and_save(
        &mut self,
        current_state: Option<&mut StatePtr>,
    ) -> bool {
        if self.cache.compiled.is_empty() {
            // Nothing to clear...
            return true;
        }
        match current_state {
            None => self.clear_cache(),
            Some(si) => {
                let cur = self.state(*si).clone();
                if !self.clear_cache() {
                    return false;
                }
                // The unwrap is OK because we just cleared the cache and
                // therefore know that the next state pointer won't exceed
                // STATE_MAX.
                *si = self.restore_state(cur).unwrap();
                true
            }
        }
    }

    /// Wipes the state cache, but saves and restores the current start state.
    ///
    /// This returns false if the cache is not cleared and the DFA should
    /// give up.
    fn clear_cache(&mut self) -> bool {
        // Bail out of the DFA if we're moving too "slowly."
        // A heuristic from RE2: assume the DFA is too slow if it is processing
        // 10 or fewer bytes per state.
        // Additionally, we permit the cache to be flushed a few times before
        // caling it quits.
        let nstates = self.cache.compiled.len();
        if self.cache.flush_count >= 3
            && self.at >= self.last_cache_flush
            && (self.at - self.last_cache_flush) <= 10 * nstates
        {
            return false;
        }
        // Update statistics tracking cache flushes.
        self.last_cache_flush = self.at;
        self.cache.flush_count += 1;

        // OK, actually flush the cache.
        let start = self.state(self.start & !STATE_START).clone();
        let last_match = if self.last_match_si <= STATE_MAX {
            Some(self.state(self.last_match_si).clone())
        } else {
            None
        };
        self.cache.reset_size();
        self.cache.trans.clear();
        self.cache.compiled.clear();
        for s in &mut self.cache.start_states {
            *s = STATE_UNKNOWN;
        }
        // The unwraps are OK because we just cleared the cache and therefore
        // know that the next state pointer won't exceed STATE_MAX.
        let start_ptr = self.restore_state(start).unwrap();
        self.start = self.start_ptr(start_ptr);
        if let Some(last_match) = last_match {
            self.last_match_si = self.restore_state(last_match).unwrap();
        }
        true
    }

    /// Restores the given state back into the cache, and returns a pointer
    /// to it.
    fn restore_state(&mut self, state: State) -> Option<StatePtr> {
        // If we've already stored this state, just return a pointer to it.
        // None will be the wiser.
        if let Some(si) = self.cache.compiled.get_ptr(&state) {
            return Some(si);
        }
        self.add_state(state)
    }

    /// Returns the next state given the current state si and current byte
    /// b. {qcur,qnext} are used as scratch space for storing ordered NFA
    /// states.
    ///
    /// This tries to fetch the next state from the cache, but if that fails,
    /// it computes the next state, caches it and returns a pointer to it.
    ///
    /// The pointer can be to a real state, or it can be STATE_DEAD.
    /// STATE_UNKNOWN cannot be returned.
    ///
    /// None is returned if a new state could not be allocated (i.e., the DFA
    /// ran out of space and thinks it's running too slowly).
    fn next_state(
        &mut self,
        qcur: &mut SparseSet,
        qnext: &mut SparseSet,
        si: StatePtr,
        b: Byte,
    ) -> Option<StatePtr> {
        if si == STATE_DEAD {
            return Some(STATE_DEAD);
        }
        match self.cache.trans.next(si, self.byte_class(b)) {
            STATE_UNKNOWN => self.exec_byte(qcur, qnext, si, b),
            STATE_QUIT => None,
            STATE_DEAD => Some(STATE_DEAD),
            nsi => Some(nsi),
        }
    }

    /// Computes and returns the start state, where searching begins at
    /// position `at` in `text`. If the state has already been computed,
    /// then it is pulled from the cache. If the state hasn't been cached,
    /// then it is computed, cached and a pointer to it is returned.
    ///
    /// This may return STATE_DEAD but never STATE_UNKNOWN.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn start_state(
        &mut self,
        q: &mut SparseSet,
        empty_flags: EmptyFlags,
        state_flags: StateFlags,
    ) -> Option<StatePtr> {
        // Compute an index into our cache of start states based on the set
        // of empty/state flags set at the current position in the input. We
        // don't use every flag since not all flags matter. For example, since
        // matches are delayed by one byte, start states can never be match
        // states.
        let flagi = {
            (((empty_flags.start as u8) << 0)
                | ((empty_flags.end as u8) << 1)
                | ((empty_flags.start_line as u8) << 2)
                | ((empty_flags.end_line as u8) << 3)
                | ((empty_flags.word_boundary as u8) << 4)
                | ((empty_flags.not_word_boundary as u8) << 5)
                | ((state_flags.is_word() as u8) << 6)) as usize
        };
        match self.cache.start_states[flagi] {
            STATE_UNKNOWN => {}
            STATE_DEAD => return Some(STATE_DEAD),
            si => return Some(si),
        }
        q.clear();
        let start = usize_to_u32(self.prog.start);
        self.follow_epsilons(start, q, empty_flags);
        // Start states can never be match states because we delay every match
        // by one byte. Given an empty string and an empty match, the match
        // won't actually occur until the DFA processes the special EOF
        // sentinel byte.
        let sp = match self.cached_state(q, state_flags, None) {
            None => return None,
            Some(sp) => self.start_ptr(sp),
        };
        self.cache.start_states[flagi] = sp;
        Some(sp)
    }

    /// Computes the set of starting flags for the given position in text.
    ///
    /// This should only be used when executing the DFA forwards over the
    /// input.
    fn start_flags(&self, text: &[u8], at: usize) -> (EmptyFlags, StateFlags) {
        let mut empty_flags = EmptyFlags::default();
        let mut state_flags = StateFlags::default();
        empty_flags.start = at == 0;
        empty_flags.end = text.is_empty();
        empty_flags.start_line = at == 0 || text[at - 1] == b'\n';
        empty_flags.end_line = text.is_empty();

        let is_word_last = at > 0 && Byte::byte(text[at - 1]).is_ascii_word();
        let is_word = at < text.len() && Byte::byte(text[at]).is_ascii_word();
        if is_word_last {
            state_flags.set_word();
        }
        if is_word == is_word_last {
            empty_flags.not_word_boundary = true;
        } else {
            empty_flags.word_boundary = true;
        }
        (empty_flags, state_flags)
    }

    /// Computes the set of starting flags for the given position in text.
    ///
    /// This should only be used when executing the DFA in reverse over the
    /// input.
    fn start_flags_reverse(
        &self,
        text: &[u8],
        at: usize,
    ) -> (EmptyFlags, StateFlags) {
        let mut empty_flags = EmptyFlags::default();
        let mut state_flags = StateFlags::default();
        empty_flags.start = at == text.len();
        empty_flags.end = text.is_empty();
        empty_flags.start_line = at == text.len() || text[at] == b'\n';
        empty_flags.end_line = text.is_empty();

        let is_word_last =
            at < text.len() && Byte::byte(text[at]).is_ascii_word();
        let is_word = at > 0 && Byte::byte(text[at - 1]).is_ascii_word();
        if is_word_last {
            state_flags.set_word();
        }
        if is_word == is_word_last {
            empty_flags.not_word_boundary = true;
        } else {
            empty_flags.word_boundary = true;
        }
        (empty_flags, state_flags)
    }

    /// Returns a reference to a State given a pointer to it.
    fn state(&self, si: StatePtr) -> &State {
        self.cache.compiled.get_state(si).unwrap()
    }

    /// Adds the given state to the DFA.
    ///
    /// This allocates room for transitions out of this state in
    /// self.cache.trans. The transitions can be set with the returned
    /// StatePtr.
    ///
    /// If None is returned, then the state limit was reached and the DFA
    /// should quit.
    fn add_state(&mut self, state: State) -> Option<StatePtr> {
        // This will fail if the next state pointer exceeds STATE_PTR. In
        // practice, the cache limit will prevent us from ever getting here,
        // but maybe callers will set the cache size to something ridiculous...
        let si = match self.cache.trans.add() {
            None => return None,
            Some(si) => si,
        };
        // If the program has a Unicode word boundary, then set any transitions
        // for non-ASCII bytes to STATE_QUIT. If the DFA stumbles over such a
        // transition, then it will quit and an alternative matching engine
        // will take over.
        if self.prog.has_unicode_word_boundary {
            for b in 128..256 {
                let cls = self.byte_class(Byte::byte(b as u8));
                self.cache.trans.set_next(si, cls, STATE_QUIT);
            }
        }
        // Finally, put our actual state on to our heap of states and index it
        // so we can find it later.
        self.cache.size += self.cache.trans.state_heap_size()
            + state.data.len()
            + (2 * mem::size_of::<State>())
            + mem::size_of::<StatePtr>();
        self.cache.compiled.insert(state, si);
        // Transition table and set of states and map should all be in sync.
        debug_assert!(
            self.cache.compiled.len() == self.cache.trans.num_states()
        );
        Some(si)
    }

    /// Quickly finds the next occurrence of any literal prefixes in the regex.
    /// If there are no literal prefixes, then the current position is
    /// returned. If there are literal prefixes and one could not be found,
    /// then None is returned.
    ///
    /// This should only be called when the DFA is in a start state.
    fn prefix_at(&self, text: &[u8], at: usize) -> Option<usize> {
        self.prog.prefixes.find(&text[at..]).map(|(s, _)| at + s)
    }

    /// Returns the number of byte classes required to discriminate transitions
    /// in each state.
    ///
    /// invariant: num_byte_classes() == len(State.next)
    fn num_byte_classes(&self) -> usize {
        // We add 1 to account for the special EOF byte.
        (self.prog.byte_classes[255] as usize + 1) + 1
    }

    /// Given an input byte or the special EOF sentinel, return its
    /// corresponding byte class.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn byte_class(&self, b: Byte) -> usize {
        match b.as_byte() {
            None => self.num_byte_classes() - 1,
            Some(b) => self.u8_class(b),
        }
    }

    /// Like byte_class, but explicitly for u8s.
    #[cfg_attr(feature = "perf-inline", inline(always))]
    fn u8_class(&self, b: u8) -> usize {
        self.prog.byte_classes[b as usize] as usize
    }

    /// Returns true if the DFA should continue searching past the first match.
    ///
    /// Leftmost first semantics in the DFA are preserved by not following NFA
    /// transitions after the first match is seen.
    ///
    /// On occasion, we want to avoid leftmost first semantics to find either
    /// the longest match (for reverse search) or all possible matches (for
    /// regex sets).
    fn continue_past_first_match(&self) -> bool {
        self.prog.is_reverse || self.prog.matches.len() > 1
    }

    /// Returns true if there is a prefix we can quickly search for.
    fn has_prefix(&self) -> bool {
        !self.prog.is_reverse
            && !self.prog.prefixes.is_empty()
            && !self.prog.is_anchored_start
    }

    /// Sets the STATE_START bit in the given state pointer if and only if
    /// we have a prefix to scan for.
    ///
    /// If there's no prefix, then it's a waste to treat the start state
    /// specially.
    fn start_ptr(&self, si: StatePtr) -> StatePtr {
        if self.has_prefix() {
            si | STATE_START
        } else {
            si
        }
    }

    /// Approximate size returns the approximate heap space currently used by
    /// the DFA. It is used to determine whether the DFA's state cache needs to
    /// be wiped. Namely, it is possible that for certain regexes on certain
    /// inputs, a new state could be created for every byte of input. (This is
    /// bad for memory use, so we bound it with a cache.)
    fn approximate_size(&self) -> usize {
        self.cache.size + self.prog.approximate_size()
    }
}

/// An abstraction for representing a map of states. The map supports two
/// different ways of state lookup. One is fast constant time access via a
/// state pointer. The other is a hashmap lookup based on the DFA's
/// constituent NFA states.
///
/// A DFA state internally uses an Arc such that we only need to store the
/// set of NFA states on the heap once, even though we support looking up
/// states by two different means. A more natural way to express this might
/// use raw pointers, but an Arc is safe and effectively achieves the same
/// thing.
#[derive(Debug)]
struct StateMap {
    /// The keys are not actually static but rely on always pointing to a
    /// buffer in `states` which will never be moved except when clearing
    /// the map or on drop, in which case the keys of this map will be
    /// removed before
    map: HashMap<State, StatePtr>,
    /// Our set of states. Note that `StatePtr / num_byte_classes` indexes
    /// this Vec rather than just a `StatePtr`.
    states: Vec<State>,
    /// The number of byte classes in the DFA. Used to index `states`.
    num_byte_classes: usize,
}

impl StateMap {
    fn new(num_byte_classes: usize) -> StateMap {
        StateMap {
            map: HashMap::new(),
            states: vec![],
            num_byte_classes: num_byte_classes,
        }
    }

    fn len(&self) -> usize {
        self.states.len()
    }

    fn is_empty(&self) -> bool {
        self.states.is_empty()
    }

    fn get_ptr(&self, state: &State) -> Option<StatePtr> {
        self.map.get(state).cloned()
    }

    fn get_state(&self, si: StatePtr) -> Option<&State> {
        self.states.get(si as usize / self.num_byte_classes)
    }

    fn insert(&mut self, state: State, si: StatePtr) {
        self.map.insert(state.clone(), si);
        self.states.push(state);
    }

    fn clear(&mut self) {
        self.map.clear();
        self.states.clear();
    }
}

impl Transitions {
    /// Create a new transition table.
    ///
    /// The number of byte classes corresponds to the stride. Every state will
    /// have `num_byte_classes` slots for transitions.
    fn new(num_byte_classes: usize) -> Transitions {
        Transitions { table: vec![], num_byte_classes: num_byte_classes }
    }

    /// Returns the total number of states currently in this table.
    fn num_states(&self) -> usize {
        self.table.len() / self.num_byte_classes
    }

    /// Allocates room for one additional state and returns a pointer to it.
    ///
    /// If there's no more room, None is returned.
    fn add(&mut self) -> Option<StatePtr> {
        let si = self.table.len();
        if si > STATE_MAX as usize {
            return None;
        }
        self.table.extend(repeat(STATE_UNKNOWN).take(self.num_byte_classes));
        Some(usize_to_u32(si))
    }

    /// Clears the table of all states.
    fn clear(&mut self) {
        self.table.clear();
    }

    /// Sets the transition from (si, cls) to next.
    fn set_next(&mut self, si: StatePtr, cls: usize, next: StatePtr) {
        self.table[si as usize + cls] = next;
    }

    /// Returns the transition corresponding to (si, cls).
    fn next(&self, si: StatePtr, cls: usize) -> StatePtr {
        self.table[si as usize + cls]
    }

    /// The heap size, in bytes, of a single state in the transition table.
    fn state_heap_size(&self) -> usize {
        self.num_byte_classes * mem::size_of::<StatePtr>()
    }

    /// Like `next`, but uses unchecked access and is therefore not safe.
    unsafe fn next_unchecked(&self, si: StatePtr, cls: usize) -> StatePtr {
        debug_assert!((si as usize) < self.table.len());
        debug_assert!(cls < self.num_byte_classes);
        *self.table.get_unchecked(si as usize + cls)
    }
}

impl StateFlags {
    fn is_match(&self) -> bool {
        self.0 & 0b0000000_1 > 0
    }

    fn set_match(&mut self) {
        self.0 |= 0b0000000_1;
    }

    fn is_word(&self) -> bool {
        self.0 & 0b000000_1_0 > 0
    }

    fn set_word(&mut self) {
        self.0 |= 0b000000_1_0;
    }

    fn has_empty(&self) -> bool {
        self.0 & 0b00000_1_00 > 0
    }

    fn set_empty(&mut self) {
        self.0 |= 0b00000_1_00;
    }
}

impl Byte {
    fn byte(b: u8) -> Self {
        Byte(b as u16)
    }
    fn eof() -> Self {
        Byte(256)
    }
    fn is_eof(&self) -> bool {
        self.0 == 256
    }

    fn is_ascii_word(&self) -> bool {
        let b = match self.as_byte() {
            None => return false,
            Some(b) => b,
        };
        match b {
            b'A'..=b'Z' | b'a'..=b'z' | b'0'..=b'9' | b'_' => true,
            _ => false,
        }
    }

    fn as_byte(&self) -> Option<u8> {
        if self.is_eof() {
            None
        } else {
            Some(self.0 as u8)
        }
    }
}

impl fmt::Debug for State {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        let ips: Vec<usize> = self.inst_ptrs().collect();
        f.debug_struct("State")
            .field("flags", &self.flags())
            .field("insts", &ips)
            .finish()
    }
}

impl fmt::Debug for Transitions {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        let mut fmtd = f.debug_map();
        for si in 0..self.num_states() {
            let s = si * self.num_byte_classes;
            let e = s + self.num_byte_classes;
            fmtd.entry(&si.to_string(), &TransitionsRow(&self.table[s..e]));
        }
        fmtd.finish()
    }
}

struct TransitionsRow<'a>(&'a [StatePtr]);

impl<'a> fmt::Debug for TransitionsRow<'a> {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        let mut fmtd = f.debug_map();
        for (b, si) in self.0.iter().enumerate() {
            match *si {
                STATE_UNKNOWN => {}
                STATE_DEAD => {
                    fmtd.entry(&vb(b as usize), &"DEAD");
                }
                si => {
                    fmtd.entry(&vb(b as usize), &si.to_string());
                }
            }
        }
        fmtd.finish()
    }
}

impl fmt::Debug for StateFlags {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        f.debug_struct("StateFlags")
            .field("is_match", &self.is_match())
            .field("is_word", &self.is_word())
            .field("has_empty", &self.has_empty())
            .finish()
    }
}

/// Helper function for formatting a byte as a nice-to-read escaped string.
fn vb(b: usize) -> String {
    use std::ascii::escape_default;

    if b > ::std::u8::MAX as usize {
        "EOF".to_owned()
    } else {
        let escaped = escape_default(b as u8).collect::<Vec<u8>>();
        String::from_utf8_lossy(&escaped).into_owned()
    }
}

fn usize_to_u32(n: usize) -> u32 {
    if (n as u64) > (::std::u32::MAX as u64) {
        panic!("BUG: {} is too big to fit into u32", n)
    }
    n as u32
}

#[allow(dead_code)] // useful for debugging
fn show_state_ptr(si: StatePtr) -> String {
    let mut s = format!("{:?}", si & STATE_MAX);
    if si == STATE_UNKNOWN {
        s = format!("{} (unknown)", s);
    }
    if si == STATE_DEAD {
        s = format!("{} (dead)", s);
    }
    if si == STATE_QUIT {
        s = format!("{} (quit)", s);
    }
    if si & STATE_START > 0 {
        s = format!("{} (start)", s);
    }
    if si & STATE_MATCH > 0 {
        s = format!("{} (match)", s);
    }
    s
}

/// https://developers.google.com/protocol-buffers/docs/encoding#varints
fn write_vari32(data: &mut Vec<u8>, n: i32) {
    let mut un = (n as u32) << 1;
    if n < 0 {
        un = !un;
    }
    write_varu32(data, un)
}

/// https://developers.google.com/protocol-buffers/docs/encoding#varints
fn read_vari32(data: &[u8]) -> (i32, usize) {
    let (un, i) = read_varu32(data);
    let mut n = (un >> 1) as i32;
    if un & 1 != 0 {
        n = !n;
    }
    (n, i)
}

/// https://developers.google.com/protocol-buffers/docs/encoding#varints
fn write_varu32(data: &mut Vec<u8>, mut n: u32) {
    while n >= 0b1000_0000 {
        data.push((n as u8) | 0b1000_0000);
        n >>= 7;
    }
    data.push(n as u8);
}

/// https://developers.google.com/protocol-buffers/docs/encoding#varints
fn read_varu32(data: &[u8]) -> (u32, usize) {
    let mut n: u32 = 0;
    let mut shift: u32 = 0;
    for (i, &b) in data.iter().enumerate() {
        if b < 0b1000_0000 {
            return (n | ((b as u32) << shift), i + 1);
        }
        n |= ((b as u32) & 0b0111_1111) << shift;
        shift += 7;
    }
    (0, 0)
}

#[cfg(test)]
mod tests {
    extern crate rand;

    use super::{
        push_inst_ptr, read_vari32, read_varu32, write_vari32, write_varu32,
        State, StateFlags,
    };
    use quickcheck::{quickcheck, Gen, QuickCheck};
    use std::sync::Arc;

    #[test]
    fn prop_state_encode_decode() {
        fn p(mut ips: Vec<u32>, flags: u8) -> bool {
            // It looks like our encoding scheme can't handle instruction
            // pointers at or above 2**31. We should fix that, but it seems
            // unlikely to occur in real code due to the amount of memory
            // required for such a state machine. So for now, we just clamp
            // our test data.
            for ip in &mut ips {
                if *ip >= 1 << 31 {
                    *ip = (1 << 31) - 1;
                }
            }
            let mut data = vec![flags];
            let mut prev = 0;
            for &ip in ips.iter() {
                push_inst_ptr(&mut data, &mut prev, ip);
            }
            let state = State { data: Arc::from(&data[..]) };

            let expected: Vec<usize> =
                ips.into_iter().map(|ip| ip as usize).collect();
            let got: Vec<usize> = state.inst_ptrs().collect();
            expected == got && state.flags() == StateFlags(flags)
        }
        QuickCheck::new()
            .gen(Gen::new(10_000))
            .quickcheck(p as fn(Vec<u32>, u8) -> bool);
    }

    #[test]
    fn prop_read_write_u32() {
        fn p(n: u32) -> bool {
            let mut buf = vec![];
            write_varu32(&mut buf, n);
            let (got, nread) = read_varu32(&buf);
            nread == buf.len() && got == n
        }
        quickcheck(p as fn(u32) -> bool);
    }

    #[test]
    fn prop_read_write_i32() {
        fn p(n: i32) -> bool {
            let mut buf = vec![];
            write_vari32(&mut buf, n);
            let (got, nread) = read_vari32(&buf);
            nread == buf.len() && got == n
        }
        quickcheck(p as fn(i32) -> bool);
    }
}