#
# Secret Labs' Regular Expression Engine core module
#
# Copyright (c) 1998-2001 by Secret Labs AB.  All rights reserved.
#
# This version of the SRE library can be redistributed under CNRI's
# Python 1.6 license.  For any other use, please contact Secret Labs
# AB (info@pythonware.com).
#
# Portions of this engine have been developed in cooperation with
# CNRI.  Hewlett-Packard provided funding for 1.6 integration and
# other compatibility work.
#
# 2010-01-16 mrab Python front-end re-written and extended

import enum
import string
import unicodedata
from collections import defaultdict

from regex import _regex

__all__ = ["A", "ASCII", "B", "BESTMATCH", "D", "DEBUG", "E", "ENHANCEMATCH",
  "F", "FULLCASE", "I", "IGNORECASE", "L", "LOCALE", "M", "MULTILINE", "P",
  "POSIX", "R", "REVERSE", "S", "DOTALL", "T", "TEMPLATE", "U", "UNICODE",
  "V0", "VERSION0", "V1", "VERSION1", "W", "WORD", "X", "VERBOSE", "error",
  "Scanner", "RegexFlag"]

# The regex exception.
class error(Exception):
    """Exception raised for invalid regular expressions.

    Attributes:

        msg: The unformatted error message
        pattern: The regular expression pattern
        pos: The position in the pattern where compilation failed, or None
        lineno: The line number where compilation failed, unless pos is None
        colno: The column number where compilation failed, unless pos is None
    """

    def __init__(self, message, pattern=None, pos=None):
        newline = '\n' if isinstance(pattern, str) else b'\n'
        self.msg = message
        self.pattern = pattern
        self.pos = pos
        if pattern is not None and pos is not None:
            self.lineno = pattern.count(newline, 0, pos) + 1
            self.colno = pos - pattern.rfind(newline, 0, pos)

            message = "{} at position {}".format(message, pos)

            if newline in pattern:
                message += " (line {}, column {})".format(self.lineno,
                  self.colno)

        Exception.__init__(self, message)

# The exception for when a positional flag has been turned on in the old
# behaviour.
class _UnscopedFlagSet(Exception):
    pass

# The exception for when parsing fails and we want to try something else.
class ParseError(Exception):
    pass

# The exception for when there isn't a valid first set.
class _FirstSetError(Exception):
    pass

# Flags.
class RegexFlag(enum.IntFlag):
    A = ASCII = 0x80          # Assume ASCII locale.
    B = BESTMATCH = 0x1000    # Best fuzzy match.
    D = DEBUG = 0x200         # Print parsed pattern.
    E = ENHANCEMATCH = 0x8000 # Attempt to improve the fit after finding the first
                              # fuzzy match.
    F = FULLCASE = 0x4000     # Unicode full case-folding.
    I = IGNORECASE = 0x2      # Ignore case.
    L = LOCALE = 0x4          # Assume current 8-bit locale.
    M = MULTILINE = 0x8       # Make anchors look for newline.
    P = POSIX = 0x10000       # POSIX-style matching (leftmost longest).
    R = REVERSE = 0x400       # Search backwards.
    S = DOTALL = 0x10         # Make dot match newline.
    U = UNICODE = 0x20        # Assume Unicode locale.
    V0 = VERSION0 = 0x2000    # Old legacy behaviour.
    V1 = VERSION1 = 0x100     # New enhanced behaviour.
    W = WORD = 0x800          # Default Unicode word breaks.
    X = VERBOSE = 0x40        # Ignore whitespace and comments.
    T = TEMPLATE = 0x1        # Template (present because re module has it).

    def __repr__(self):
        if self._name_ is not None:
            return 'regex.%s' % self._name_

        value = self._value_
        members = []
        negative = value < 0

        if negative:
            value = ~value

        for m in self.__class__:
            if value & m._value_:
                value &= ~m._value_
                members.append('regex.%s' % m._name_)

        if value:
            members.append(hex(value))

        res = '|'.join(members)

        if negative:
            if len(members) > 1:
                res = '~(%s)' % res
            else:
                res = '~%s' % res

        return res

    __str__ = object.__str__

# Put the flags into the module namespace. Being explicit here helps tools like
# linters and IDEs understand the code better.
ASCII = RegexFlag.ASCII
BESTMATCH = RegexFlag.BESTMATCH
DEBUG = RegexFlag.DEBUG
DOTALL = RegexFlag.DOTALL
ENHANCEMATCH = RegexFlag.ENHANCEMATCH
FULLCASE = RegexFlag.FULLCASE
IGNORECASE = RegexFlag.IGNORECASE
LOCALE = RegexFlag.LOCALE
MULTILINE = RegexFlag.MULTILINE
POSIX = RegexFlag.POSIX
REVERSE = RegexFlag.REVERSE
TEMPLATE = RegexFlag.TEMPLATE
UNICODE = RegexFlag.UNICODE
VERBOSE = RegexFlag.VERBOSE
VERSION0 = RegexFlag.VERSION0
VERSION1 = RegexFlag.VERSION1
WORD = RegexFlag.WORD
A = RegexFlag.A
B = RegexFlag.B
D = RegexFlag.D
E = RegexFlag.E
F = RegexFlag.F
I = RegexFlag.I
L = RegexFlag.L
M = RegexFlag.M
P = RegexFlag.P
R = RegexFlag.R
S = RegexFlag.S
U = RegexFlag.U
V0 = RegexFlag.V0
V1 = RegexFlag.V1
W = RegexFlag.W
X = RegexFlag.X
T = RegexFlag.T

DEFAULT_VERSION = VERSION1

_ALL_VERSIONS = VERSION0 | VERSION1
_ALL_ENCODINGS = ASCII | LOCALE | UNICODE

# The default flags for the various versions.
DEFAULT_FLAGS = {VERSION0: 0, VERSION1: FULLCASE}

# The mask for the flags.
GLOBAL_FLAGS = (_ALL_VERSIONS | BESTMATCH | DEBUG | ENHANCEMATCH | POSIX |
  REVERSE)
SCOPED_FLAGS = (FULLCASE | IGNORECASE | MULTILINE | DOTALL | WORD | VERBOSE |
  _ALL_ENCODINGS)

ALPHA = frozenset(string.ascii_letters)
DIGITS = frozenset(string.digits)
ALNUM = ALPHA | DIGITS
OCT_DIGITS = frozenset(string.octdigits)
HEX_DIGITS = frozenset(string.hexdigits)
SPECIAL_CHARS = frozenset("()|?*+{^$.[\\#") | frozenset([""])
NAMED_CHAR_PART = ALNUM | frozenset(" -")
PROPERTY_NAME_PART = ALNUM | frozenset(" &_-.")
SET_OPS = ("||", "~~", "&&", "--")

# The width of the code words inside the regex engine.
BYTES_PER_CODE = _regex.get_code_size()
BITS_PER_CODE = BYTES_PER_CODE * 8

# The repeat count which represents infinity.
UNLIMITED = (1 << BITS_PER_CODE) - 1

# The regular expression flags.
REGEX_FLAGS = {"a": ASCII, "b": BESTMATCH, "e": ENHANCEMATCH, "f": FULLCASE,
  "i": IGNORECASE, "L": LOCALE, "m": MULTILINE, "p": POSIX, "r": REVERSE,
  "s": DOTALL, "u": UNICODE, "V0": VERSION0, "V1": VERSION1, "w": WORD, "x":
  VERBOSE}

# The case flags.
CASE_FLAGS = FULLCASE | IGNORECASE
NOCASE = 0
FULLIGNORECASE = FULLCASE | IGNORECASE

FULL_CASE_FOLDING = UNICODE | FULLIGNORECASE

CASE_FLAGS_COMBINATIONS = {0: 0, FULLCASE: 0, IGNORECASE: IGNORECASE,
  FULLIGNORECASE: FULLIGNORECASE}

# The number of digits in hexadecimal escapes.
HEX_ESCAPES = {"x": 2, "u": 4, "U": 8}

# The names of the opcodes.
OPCODES = """
FAILURE
SUCCESS
ANY
ANY_ALL
ANY_ALL_REV
ANY_REV
ANY_U
ANY_U_REV
ATOMIC
BOUNDARY
BRANCH
CALL_REF
CHARACTER
CHARACTER_IGN
CHARACTER_IGN_REV
CHARACTER_REV
CONDITIONAL
DEFAULT_BOUNDARY
DEFAULT_END_OF_WORD
DEFAULT_START_OF_WORD
END
END_OF_LINE
END_OF_LINE_U
END_OF_STRING
END_OF_STRING_LINE
END_OF_STRING_LINE_U
END_OF_WORD
FUZZY
GRAPHEME_BOUNDARY
GREEDY_REPEAT
GROUP
GROUP_CALL
GROUP_EXISTS
KEEP
LAZY_REPEAT
LOOKAROUND
NEXT
PROPERTY
PROPERTY_IGN
PROPERTY_IGN_REV
PROPERTY_REV
PRUNE
RANGE
RANGE_IGN
RANGE_IGN_REV
RANGE_REV
REF_GROUP
REF_GROUP_FLD
REF_GROUP_FLD_REV
REF_GROUP_IGN
REF_GROUP_IGN_REV
REF_GROUP_REV
SEARCH_ANCHOR
SET_DIFF
SET_DIFF_IGN
SET_DIFF_IGN_REV
SET_DIFF_REV
SET_INTER
SET_INTER_IGN
SET_INTER_IGN_REV
SET_INTER_REV
SET_SYM_DIFF
SET_SYM_DIFF_IGN
SET_SYM_DIFF_IGN_REV
SET_SYM_DIFF_REV
SET_UNION
SET_UNION_IGN
SET_UNION_IGN_REV
SET_UNION_REV
SKIP
START_OF_LINE
START_OF_LINE_U
START_OF_STRING
START_OF_WORD
STRING
STRING_FLD
STRING_FLD_REV
STRING_IGN
STRING_IGN_REV
STRING_REV
FUZZY_EXT
"""

# Define the opcodes in a namespace.
class Namespace:
    pass

OP = Namespace()
for i, op in enumerate(OPCODES.split()):
    setattr(OP, op, i)

def _shrink_cache(cache_dict, args_dict, locale_sensitive, max_length, divisor=5):
    """Make room in the given cache.

    Args:
        cache_dict: The cache dictionary to modify.
        args_dict: The dictionary of named list args used by patterns.
        max_length: Maximum # of entries in cache_dict before it is shrunk.
        divisor: Cache will shrink to max_length - 1/divisor*max_length items.
    """
    # Toss out a fraction of the entries at random to make room for new ones.
    # A random algorithm was chosen as opposed to simply cache_dict.popitem()
    # as popitem could penalize the same regular expression repeatedly based
    # on its internal hash value.  Being random should spread the cache miss
    # love around.
    cache_keys = tuple(cache_dict.keys())
    overage = len(cache_keys) - max_length
    if overage < 0:
        # Cache is already within limits.  Normally this should not happen
        # but it could due to multithreading.
        return

    number_to_toss = max_length // divisor + overage

    # The import is done here to avoid a circular dependency.
    import random
    if not hasattr(random, 'sample'):
        # Do nothing while resolving the circular dependency:
        #  re->random->warnings->tokenize->string->re
        return

    for doomed_key in random.sample(cache_keys, number_to_toss):
        try:
            del cache_dict[doomed_key]
        except KeyError:
            # Ignore problems if the cache changed from another thread.
            pass

    # Rebuild the arguments and locale-sensitivity dictionaries.
    args_dict.clear()
    sensitivity_dict = {}
    for pattern, pattern_type, flags, args, default_version, locale in tuple(cache_dict):
        args_dict[pattern, pattern_type, flags, default_version, locale] = args
        try:
            sensitivity_dict[pattern_type, pattern] = locale_sensitive[pattern_type, pattern]
        except KeyError:
            pass

    locale_sensitive.clear()
    locale_sensitive.update(sensitivity_dict)

def _fold_case(info, string):
    "Folds the case of a string."
    flags = info.flags
    if (flags & _ALL_ENCODINGS) == 0:
        flags |= info.guess_encoding

    return _regex.fold_case(flags, string)

def is_cased_i(info, char):
    "Checks whether a character is cased."
    return len(_regex.get_all_cases(info.flags, char)) > 1

def is_cased_f(flags, char):
    "Checks whether a character is cased."
    return len(_regex.get_all_cases(flags, char)) > 1

def _compile_firstset(info, fs):
    "Compiles the firstset for the pattern."
    reverse = bool(info.flags & REVERSE)
    fs = _check_firstset(info, reverse, fs)
    if not fs or isinstance(fs, AnyAll):
        return []

    # Compile the firstset.
    return fs.compile(reverse)

def _check_firstset(info, reverse, fs):
    "Checks the firstset for the pattern."
    if not fs or None in fs:
        return None

    # If we ignore the case, for simplicity we won't build a firstset.
    members = set()
    case_flags = NOCASE
    for i in fs:
        if isinstance(i, Character) and not i.positive:
            return None

#        if i.case_flags:
#            if isinstance(i, Character):
#                if is_cased_i(info, i.value):
#                    return []
#            elif isinstance(i, SetBase):
#                return []
        case_flags |= i.case_flags
        members.add(i.with_flags(case_flags=NOCASE))

    if case_flags == (FULLCASE | IGNORECASE):
        return None

    # Build the firstset.
    fs = SetUnion(info, list(members), case_flags=case_flags & ~FULLCASE,
      zerowidth=True)
    fs = fs.optimise(info, reverse, in_set=True)

    return fs

def _flatten_code(code):
    "Flattens the code from a list of tuples."
    flat_code = []
    for c in code:
        flat_code.extend(c)

    return flat_code

def make_case_flags(info):
    "Makes the case flags."
    flags = info.flags & CASE_FLAGS

    # Turn off FULLCASE if ASCII is turned on.
    if info.flags & ASCII:
        flags &= ~FULLCASE

    return flags

def make_character(info, value, in_set=False):
    "Makes a character literal."
    if in_set:
        # A character set is built case-sensitively.
        return Character(value)

    return Character(value, case_flags=make_case_flags(info))

def make_ref_group(info, name, position):
    "Makes a group reference."
    return RefGroup(info, name, position, case_flags=make_case_flags(info))

def make_string_set(info, name):
    "Makes a string set."
    return StringSet(info, name, case_flags=make_case_flags(info))

def make_property(info, prop, in_set):
    "Makes a property."
    if in_set:
        return prop

    return prop.with_flags(case_flags=make_case_flags(info))

def _parse_pattern(source, info):
    "Parses a pattern, eg. 'a|b|c'."
    branches = [parse_sequence(source, info)]
    while source.match("|"):
        branches.append(parse_sequence(source, info))

    if len(branches) == 1:
        return branches[0]
    return Branch(branches)

def parse_sequence(source, info):
    "Parses a sequence, eg. 'abc'."
    sequence = [None]
    case_flags = make_case_flags(info)
    while True:
        saved_pos = source.pos
        ch = source.get()
        if ch in SPECIAL_CHARS:
            if ch in ")|":
                # The end of a sequence. At the end of the pattern ch is "".
                source.pos = saved_pos
                break
            elif ch == "\\":
                # An escape sequence outside a set.
                sequence.append(parse_escape(source, info, False))
            elif ch == "(":
                # A parenthesised subpattern or a flag.
                element = parse_paren(source, info)
                if element is None:
                    case_flags = make_case_flags(info)
                else:
                    sequence.append(element)
            elif ch == ".":
                # Any character.
                if info.flags & DOTALL:
                    sequence.append(AnyAll())
                elif info.flags & WORD:
                    sequence.append(AnyU())
                else:
                    sequence.append(Any())
            elif ch == "[":
                # A character set.
                sequence.append(parse_set(source, info))
            elif ch == "^":
                # The start of a line or the string.
                if info.flags & MULTILINE:
                    if info.flags & WORD:
                        sequence.append(StartOfLineU())
                    else:
                        sequence.append(StartOfLine())
                else:
                    sequence.append(StartOfString())
            elif ch == "$":
                # The end of a line or the string.
                if info.flags & MULTILINE:
                    if info.flags & WORD:
                        sequence.append(EndOfLineU())
                    else:
                        sequence.append(EndOfLine())
                else:
                    if info.flags & WORD:
                        sequence.append(EndOfStringLineU())
                    else:
                        sequence.append(EndOfStringLine())
            elif ch in "?*+{":
                # Looks like a quantifier.
                counts = parse_quantifier(source, info, ch)
                if counts:
                    # It _is_ a quantifier.
                    apply_quantifier(source, info, counts, case_flags, ch,
                      saved_pos, sequence)
                    sequence.append(None)
                else:
                    # It's not a quantifier. Maybe it's a fuzzy constraint.
                    constraints = parse_fuzzy(source, info, ch, case_flags)

                    if constraints:
                        # It _is_ a fuzzy constraint.
                        if is_actually_fuzzy(constraints):
                            apply_constraint(source, info, constraints, case_flags,
                              saved_pos, sequence)
                            sequence.append(None)
                    else:
                        # The element was just a literal.
                        sequence.append(Character(ord(ch),
                          case_flags=case_flags))
            else:
                # A literal.
                sequence.append(Character(ord(ch), case_flags=case_flags))
        else:
            # A literal.
            sequence.append(Character(ord(ch), case_flags=case_flags))

    sequence = [item for item in sequence if item is not None]
    return Sequence(sequence)

def is_actually_fuzzy(constraints):
    "Checks whether a fuzzy constraint is actually fuzzy."
    if constraints.get("e") == (0, 0):
        return False

    if (constraints.get("s"), constraints.get("i"), constraints.get("d")) == ((0, 0), (0, 0), (0, 0)):
        return False

    return True

def apply_quantifier(source, info, counts, case_flags, ch, saved_pos,
  sequence):
    element = sequence.pop()
    if element is None:
        if sequence:
            raise error("multiple repeat", source.string, saved_pos)
        raise error("nothing to repeat", source.string, saved_pos)

    if isinstance(element, (GreedyRepeat, LazyRepeat, PossessiveRepeat)):
        raise error("multiple repeat", source.string, saved_pos)

    min_count, max_count = counts
    saved_pos = source.pos
    ch = source.get()
    if ch == "?":
        # The "?" suffix that means it's a lazy repeat.
        repeated = LazyRepeat
    elif ch == "+":
        # The "+" suffix that means it's a possessive repeat.
        repeated = PossessiveRepeat
    else:
        # No suffix means that it's a greedy repeat.
        source.pos = saved_pos
        repeated = GreedyRepeat

    # Ignore the quantifier if it applies to a zero-width item or the number of
    # repeats is fixed at 1.
    if not element.is_empty() and (min_count != 1 or max_count != 1):
        element = repeated(element, min_count, max_count)

    sequence.append(element)

def apply_constraint(source, info, constraints, case_flags, saved_pos,
  sequence):
    element = sequence.pop()
    if element is None:
        raise error("nothing for fuzzy constraint", source.string, saved_pos)

    # If a group is marked as fuzzy then put all of the fuzzy part in the
    # group.
    if isinstance(element, Group):
        element.subpattern = Fuzzy(element.subpattern, constraints)
        sequence.append(element)
    else:
        sequence.append(Fuzzy(element, constraints))

_QUANTIFIERS = {"?": (0, 1), "*": (0, None), "+": (1, None)}

def parse_quantifier(source, info, ch):
    "Parses a quantifier."
    q = _QUANTIFIERS.get(ch)
    if q:
        # It's a quantifier.
        return q

    if ch == "{":
        # Looks like a limited repeated element, eg. 'a{2,3}'.
        counts = parse_limited_quantifier(source)
        if counts:
            return counts

    return None

def is_above_limit(count):
    "Checks whether a count is above the maximum."
    return count is not None and count >= UNLIMITED

def parse_limited_quantifier(source):
    "Parses a limited quantifier."
    saved_pos = source.pos
    min_count = parse_count(source)
    if source.match(","):
        max_count = parse_count(source)

        # No minimum means 0 and no maximum means unlimited.
        min_count = int(min_count or 0)
        max_count = int(max_count) if max_count else None
    else:
        if not min_count:
            source.pos = saved_pos
            return None

        min_count = max_count = int(min_count)

    if not source.match ("}"):
        source.pos = saved_pos
        return None

    if is_above_limit(min_count) or is_above_limit(max_count):
        raise error("repeat count too big", source.string, saved_pos)

    if max_count is not None and min_count > max_count:
        raise error("min repeat greater than max repeat", source.string,
          saved_pos)

    return min_count, max_count

def parse_fuzzy(source, info, ch, case_flags):
    "Parses a fuzzy setting, if present."
    saved_pos = source.pos

    if ch != "{":
        return None

    constraints = {}
    try:
        parse_fuzzy_item(source, constraints)
        while source.match(","):
            parse_fuzzy_item(source, constraints)
    except ParseError:
        source.pos = saved_pos
        return None

    if source.match(":"):
        constraints["test"] = parse_fuzzy_test(source, info, case_flags)

    if not source.match("}"):
        raise error("expected }", source.string, source.pos)

    return constraints

def parse_fuzzy_item(source, constraints):
    "Parses a fuzzy setting item."
    saved_pos = source.pos
    try:
        parse_cost_constraint(source, constraints)
    except ParseError:
        source.pos = saved_pos

        parse_cost_equation(source, constraints)

def parse_cost_constraint(source, constraints):
    "Parses a cost constraint."
    saved_pos = source.pos
    ch = source.get()
    if ch in ALPHA:
        # Syntax: constraint [("<=" | "<") cost]
        constraint = parse_constraint(source, constraints, ch)

        max_inc = parse_fuzzy_compare(source)

        if max_inc is None:
            # No maximum cost.
            constraints[constraint] = 0, None
        else:
            # There's a maximum cost.
            cost_pos = source.pos
            max_cost = parse_cost_limit(source)

            # Inclusive or exclusive limit?
            if not max_inc:
                max_cost -= 1

            if max_cost < 0:
                raise error("bad fuzzy cost limit", source.string, cost_pos)

            constraints[constraint] = 0, max_cost
    elif ch in DIGITS:
        # Syntax: cost ("<=" | "<") constraint ("<=" | "<") cost
        source.pos = saved_pos

        # Minimum cost.
        cost_pos = source.pos
        min_cost = parse_cost_limit(source)

        min_inc = parse_fuzzy_compare(source)
        if min_inc is None:
            raise ParseError()

        constraint = parse_constraint(source, constraints, source.get())

        max_inc = parse_fuzzy_compare(source)
        if max_inc is None:
            raise ParseError()

        # Maximum cost.
        cost_pos = source.pos
        max_cost = parse_cost_limit(source)

        # Inclusive or exclusive limits?
        if not min_inc:
            min_cost += 1
        if not max_inc:
            max_cost -= 1

        if not 0 <= min_cost <= max_cost:
            raise error("bad fuzzy cost limit", source.string, cost_pos)

        constraints[constraint] = min_cost, max_cost
    else:
        raise ParseError()

def parse_cost_limit(source):
    "Parses a cost limit."
    cost_pos = source.pos
    digits = parse_count(source)

    try:
        return int(digits)
    except ValueError:
        pass

    raise error("bad fuzzy cost limit", source.string, cost_pos)

def parse_constraint(source, constraints, ch):
    "Parses a constraint."
    if ch not in "deis":
        raise ParseError()

    if ch in constraints:
        raise ParseError()

    return ch

def parse_fuzzy_compare(source):
    "Parses a cost comparator."
    if source.match("<="):
        return True
    elif source.match("<"):
        return False
    else:
        return None

def parse_cost_equation(source, constraints):
    "Parses a cost equation."
    if "cost" in constraints:
        raise error("more than one cost equation", source.string, source.pos)

    cost = {}

    parse_cost_term(source, cost)
    while source.match("+"):
        parse_cost_term(source, cost)

    max_inc = parse_fuzzy_compare(source)
    if max_inc is None:
        raise ParseError()

    max_cost = int(parse_count(source))

    if not max_inc:
        max_cost -= 1

    if max_cost < 0:
        raise error("bad fuzzy cost limit", source.string, source.pos)

    cost["max"] = max_cost

    constraints["cost"] = cost

def parse_cost_term(source, cost):
    "Parses a cost equation term."
    coeff = parse_count(source)
    ch = source.get()
    if ch not in "dis":
        raise ParseError()

    if ch in cost:
        raise error("repeated fuzzy cost", source.string, source.pos)

    cost[ch] = int(coeff or 1)

def parse_fuzzy_test(source, info, case_flags):
    saved_pos = source.pos
    ch = source.get()
    if ch in SPECIAL_CHARS:
        if ch == "\\":
            # An escape sequence outside a set.
            return parse_escape(source, info, False)
        elif ch == ".":
            # Any character.
            if info.flags & DOTALL:
                return AnyAll()
            elif info.flags & WORD:
                return AnyU()
            else:
                return Any()
        elif ch == "[":
            # A character set.
            return parse_set(source, info)
        else:
            raise error("expected character set", source.string, saved_pos)
    elif ch:
        # A literal.
        return Character(ord(ch), case_flags=case_flags)
    else:
        raise error("expected character set", source.string, saved_pos)

def parse_count(source):
    "Parses a quantifier's count, which can be empty."
    return source.get_while(DIGITS)

def parse_paren(source, info):
    """Parses a parenthesised subpattern or a flag. Returns FLAGS if it's an
    inline flag.
    """
    saved_pos = source.pos
    ch = source.get(True)
    if ch == "?":
        # (?...
        saved_pos_2 = source.pos
        ch = source.get(True)
        if ch == "<":
            # (?<...
            saved_pos_3 = source.pos
            ch = source.get()
            if ch in ("=", "!"):
                # (?<=... or (?<!...: lookbehind.
                return parse_lookaround(source, info, True, ch == "=")

            # (?<...: a named capture group.
            source.pos = saved_pos_3
            name = parse_name(source)
            group = info.open_group(name)
            source.expect(">")
            saved_flags = info.flags
            try:
                subpattern = _parse_pattern(source, info)
                source.expect(")")
            finally:
                info.flags = saved_flags
                source.ignore_space = bool(info.flags & VERBOSE)

            info.close_group()
            return Group(info, group, subpattern)
        if ch in ("=", "!"):
            # (?=... or (?!...: lookahead.
            return parse_lookaround(source, info, False, ch == "=")
        if ch == "P":
            # (?P...: a Python extension.
            return parse_extension(source, info)
        if ch == "#":
            # (?#...: a comment.
            return parse_comment(source)
        if ch == "(":
            # (?(...: a conditional subpattern.
            return parse_conditional(source, info)
        if ch == ">":
            # (?>...: an atomic subpattern.
            return parse_atomic(source, info)
        if ch == "|":
            # (?|...: a common/reset groups branch.
            return parse_common(source, info)
        if ch == "R" or "0" <= ch <= "9":
            # (?R...: probably a call to a group.
            return parse_call_group(source, info, ch, saved_pos_2)
        if ch == "&":
            # (?&...: a call to a named group.
            return parse_call_named_group(source, info, saved_pos_2)
        if (ch == "+" or ch == "-") and source.peek() in DIGITS:
            return parse_rel_call_group(source, info, ch, saved_pos_2)

        # (?...: probably a flags subpattern.
        source.pos = saved_pos_2
        return parse_flags_subpattern(source, info)

    if ch == "*":
        # (*...
        saved_pos_2 = source.pos
        word = source.get_while(set(")>"), include=False)
        if word[ : 1].isalpha():
            verb = VERBS.get(word)
            if not verb:
                raise error("unknown verb", source.string, saved_pos_2)

            source.expect(")")

            return verb

    # (...: an unnamed capture group.
    source.pos = saved_pos
    group = info.open_group()
    saved_flags = info.flags
    try:
        subpattern = _parse_pattern(source, info)
        source.expect(")")
    finally:
        info.flags = saved_flags
        source.ignore_space = bool(info.flags & VERBOSE)

    info.close_group()

    return Group(info, group, subpattern)

def parse_extension(source, info):
    "Parses a Python extension."
    saved_pos = source.pos
    ch = source.get()
    if ch == "<":
        # (?P<...: a named capture group.
        name = parse_name(source)
        group = info.open_group(name)
        source.expect(">")
        saved_flags = info.flags
        try:
            subpattern = _parse_pattern(source, info)
            source.expect(")")
        finally:
            info.flags = saved_flags
            source.ignore_space = bool(info.flags & VERBOSE)

        info.close_group()

        return Group(info, group, subpattern)
    if ch == "=":
        # (?P=...: a named group reference.
        name = parse_name(source, allow_numeric=True)
        source.expect(")")
        if info.is_open_group(name):
            raise error("cannot refer to an open group", source.string,
              saved_pos)

        return make_ref_group(info, name, saved_pos)
    if ch == ">" or ch == "&":
        # (?P>...: a call to a group.
        return parse_call_named_group(source, info, saved_pos)

    source.pos = saved_pos
    raise error("unknown extension", source.string, saved_pos)

def parse_comment(source):
    "Parses a comment."
    while True:
        saved_pos = source.pos
        c = source.get(True)

        if not c or c == ")":
            break

        if c == "\\":
            c = source.get(True)

    source.pos = saved_pos
    source.expect(")")

    return None

def parse_lookaround(source, info, behind, positive):
    "Parses a lookaround."
    saved_flags = info.flags
    try:
        subpattern = _parse_pattern(source, info)
        source.expect(")")
    finally:
        info.flags = saved_flags
        source.ignore_space = bool(info.flags & VERBOSE)

    return LookAround(behind, positive, subpattern)

def parse_conditional(source, info):
    "Parses a conditional subpattern."
    saved_flags = info.flags
    saved_pos = source.pos
    ch = source.get()
    if ch == "?":
        # (?(?...
        ch = source.get()
        if ch in ("=", "!"):
            # (?(?=... or (?(?!...: lookahead conditional.
            return parse_lookaround_conditional(source, info, False, ch == "=")
        if ch == "<":
            # (?(?<...
            ch = source.get()
            if ch in ("=", "!"):
                # (?(?<=... or (?(?<!...: lookbehind conditional.
                return parse_lookaround_conditional(source, info, True, ch ==
                  "=")

        source.pos = saved_pos
        raise error("expected lookaround conditional", source.string,
          source.pos)

    source.pos = saved_pos
    try:
        group = parse_name(source, True)
        source.expect(")")
        yes_branch = parse_sequence(source, info)
        if source.match("|"):
            no_branch = parse_sequence(source, info)
        else:
            no_branch = Sequence()

        source.expect(")")
    finally:
        info.flags = saved_flags
        source.ignore_space = bool(info.flags & VERBOSE)

    if yes_branch.is_empty() and no_branch.is_empty():
        return Sequence()

    return Conditional(info, group, yes_branch, no_branch, saved_pos)

def parse_lookaround_conditional(source, info, behind, positive):
    saved_flags = info.flags
    try:
        subpattern = _parse_pattern(source, info)
        source.expect(")")
    finally:
        info.flags = saved_flags
        source.ignore_space = bool(info.flags & VERBOSE)

    yes_branch = parse_sequence(source, info)
    if source.match("|"):
        no_branch = parse_sequence(source, info)
    else:
        no_branch = Sequence()

    source.expect(")")

    return LookAroundConditional(behind, positive, subpattern, yes_branch,
      no_branch)

def parse_atomic(source, info):
    "Parses an atomic subpattern."
    saved_flags = info.flags
    try:
        subpattern = _parse_pattern(source, info)
        source.expect(")")
    finally:
        info.flags = saved_flags
        source.ignore_space = bool(info.flags & VERBOSE)

    return Atomic(subpattern)

def parse_common(source, info):
    "Parses a common groups branch."
    # Capture group numbers in different branches can reuse the group numbers.
    initial_group_count = info.group_count
    branches = [parse_sequence(source, info)]
    final_group_count = info.group_count
    while source.match("|"):
        info.group_count = initial_group_count
        branches.append(parse_sequence(source, info))
        final_group_count = max(final_group_count, info.group_count)

    info.group_count = final_group_count
    source.expect(")")

    if len(branches) == 1:
        return branches[0]
    return Branch(branches)

def parse_call_group(source, info, ch, pos):
    "Parses a call to a group."
    if ch == "R":
        group = "0"
    else:
        group = ch + source.get_while(DIGITS)

    source.expect(")")

    return CallGroup(info, group, pos)

def parse_rel_call_group(source, info, ch, pos):
    "Parses a relative call to a group."
    digits = source.get_while(DIGITS)
    if not digits:
        raise error("missing relative group number", source.string, source.pos)

    offset = int(digits)
    group = info.group_count + offset if ch == "+" else info.group_count - offset + 1
    if group <= 0:
        raise error("invalid relative group number", source.string, source.pos)

    source.expect(")")

    return CallGroup(info, group, pos)

def parse_call_named_group(source, info, pos):
    "Parses a call to a named group."
    group = parse_name(source)
    source.expect(")")

    return CallGroup(info, group, pos)

def parse_flag_set(source):
    "Parses a set of inline flags."
    flags = 0

    try:
        while True:
            saved_pos = source.pos
            ch = source.get()
            if ch == "V":
                ch += source.get()
            flags |= REGEX_FLAGS[ch]
    except KeyError:
        source.pos = saved_pos

    return flags

def parse_flags(source, info):
    "Parses flags being turned on/off."
    flags_on = parse_flag_set(source)
    if source.match("-"):
        flags_off = parse_flag_set(source)
        if not flags_off:
            raise error("bad inline flags: no flags after '-'", source.string,
              source.pos)
    else:
        flags_off = 0

    if flags_on & LOCALE:
        # Remember that this pattern as an inline locale flag.
        info.inline_locale = True

    return flags_on, flags_off

def parse_subpattern(source, info, flags_on, flags_off):
    "Parses a subpattern with scoped flags."
    saved_flags = info.flags
    info.flags = (info.flags | flags_on) & ~flags_off

    # Ensure that there aren't multiple encoding flags set.
    if info.flags & (ASCII | LOCALE | UNICODE):
        info.flags = (info.flags & ~_ALL_ENCODINGS) | flags_on

    source.ignore_space = bool(info.flags & VERBOSE)
    try:
        subpattern = _parse_pattern(source, info)
        source.expect(")")
    finally:
        info.flags = saved_flags
        source.ignore_space = bool(info.flags & VERBOSE)

    return subpattern

def parse_flags_subpattern(source, info):
    """Parses a flags subpattern. It could be inline flags or a subpattern
    possibly with local flags. If it's a subpattern, then that's returned;
    if it's a inline flags, then None is returned.
    """
    flags_on, flags_off = parse_flags(source, info)

    if flags_off & GLOBAL_FLAGS:
        raise error("bad inline flags: cannot turn off global flag",
          source.string, source.pos)

    if flags_on & flags_off:
        raise error("bad inline flags: flag turned on and off", source.string,
          source.pos)

    # Handle flags which are global in all regex behaviours.
    new_global_flags = (flags_on & ~info.global_flags) & GLOBAL_FLAGS
    if new_global_flags:
        info.global_flags |= new_global_flags

        # A global has been turned on, so reparse the pattern.
        raise _UnscopedFlagSet(info.global_flags)

    # Ensure that from now on we have only scoped flags.
    flags_on &= ~GLOBAL_FLAGS

    if source.match(":"):
        return parse_subpattern(source, info, flags_on, flags_off)

    if source.match(")"):
        parse_positional_flags(source, info, flags_on, flags_off)
        return None

    raise error("unknown extension", source.string, source.pos)

def parse_positional_flags(source, info, flags_on, flags_off):
    "Parses positional flags."
    info.flags = (info.flags | flags_on) & ~flags_off
    source.ignore_space = bool(info.flags & VERBOSE)

def parse_name(source, allow_numeric=False, allow_group_0=False):
    "Parses a name."
    name = source.get_while(set(")>"), include=False)

    if not name:
        raise error("missing group name", source.string, source.pos)

    if name.isdigit():
        min_group = 0 if allow_group_0 else 1
        if not allow_numeric or int(name) < min_group:
            raise error("bad character in group name", source.string,
              source.pos)
    else:
        if not name.isidentifier():
            raise error("bad character in group name", source.string,
              source.pos)

    return name

def is_octal(string):
    "Checks whether a string is octal."
    return all(ch in OCT_DIGITS for ch in string)

def is_decimal(string):
    "Checks whether a string is decimal."
    return all(ch in DIGITS for ch in string)

def is_hexadecimal(string):
    "Checks whether a string is hexadecimal."
    return all(ch in HEX_DIGITS for ch in string)

def parse_escape(source, info, in_set):
    "Parses an escape sequence."
    saved_ignore = source.ignore_space
    source.ignore_space = False
    ch = source.get()
    source.ignore_space = saved_ignore
    if not ch:
        # A backslash at the end of the pattern.
        raise error("bad escape (end of pattern)", source.string, source.pos)
    if ch in HEX_ESCAPES:
        # A hexadecimal escape sequence.
        return parse_hex_escape(source, info, ch, HEX_ESCAPES[ch], in_set, ch)
    elif ch == "g" and not in_set:
        # A group reference.
        saved_pos = source.pos
        try:
            return parse_group_ref(source, info)
        except error:
            # Invalid as a group reference, so assume it's a literal.
            source.pos = saved_pos

        return make_character(info, ord(ch), in_set)
    elif ch == "G" and not in_set:
        # A search anchor.
        return SearchAnchor()
    elif ch == "L" and not in_set:
        # A string set.
        return parse_string_set(source, info)
    elif ch == "N":
        # A named codepoint.
        return parse_named_char(source, info, in_set)
    elif ch in "pP":
        # A Unicode property, positive or negative.
        return parse_property(source, info, ch == "p", in_set)
    elif ch == "R" and not in_set:
        # A line ending.
        charset = [0x0A, 0x0B, 0x0C, 0x0D]
        if info.guess_encoding == UNICODE:
            charset.extend([0x85, 0x2028, 0x2029])

        return Atomic(Branch([String([0x0D, 0x0A]), SetUnion(info, [Character(c)
          for c in charset])]))
    elif ch == "X" and not in_set:
        # A grapheme cluster.
        return Grapheme()
    elif ch in ALPHA:
        # An alphabetic escape sequence.
        # Positional escapes aren't allowed inside a character set.
        if not in_set:
            if info.flags & WORD:
                value = WORD_POSITION_ESCAPES.get(ch)
            elif info.flags & ASCII:
                value = ASCII_POSITION_ESCAPES.get(ch)
            elif info.flags & UNICODE:
                value = UNICODE_POSITION_ESCAPES.get(ch)
            else:
                value = POSITION_ESCAPES.get(ch)

            if value:
                return value

        if info.flags & ASCII:
            value = ASCII_CHARSET_ESCAPES.get(ch)
        elif info.flags & UNICODE:
            value = UNICODE_CHARSET_ESCAPES.get(ch)
        else:
            value = CHARSET_ESCAPES.get(ch)

        if value:
            return value

        value = CHARACTER_ESCAPES.get(ch)
        if value:
            return Character(ord(value))

        raise error("bad escape \\%s" % ch, source.string, source.pos)
    elif ch in DIGITS:
        # A numeric escape sequence.
        return parse_numeric_escape(source, info, ch, in_set)
    else:
        # A literal.
        return make_character(info, ord(ch), in_set)

def parse_numeric_escape(source, info, ch, in_set):
    "Parses a numeric escape sequence."
    if in_set or ch == "0":
        # Octal escape sequence, max 3 digits.
        return parse_octal_escape(source, info, [ch], in_set)

    # At least 1 digit, so either octal escape or group.
    digits = ch
    saved_pos = source.pos
    ch = source.get()
    if ch in DIGITS:
        # At least 2 digits, so either octal escape or group.
        digits += ch
        saved_pos = source.pos
        ch = source.get()
        if is_octal(digits) and ch in OCT_DIGITS:
            # 3 octal digits, so octal escape sequence.
            encoding = info.flags & _ALL_ENCODINGS
            if encoding == ASCII or encoding == LOCALE:
                octal_mask = 0xFF
            else:
                octal_mask = 0x1FF

            value = int(digits + ch, 8) & octal_mask
            return make_character(info, value)

    # Group reference.
    source.pos = saved_pos
    if info.is_open_group(digits):
        raise error("cannot refer to an open group", source.string, source.pos)

    return make_ref_group(info, digits, source.pos)

def parse_octal_escape(source, info, digits, in_set):
    "Parses an octal escape sequence."
    saved_pos = source.pos
    ch = source.get()
    while len(digits) < 3 and ch in OCT_DIGITS:
        digits.append(ch)
        saved_pos = source.pos
        ch = source.get()

    source.pos = saved_pos
    try:
        value = int("".join(digits), 8)
        return make_character(info, value, in_set)
    except ValueError:
        if digits[0] in OCT_DIGITS:
            raise error("incomplete escape \\%s" % ''.join(digits),
              source.string, source.pos)
        else:
            raise error("bad escape \\%s" % digits[0], source.string,
              source.pos)

def parse_hex_escape(source, info, esc, expected_len, in_set, type):
    "Parses a hex escape sequence."
    saved_pos = source.pos
    digits = []
    for i in range(expected_len):
        ch = source.get()
        if ch not in HEX_DIGITS:
            raise error("incomplete escape \\%s%s" % (type, ''.join(digits)),
              source.string, saved_pos)
        digits.append(ch)

    try:
        value = int("".join(digits), 16)
    except ValueError:
        pass
    else:
        if value < 0x110000:
            return make_character(info, value, in_set)

    # Bad hex escape.
    raise error("bad hex escape \\%s%s" % (esc, ''.join(digits)),
      source.string, saved_pos)

def parse_group_ref(source, info):
    "Parses a group reference."
    source.expect("<")
    saved_pos = source.pos
    name = parse_name(source, True)
    source.expect(">")
    if info.is_open_group(name):
        raise error("cannot refer to an open group", source.string, source.pos)

    return make_ref_group(info, name, saved_pos)

def parse_string_set(source, info):
    "Parses a string set reference."
    source.expect("<")
    name = parse_name(source, True)
    source.expect(">")
    if name is None or name not in info.kwargs:
        raise error("undefined named list", source.string, source.pos)

    return make_string_set(info, name)

def parse_named_char(source, info, in_set):
    "Parses a named character."
    saved_pos = source.pos
    if source.match("{"):
        name = source.get_while(NAMED_CHAR_PART, keep_spaces=True)
        if source.match("}"):
            try:
                value = unicodedata.lookup(name)
                return make_character(info, ord(value), in_set)
            except KeyError:
                raise error("undefined character name", source.string,
                  source.pos)

    source.pos = saved_pos
    return make_character(info, ord("N"), in_set)

def parse_property(source, info, positive, in_set):
    "Parses a Unicode property."
    saved_pos = source.pos
    ch = source.get()
    if ch == "{":
        negate = source.match("^")
        prop_name, name = parse_property_name(source)
        if source.match("}"):
            # It's correctly delimited.
            if info.flags & ASCII:
                encoding = ASCII_ENCODING
            elif info.flags & UNICODE:
                encoding = UNICODE_ENCODING
            else:
                encoding = 0

            prop = lookup_property(prop_name, name, positive != negate, source,
              encoding=encoding)
            return make_property(info, prop, in_set)
    elif ch and ch in "CLMNPSZ":
        # An abbreviated property, eg \pL.
        if info.flags & ASCII:
            encoding = ASCII_ENCODING
        elif info.flags & UNICODE:
            encoding = UNICODE_ENCODING
        else:
            encoding = 0

        prop = lookup_property(None, ch, positive, source, encoding=encoding)
        return make_property(info, prop, in_set)

    # Not a property, so treat as a literal "p" or "P".
    source.pos = saved_pos
    ch = "p" if positive else "P"
    return make_character(info, ord(ch), in_set)

def parse_property_name(source):
    "Parses a property name, which may be qualified."
    name = source.get_while(PROPERTY_NAME_PART)
    saved_pos = source.pos

    ch = source.get()
    if ch and ch in ":=":
        prop_name = name
        name = source.get_while(ALNUM | set(" &_-./")).strip()

        if name:
            # Name after the ":" or "=", so it's a qualified name.
            saved_pos = source.pos
        else:
            # No name after the ":" or "=", so assume it's an unqualified name.
            prop_name, name = None, prop_name
    else:
        prop_name = None

    source.pos = saved_pos
    return prop_name, name

def parse_set(source, info):
    "Parses a character set."
    version = (info.flags & _ALL_VERSIONS) or DEFAULT_VERSION

    saved_ignore = source.ignore_space
    source.ignore_space = False
    # Negative set?
    negate = source.match("^")
    try:
        if version == VERSION0:
            item = parse_set_imp_union(source, info)
        else:
            item = parse_set_union(source, info)

        if not source.match("]"):
            raise error("missing ]", source.string, source.pos)
    finally:
        source.ignore_space = saved_ignore

    if negate:
        item = item.with_flags(positive=not item.positive)

    item = item.with_flags(case_flags=make_case_flags(info))

    return item

def parse_set_union(source, info):
    "Parses a set union ([x||y])."
    items = [parse_set_symm_diff(source, info)]
    while source.match("||"):
        items.append(parse_set_symm_diff(source, info))

    if len(items) == 1:
        return items[0]
    return SetUnion(info, items)

def parse_set_symm_diff(source, info):
    "Parses a set symmetric difference ([x~~y])."
    items = [parse_set_inter(source, info)]
    while source.match("~~"):
        items.append(parse_set_inter(source, info))

    if len(items) == 1:
        return items[0]
    return SetSymDiff(info, items)

def parse_set_inter(source, info):
    "Parses a set intersection ([x&&y])."
    items = [parse_set_diff(source, info)]
    while source.match("&&"):
        items.append(parse_set_diff(source, info))

    if len(items) == 1:
        return items[0]
    return SetInter(info, items)

def parse_set_diff(source, info):
    "Parses a set difference ([x--y])."
    items = [parse_set_imp_union(source, info)]
    while source.match("--"):
        items.append(parse_set_imp_union(source, info))

    if len(items) == 1:
        return items[0]
    return SetDiff(info, items)

def parse_set_imp_union(source, info):
    "Parses a set implicit union ([xy])."
    version = (info.flags & _ALL_VERSIONS) or DEFAULT_VERSION

    items = [parse_set_member(source, info)]
    while True:
        saved_pos = source.pos
        if source.match("]"):
            # End of the set.
            source.pos = saved_pos
            break

        if version == VERSION1 and any(source.match(op) for op in SET_OPS):
            # The new behaviour has set operators.
            source.pos = saved_pos
            break

        items.append(parse_set_member(source, info))

    if len(items) == 1:
        return items[0]
    return SetUnion(info, items)

def parse_set_member(source, info):
    "Parses a member in a character set."
    # Parse a set item.
    start = parse_set_item(source, info)
    saved_pos1 = source.pos
    if (not isinstance(start, Character) or not start.positive or not
      source.match("-")):
        # It's not the start of a range.
        return start

    version = (info.flags & _ALL_VERSIONS) or DEFAULT_VERSION

    # It looks like the start of a range of characters.
    saved_pos2 = source.pos
    if version == VERSION1 and source.match("-"):
        # It's actually the set difference operator '--', so return the
        # character.
        source.pos = saved_pos1
        return start

    if source.match("]"):
        # We've reached the end of the set, so return both the character and
        # hyphen.
        source.pos = saved_pos2
        return SetUnion(info, [start, Character(ord("-"))])

    # Parse a set item.
    end = parse_set_item(source, info)
    if not isinstance(end, Character) or not end.positive:
        # It's not a range, so return the character, hyphen and property.
        return SetUnion(info, [start, Character(ord("-")), end])

    # It _is_ a range.
    if start.value > end.value:
        raise error("bad character range", source.string, source.pos)

    if start.value == end.value:
        return start

    return Range(start.value, end.value)

def parse_set_item(source, info):
    "Parses an item in a character set."
    version = (info.flags & _ALL_VERSIONS) or DEFAULT_VERSION

    if source.match("\\"):
        # An escape sequence in a set.
        return parse_escape(source, info, True)

    saved_pos = source.pos
    if source.match("[:"):
        # Looks like a POSIX character class.
        try:
            return parse_posix_class(source, info)
        except ParseError:
            # Not a POSIX character class.
            source.pos = saved_pos

    if version == VERSION1 and source.match("["):
        # It's the start of a nested set.

        # Negative set?
        negate = source.match("^")
        item = parse_set_union(source, info)

        if not source.match("]"):
            raise error("missing ]", source.string, source.pos)

        if negate:
            item = item.with_flags(positive=not item.positive)

        return item

    ch = source.get()
    if not ch:
        raise error("unterminated character set", source.string, source.pos)

    return Character(ord(ch))

def parse_posix_class(source, info):
    "Parses a POSIX character class."
    negate = source.match("^")
    prop_name, name = parse_property_name(source)
    if not source.match(":]"):
        raise ParseError()

    return lookup_property(prop_name, name, not negate, source, posix=True)

def float_to_rational(flt):
    "Converts a float to a rational pair."
    int_part = int(flt)
    error = flt - int_part
    if abs(error) < 0.0001:
        return int_part, 1

    den, num = float_to_rational(1.0 / error)

    return int_part * den + num, den

def numeric_to_rational(numeric):
    "Converts a numeric string to a rational string, if possible."
    if numeric[ : 1] == "-":
        sign, numeric = numeric[0], numeric[1 : ]
    else:
        sign = ""

    parts = numeric.split("/")
    if len(parts) == 2:
        num, den = float_to_rational(float(parts[0]) / float(parts[1]))
    elif len(parts) == 1:
        num, den = float_to_rational(float(parts[0]))
    else:
        raise ValueError()

    result = "{}{}/{}".format(sign, num, den)
    if result.endswith("/1"):
        return result[ : -2]

    return result

def standardise_name(name):
    "Standardises a property or value name."
    try:
        return numeric_to_rational("".join(name))
    except (ValueError, ZeroDivisionError):
        return "".join(ch for ch in name if ch not in "_- ").upper()

_POSIX_CLASSES = set('ALNUM DIGIT PUNCT XDIGIT'.split())

_BINARY_VALUES = set('YES Y NO N TRUE T FALSE F'.split())

def lookup_property(property, value, positive, source=None, posix=False, encoding=0):
    "Looks up a property."
    # Normalise the names (which may still be lists).
    property = standardise_name(property) if property else None
    value = standardise_name(value)

    if (property, value) == ("GENERALCATEGORY", "ASSIGNED"):
        property, value, positive = "GENERALCATEGORY", "UNASSIGNED", not positive

    if posix and not property and value.upper() in _POSIX_CLASSES:
        value = 'POSIX' + value

    if property:
        # Both the property and the value are provided.
        prop = PROPERTIES.get(property)
        if not prop:
            if not source:
                raise error("unknown property")

            raise error("unknown property", source.string, source.pos)

        prop_id, value_dict = prop
        val_id = value_dict.get(value)
        if val_id is None:
            if not source:
                raise error("unknown property value")

            raise error("unknown property value", source.string, source.pos)

        return Property((prop_id << 16) | val_id, positive, encoding=encoding)

    # Only the value is provided.
    # It might be the name of a GC, script or block value.
    for property in ("GC", "SCRIPT", "BLOCK"):
        prop_id, value_dict = PROPERTIES.get(property)
        val_id = value_dict.get(value)
        if val_id is not None:
            return Property((prop_id << 16) | val_id, positive, encoding=encoding)

    # It might be the name of a binary property.
    prop = PROPERTIES.get(value)
    if prop:
        prop_id, value_dict = prop
        if set(value_dict) == _BINARY_VALUES:
            return Property((prop_id << 16) | 1, positive, encoding=encoding)

        return Property(prop_id << 16, not positive, encoding=encoding)

    # It might be the name of a binary property starting with a prefix.
    if value.startswith("IS"):
        prop = PROPERTIES.get(value[2 : ])
        if prop:
            prop_id, value_dict = prop
            if "YES" in value_dict:
                return Property((prop_id << 16) | 1, positive, encoding=encoding)

    # It might be the name of a script or block starting with a prefix.
    for prefix, property in (("IS", "SCRIPT"), ("IN", "BLOCK")):
        if value.startswith(prefix):
            prop_id, value_dict = PROPERTIES.get(property)
            val_id = value_dict.get(value[2 : ])
            if val_id is not None:
                return Property((prop_id << 16) | val_id, positive, encoding=encoding)

    # Unknown property.
    if not source:
        raise error("unknown property")

    raise error("unknown property", source.string, source.pos)

def _compile_replacement(source, pattern, is_unicode):
    "Compiles a replacement template escape sequence."
    ch = source.get()
    if ch in ALPHA:
        # An alphabetic escape sequence.
        value = CHARACTER_ESCAPES.get(ch)
        if value:
            return False, [ord(value)]

        if ch in HEX_ESCAPES and (ch == "x" or is_unicode):
            # A hexadecimal escape sequence.
            return False, [parse_repl_hex_escape(source, HEX_ESCAPES[ch], ch)]

        if ch == "g":
            # A group preference.
            return True, [compile_repl_group(source, pattern)]

        if ch == "N" and is_unicode:
            # A named character.
            value = parse_repl_named_char(source)
            if value is not None:
                return False, [value]

        raise error("bad escape \\%s" % ch, source.string, source.pos)

    if isinstance(source.sep, bytes):
        octal_mask = 0xFF
    else:
        octal_mask = 0x1FF

    if ch == "0":
        # An octal escape sequence.
        digits = ch
        while len(digits) < 3:
            saved_pos = source.pos
            ch = source.get()
            if ch not in OCT_DIGITS:
                source.pos = saved_pos
                break
            digits += ch

        return False, [int(digits, 8) & octal_mask]

    if ch in DIGITS:
        # Either an octal escape sequence (3 digits) or a group reference (max
        # 2 digits).
        digits = ch
        saved_pos = source.pos
        ch = source.get()
        if ch in DIGITS:
            digits += ch
            saved_pos = source.pos
            ch = source.get()
            if ch and is_octal(digits + ch):
                # An octal escape sequence.
                return False, [int(digits + ch, 8) & octal_mask]

        # A group reference.
        source.pos = saved_pos
        return True, [int(digits)]

    if ch == "\\":
        # An escaped backslash is a backslash.
        return False, [ord("\\")]

    if not ch:
        # A trailing backslash.
        raise error("bad escape (end of pattern)", source.string, source.pos)

    # An escaped non-backslash is a backslash followed by the literal.
    return False, [ord("\\"), ord(ch)]

def parse_repl_hex_escape(source, expected_len, type):
    "Parses a hex escape sequence in a replacement string."
    digits = []
    for i in range(expected_len):
        ch = source.get()
        if ch not in HEX_DIGITS:
            raise error("incomplete escape \\%s%s" % (type, ''.join(digits)),
              source.string, source.pos)
        digits.append(ch)

    return int("".join(digits), 16)

def parse_repl_named_char(source):
    "Parses a named character in a replacement string."
    saved_pos = source.pos
    if source.match("{"):
        name = source.get_while(ALPHA | set(" "))

        if source.match("}"):
            try:
                value = unicodedata.lookup(name)
                return ord(value)
            except KeyError:
                raise error("undefined character name", source.string,
                  source.pos)

    source.pos = saved_pos
    return None

def compile_repl_group(source, pattern):
    "Compiles a replacement template group reference."
    source.expect("<")
    name = parse_name(source, True, True)

    source.expect(">")
    if name.isdigit():
        index = int(name)
        if not 0 <= index <= pattern.groups:
            raise error("invalid group reference", source.string, source.pos)

        return index

    try:
        return pattern.groupindex[name]
    except KeyError:
        raise IndexError("unknown group")

# The regular expression is parsed into a syntax tree. The different types of
# node are defined below.

INDENT = "  "
POSITIVE_OP = 0x1
ZEROWIDTH_OP = 0x2
FUZZY_OP = 0x4
REVERSE_OP = 0x8
REQUIRED_OP = 0x10
ENCODING_OP_SHIFT = 5

POS_TEXT = {False: "NON-MATCH", True: "MATCH"}
CASE_TEXT = {NOCASE: "", IGNORECASE: " SIMPLE_IGNORE_CASE", FULLCASE: "",
  FULLIGNORECASE: " FULL_IGNORE_CASE"}

def make_sequence(items):
    if len(items) == 1:
        return items[0]
    return Sequence(items)

# Common base class for all nodes.
class RegexBase:
    def __init__(self):
        self._key = self.__class__

    def with_flags(self, positive=None, case_flags=None, zerowidth=None):
        if positive is None:
            positive = self.positive
        else:
            positive = bool(positive)
        if case_flags is None:
            case_flags = self.case_flags
        else:
            case_flags = CASE_FLAGS_COMBINATIONS[case_flags & CASE_FLAGS]
        if zerowidth is None:
            zerowidth = self.zerowidth
        else:
            zerowidth = bool(zerowidth)

        if (positive == self.positive and case_flags == self.case_flags and
          zerowidth == self.zerowidth):
            return self

        return self.rebuild(positive, case_flags, zerowidth)

    def fix_groups(self, pattern, reverse, fuzzy):
        pass

    def optimise(self, info, reverse):
        return self

    def pack_characters(self, info):
        return self

    def remove_captures(self):
        return self

    def is_atomic(self):
        return True

    def can_be_affix(self):
        return True

    def contains_group(self):
        return False

    def get_firstset(self, reverse):
        raise _FirstSetError()

    def has_simple_start(self):
        return False

    def compile(self, reverse=False, fuzzy=False):
        return self._compile(reverse, fuzzy)

    def is_empty(self):
        return False

    def __hash__(self):
        return hash(self._key)

    def __eq__(self, other):
        return type(self) is type(other) and self._key == other._key

    def __ne__(self, other):
        return not self.__eq__(other)

    def get_required_string(self, reverse):
        return self.max_width(), None

# Base class for zero-width nodes.
class ZeroWidthBase(RegexBase):
    def __init__(self, positive=True, encoding=0):
        RegexBase.__init__(self)
        self.positive = bool(positive)
        self.encoding = encoding

        self._key = self.__class__, self.positive

    def get_firstset(self, reverse):
        return set([None])

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if fuzzy:
            flags |= FUZZY_OP
        if reverse:
            flags |= REVERSE_OP
        flags |= self.encoding << ENCODING_OP_SHIFT
        return [(self._opcode, flags)]

    def dump(self, indent, reverse):
        print("{}{} {}{}".format(INDENT * indent, self._op_name,
          POS_TEXT[self.positive], ["", " ASCII"][self.encoding]))

    def max_width(self):
        return 0

class Any(RegexBase):
    _opcode = {False: OP.ANY, True: OP.ANY_REV}
    _op_name = "ANY"

    def has_simple_start(self):
        return True

    def _compile(self, reverse, fuzzy):
        flags = 0
        if fuzzy:
            flags |= FUZZY_OP
        return [(self._opcode[reverse], flags)]

    def dump(self, indent, reverse):
        print("{}{}".format(INDENT * indent, self._op_name))

    def max_width(self):
        return 1

class AnyAll(Any):
    _opcode = {False: OP.ANY_ALL, True: OP.ANY_ALL_REV}
    _op_name = "ANY_ALL"

    def __init__(self):
        self.positive = True
        self.zerowidth = False
        self.case_flags = 0

        self._key = self.__class__, self.positive

class AnyU(Any):
    _opcode = {False: OP.ANY_U, True: OP.ANY_U_REV}
    _op_name = "ANY_U"

class Atomic(RegexBase):
    def __init__(self, subpattern):
        RegexBase.__init__(self)
        self.subpattern = subpattern

    def fix_groups(self, pattern, reverse, fuzzy):
        self.subpattern.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        self.subpattern = self.subpattern.optimise(info, reverse)

        if self.subpattern.is_empty():
            return self.subpattern
        return self

    def pack_characters(self, info):
        self.subpattern = self.subpattern.pack_characters(info)
        return self

    def remove_captures(self):
        self.subpattern = self.subpattern.remove_captures()
        return self

    def can_be_affix(self):
        return self.subpattern.can_be_affix()

    def contains_group(self):
        return self.subpattern.contains_group()

    def get_firstset(self, reverse):
        return self.subpattern.get_firstset(reverse)

    def has_simple_start(self):
        return self.subpattern.has_simple_start()

    def _compile(self, reverse, fuzzy):
        return ([(OP.ATOMIC, )] + self.subpattern.compile(reverse, fuzzy) +
          [(OP.END, )])

    def dump(self, indent, reverse):
        print("{}ATOMIC".format(INDENT * indent))
        self.subpattern.dump(indent + 1, reverse)

    def is_empty(self):
        return self.subpattern.is_empty()

    def __eq__(self, other):
        return (type(self) is type(other) and self.subpattern ==
          other.subpattern)

    def max_width(self):
        return self.subpattern.max_width()

    def get_required_string(self, reverse):
        return self.subpattern.get_required_string(reverse)

class Boundary(ZeroWidthBase):
    _opcode = OP.BOUNDARY
    _op_name = "BOUNDARY"

class Branch(RegexBase):
    def __init__(self, branches):
        RegexBase.__init__(self)
        self.branches = branches

    def fix_groups(self, pattern, reverse, fuzzy):
        for b in self.branches:
            b.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        if not self.branches:
            return Sequence([])

        # Flatten branches within branches.
        branches = Branch._flatten_branches(info, reverse, self.branches)

        # Move any common prefix or suffix out of the branches.
        if reverse:
            suffix, branches = Branch._split_common_suffix(info, branches)
            prefix = []
        else:
            prefix, branches = Branch._split_common_prefix(info, branches)
            suffix = []

        # Try to reduce adjacent single-character branches to sets.
        branches = Branch._reduce_to_set(info, reverse, branches)

        if len(branches) > 1:
            sequence = [Branch(branches)]

            if not prefix or not suffix:
                # We might be able to add a quick precheck before the branches.
                firstset = self._add_precheck(info, reverse, branches)

                if firstset:
                    if reverse:
                        sequence.append(firstset)
                    else:
                        sequence.insert(0, firstset)
        else:
            sequence = branches

        return make_sequence(prefix + sequence + suffix)

    def _add_precheck(self, info, reverse, branches):
        charset = set()
        pos = -1 if reverse else 0

        for branch in branches:
            if type(branch) is Literal and branch.case_flags == NOCASE:
                charset.add(branch.characters[pos])
            else:
                return

        if not charset:
            return None

        return _check_firstset(info, reverse, [Character(c) for c in charset])

    def pack_characters(self, info):
        self.branches = [b.pack_characters(info) for b in self.branches]
        return self

    def remove_captures(self):
        self.branches = [b.remove_captures() for b in self.branches]
        return self

    def is_atomic(self):
        return all(b.is_atomic() for b in self.branches)

    def can_be_affix(self):
        return all(b.can_be_affix() for b in self.branches)

    def contains_group(self):
        return any(b.contains_group() for b in self.branches)

    def get_firstset(self, reverse):
        fs = set()
        for b in self.branches:
            fs |= b.get_firstset(reverse)

        return fs or set([None])

    def _compile(self, reverse, fuzzy):
        if not self.branches:
            return []

        code = [(OP.BRANCH, )]
        for b in self.branches:
            code.extend(b.compile(reverse, fuzzy))
            code.append((OP.NEXT, ))

        code[-1] = (OP.END, )

        return code

    def dump(self, indent, reverse):
        print("{}BRANCH".format(INDENT * indent))
        self.branches[0].dump(indent + 1, reverse)
        for b in self.branches[1 : ]:
            print("{}OR".format(INDENT * indent))
            b.dump(indent + 1, reverse)

    @staticmethod
    def _flatten_branches(info, reverse, branches):
        # Flatten the branches so that there aren't branches of branches.
        new_branches = []
        for b in branches:
            b = b.optimise(info, reverse)
            if isinstance(b, Branch):
                new_branches.extend(b.branches)
            else:
                new_branches.append(b)

        return new_branches

    @staticmethod
    def _split_common_prefix(info, branches):
        # Common leading items can be moved out of the branches.
        # Get the items in the branches.
        alternatives = []
        for b in branches:
            if isinstance(b, Sequence):
                alternatives.append(b.items)
            else:
                alternatives.append([b])

        # What is the maximum possible length of the prefix?
        max_count = min(len(a) for a in alternatives)

        # What is the longest common prefix?
        prefix = alternatives[0]
        pos = 0
        end_pos = max_count
        while pos < end_pos and prefix[pos].can_be_affix() and all(a[pos] ==
          prefix[pos] for a in alternatives):
            pos += 1
        count = pos

        if info.flags & UNICODE:
            # We need to check that we're not splitting a sequence of
            # characters which could form part of full case-folding.
            count = pos
            while count > 0 and not all(Branch._can_split(a, count) for a in
              alternatives):
                count -= 1

        # No common prefix is possible.
        if count == 0:
            return [], branches

        # Rebuild the branches.
        new_branches = []
        for a in alternatives:
            new_branches.append(make_sequence(a[count : ]))

        return prefix[ : count], new_branches

    @staticmethod
    def _split_common_suffix(info, branches):
        # Common trailing items can be moved out of the branches.
        # Get the items in the branches.
        alternatives = []
        for b in branches:
            if isinstance(b, Sequence):
                alternatives.append(b.items)
            else:
                alternatives.append([b])

        # What is the maximum possible length of the suffix?
        max_count = min(len(a) for a in alternatives)

        # What is the longest common suffix?
        suffix = alternatives[0]
        pos = -1
        end_pos = -1 - max_count
        while pos > end_pos and suffix[pos].can_be_affix() and all(a[pos] ==
          suffix[pos] for a in alternatives):
            pos -= 1
        count = -1 - pos

        if info.flags & UNICODE:
            # We need to check that we're not splitting a sequence of
            # characters which could form part of full case-folding.
            while count > 0 and not all(Branch._can_split_rev(a, count) for a
              in alternatives):
                count -= 1

        # No common suffix is possible.
        if count == 0:
            return [], branches

        # Rebuild the branches.
        new_branches = []
        for a in alternatives:
            new_branches.append(make_sequence(a[ : -count]))

        return suffix[-count : ], new_branches

    @staticmethod
    def _can_split(items, count):
        # Check the characters either side of the proposed split.
        if not Branch._is_full_case(items, count - 1):
            return True

        if not Branch._is_full_case(items, count):
            return True

        # Check whether a 1-1 split would be OK.
        if Branch._is_folded(items[count - 1 : count + 1]):
            return False

        # Check whether a 1-2 split would be OK.
        if (Branch._is_full_case(items, count + 2) and
          Branch._is_folded(items[count - 1 : count + 2])):
            return False

        # Check whether a 2-1 split would be OK.
        if (Branch._is_full_case(items, count - 2) and
          Branch._is_folded(items[count - 2 : count + 1])):
            return False

        return True

    @staticmethod
    def _can_split_rev(items, count):
        end = len(items)

        # Check the characters either side of the proposed split.
        if not Branch._is_full_case(items, end - count):
            return True

        if not Branch._is_full_case(items, end - count - 1):
            return True

        # Check whether a 1-1 split would be OK.
        if Branch._is_folded(items[end - count - 1 : end - count + 1]):
            return False

        # Check whether a 1-2 split would be OK.
        if (Branch._is_full_case(items, end - count + 2) and
          Branch._is_folded(items[end - count - 1 : end - count + 2])):
            return False

        # Check whether a 2-1 split would be OK.
        if (Branch._is_full_case(items, end - count - 2) and
          Branch._is_folded(items[end - count - 2 : end - count + 1])):
            return False

        return True

    @staticmethod
    def _merge_common_prefixes(info, reverse, branches):
        # Branches with the same case-sensitive character prefix can be grouped
        # together if they are separated only by other branches with a
        # character prefix.
        prefixed = defaultdict(list)
        order = {}
        new_branches = []
        for b in branches:
            if Branch._is_simple_character(b):
                # Branch starts with a simple character.
                prefixed[b.value].append([b])
                order.setdefault(b.value, len(order))
            elif (isinstance(b, Sequence) and b.items and
              Branch._is_simple_character(b.items[0])):
                # Branch starts with a simple character.
                prefixed[b.items[0].value].append(b.items)
                order.setdefault(b.items[0].value, len(order))
            else:
                Branch._flush_char_prefix(info, reverse, prefixed, order,
                  new_branches)

                new_branches.append(b)

        Branch._flush_char_prefix(info, prefixed, order, new_branches)

        return new_branches

    @staticmethod
    def _is_simple_character(c):
        return isinstance(c, Character) and c.positive and not c.case_flags

    @staticmethod
    def _reduce_to_set(info, reverse, branches):
        # Can the branches be reduced to a set?
        new_branches = []
        items = set()
        case_flags = NOCASE
        for b in branches:
            if isinstance(b, (Character, Property, SetBase)):
                # Branch starts with a single character.
                if b.case_flags != case_flags:
                    # Different case sensitivity, so flush.
                    Branch._flush_set_members(info, reverse, items, case_flags,
                      new_branches)

                    case_flags = b.case_flags

                items.add(b.with_flags(case_flags=NOCASE))
            else:
                Branch._flush_set_members(info, reverse, items, case_flags,
                  new_branches)

                new_branches.append(b)

        Branch._flush_set_members(info, reverse, items, case_flags,
          new_branches)

        return new_branches

    @staticmethod
    def _flush_char_prefix(info, reverse, prefixed, order, new_branches):
        # Flush the prefixed branches.
        if not prefixed:
            return

        for value, branches in sorted(prefixed.items(), key=lambda pair:
          order[pair[0]]):
            if len(branches) == 1:
                new_branches.append(make_sequence(branches[0]))
            else:
                subbranches = []
                optional = False
                for b in branches:
                    if len(b) > 1:
                        subbranches.append(make_sequence(b[1 : ]))
                    elif not optional:
                        subbranches.append(Sequence())
                        optional = True

                sequence = Sequence([Character(value), Branch(subbranches)])
                new_branches.append(sequence.optimise(info, reverse))

        prefixed.clear()
        order.clear()

    @staticmethod
    def _flush_set_members(info, reverse, items, case_flags, new_branches):
        # Flush the set members.
        if not items:
            return

        if len(items) == 1:
            item = list(items)[0]
        else:
            item = SetUnion(info, list(items)).optimise(info, reverse)

        new_branches.append(item.with_flags(case_flags=case_flags))

        items.clear()

    @staticmethod
    def _is_full_case(items, i):
        if not 0 <= i < len(items):
            return False

        item = items[i]
        return (isinstance(item, Character) and item.positive and
          (item.case_flags & FULLIGNORECASE) == FULLIGNORECASE)

    @staticmethod
    def _is_folded(items):
        if len(items) < 2:
            return False

        for i in items:
            if (not isinstance(i, Character) or not i.positive or not
              i.case_flags):
                return False

        folded = "".join(chr(i.value) for i in items)
        folded = _regex.fold_case(FULL_CASE_FOLDING, folded)

        # Get the characters which expand to multiple codepoints on folding.
        expanding_chars = _regex.get_expand_on_folding()

        for c in expanding_chars:
            if folded == _regex.fold_case(FULL_CASE_FOLDING, c):
                return True

        return False

    def is_empty(self):
        return all(b.is_empty() for b in self.branches)

    def __eq__(self, other):
        return type(self) is type(other) and self.branches == other.branches

    def max_width(self):
        return max(b.max_width() for b in self.branches)

class CallGroup(RegexBase):
    def __init__(self, info, group, position):
        RegexBase.__init__(self)
        self.info = info
        self.group = group
        self.position = position

        self._key = self.__class__, self.group

    def fix_groups(self, pattern, reverse, fuzzy):
        try:
            self.group = int(self.group)
        except ValueError:
            try:
                self.group = self.info.group_index[self.group]
            except KeyError:
                raise error("invalid group reference", pattern, self.position)

        if not 0 <= self.group <= self.info.group_count:
            raise error("unknown group", pattern, self.position)

        if self.group > 0 and self.info.open_group_count[self.group] > 1:
            raise error("ambiguous group reference", pattern, self.position)

        self.info.group_calls.append((self, reverse, fuzzy))

        self._key = self.__class__, self.group

    def remove_captures(self):
        raise error("group reference not allowed", self.pattern, self.position)

    def _compile(self, reverse, fuzzy):
        return [(OP.GROUP_CALL, self.call_ref)]

    def dump(self, indent, reverse):
        print("{}GROUP_CALL {}".format(INDENT * indent, self.group))

    def __eq__(self, other):
        return type(self) is type(other) and self.group == other.group

    def max_width(self):
        return UNLIMITED

    def __del__(self):
        self.info = None

class CallRef(RegexBase):
    def __init__(self, ref, parsed):
        self.ref = ref
        self.parsed = parsed

    def _compile(self, reverse, fuzzy):
        return ([(OP.CALL_REF, self.ref)] + self.parsed._compile(reverse,
          fuzzy) + [(OP.END, )])

class Character(RegexBase):
    _opcode = {(NOCASE, False): OP.CHARACTER, (IGNORECASE, False):
      OP.CHARACTER_IGN, (FULLCASE, False): OP.CHARACTER, (FULLIGNORECASE,
      False): OP.CHARACTER_IGN, (NOCASE, True): OP.CHARACTER_REV, (IGNORECASE,
      True): OP.CHARACTER_IGN_REV, (FULLCASE, True): OP.CHARACTER_REV,
      (FULLIGNORECASE, True): OP.CHARACTER_IGN_REV}

    def __init__(self, value, positive=True, case_flags=NOCASE,
      zerowidth=False):
        RegexBase.__init__(self)
        self.value = value
        self.positive = bool(positive)
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]
        self.zerowidth = bool(zerowidth)

        if (self.positive and (self.case_flags & FULLIGNORECASE) ==
          FULLIGNORECASE):
            self.folded = _regex.fold_case(FULL_CASE_FOLDING, chr(self.value))
        else:
            self.folded = chr(self.value)

        self._key = (self.__class__, self.value, self.positive,
          self.case_flags, self.zerowidth)

    def rebuild(self, positive, case_flags, zerowidth):
        return Character(self.value, positive, case_flags, zerowidth)

    def optimise(self, info, reverse, in_set=False):
        return self

    def get_firstset(self, reverse):
        return set([self])

    def has_simple_start(self):
        return True

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if self.zerowidth:
            flags |= ZEROWIDTH_OP
        if fuzzy:
            flags |= FUZZY_OP

        code = PrecompiledCode([self._opcode[self.case_flags, reverse], flags,
          self.value])

        if len(self.folded) > 1:
            # The character expands on full case-folding.
            code = Branch([code, String([ord(c) for c in self.folded],
              case_flags=self.case_flags)])

        return code.compile(reverse, fuzzy)

    def dump(self, indent, reverse):
        display = ascii(chr(self.value)).lstrip("bu")
        print("{}CHARACTER {} {}{}".format(INDENT * indent,
          POS_TEXT[self.positive], display, CASE_TEXT[self.case_flags]))

    def matches(self, ch):
        return (ch == self.value) == self.positive

    def max_width(self):
        return len(self.folded)

    def get_required_string(self, reverse):
        if not self.positive:
            return 1, None

        self.folded_characters = tuple(ord(c) for c in self.folded)

        return 0, self

class Conditional(RegexBase):
    def __init__(self, info, group, yes_item, no_item, position):
        RegexBase.__init__(self)
        self.info = info
        self.group = group
        self.yes_item = yes_item
        self.no_item = no_item
        self.position = position

    def fix_groups(self, pattern, reverse, fuzzy):
        try:
            self.group = int(self.group)
        except ValueError:
            try:
                self.group = self.info.group_index[self.group]
            except KeyError:
                if self.group == 'DEFINE':
                    # 'DEFINE' is a special name unless there's a group with
                    # that name.
                    self.group = 0
                else:
                    raise error("unknown group", pattern, self.position)

        if not 0 <= self.group <= self.info.group_count:
            raise error("invalid group reference", pattern, self.position)

        self.yes_item.fix_groups(pattern, reverse, fuzzy)
        self.no_item.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        yes_item = self.yes_item.optimise(info, reverse)
        no_item = self.no_item.optimise(info, reverse)

        return Conditional(info, self.group, yes_item, no_item, self.position)

    def pack_characters(self, info):
        self.yes_item = self.yes_item.pack_characters(info)
        self.no_item = self.no_item.pack_characters(info)
        return self

    def remove_captures(self):
        self.yes_item = self.yes_item.remove_captures()
        self.no_item = self.no_item.remove_captures()

    def is_atomic(self):
        return self.yes_item.is_atomic() and self.no_item.is_atomic()

    def can_be_affix(self):
        return self.yes_item.can_be_affix() and self.no_item.can_be_affix()

    def contains_group(self):
        return self.yes_item.contains_group() or self.no_item.contains_group()

    def get_firstset(self, reverse):
        return (self.yes_item.get_firstset(reverse) |
          self.no_item.get_firstset(reverse))

    def _compile(self, reverse, fuzzy):
        code = [(OP.GROUP_EXISTS, self.group)]
        code.extend(self.yes_item.compile(reverse, fuzzy))
        add_code = self.no_item.compile(reverse, fuzzy)
        if add_code:
            code.append((OP.NEXT, ))
            code.extend(add_code)

        code.append((OP.END, ))

        return code

    def dump(self, indent, reverse):
        print("{}GROUP_EXISTS {}".format(INDENT * indent, self.group))
        self.yes_item.dump(indent + 1, reverse)
        if not self.no_item.is_empty():
            print("{}OR".format(INDENT * indent))
            self.no_item.dump(indent + 1, reverse)

    def is_empty(self):
        return self.yes_item.is_empty() and self.no_item.is_empty()

    def __eq__(self, other):
        return type(self) is type(other) and (self.group, self.yes_item,
          self.no_item) == (other.group, other.yes_item, other.no_item)

    def max_width(self):
        return max(self.yes_item.max_width(), self.no_item.max_width())

    def __del__(self):
        self.info = None

class DefaultBoundary(ZeroWidthBase):
    _opcode = OP.DEFAULT_BOUNDARY
    _op_name = "DEFAULT_BOUNDARY"

class DefaultEndOfWord(ZeroWidthBase):
    _opcode = OP.DEFAULT_END_OF_WORD
    _op_name = "DEFAULT_END_OF_WORD"

class DefaultStartOfWord(ZeroWidthBase):
    _opcode = OP.DEFAULT_START_OF_WORD
    _op_name = "DEFAULT_START_OF_WORD"

class EndOfLine(ZeroWidthBase):
    _opcode = OP.END_OF_LINE
    _op_name = "END_OF_LINE"

class EndOfLineU(EndOfLine):
    _opcode = OP.END_OF_LINE_U
    _op_name = "END_OF_LINE_U"

class EndOfString(ZeroWidthBase):
    _opcode = OP.END_OF_STRING
    _op_name = "END_OF_STRING"

class EndOfStringLine(ZeroWidthBase):
    _opcode = OP.END_OF_STRING_LINE
    _op_name = "END_OF_STRING_LINE"

class EndOfStringLineU(EndOfStringLine):
    _opcode = OP.END_OF_STRING_LINE_U
    _op_name = "END_OF_STRING_LINE_U"

class EndOfWord(ZeroWidthBase):
    _opcode = OP.END_OF_WORD
    _op_name = "END_OF_WORD"

class Failure(ZeroWidthBase):
    _op_name = "FAILURE"

    def _compile(self, reverse, fuzzy):
        return [(OP.FAILURE, )]

class Fuzzy(RegexBase):
    def __init__(self, subpattern, constraints=None):
        RegexBase.__init__(self)
        if constraints is None:
            constraints = {}
        self.subpattern = subpattern
        self.constraints = constraints

        # If an error type is mentioned in the cost equation, then its maximum
        # defaults to unlimited.
        if "cost" in constraints:
            for e in "dis":
                if e in constraints["cost"]:
                    constraints.setdefault(e, (0, None))

        # If any error type is mentioned, then all the error maxima default to
        # 0, otherwise they default to unlimited.
        if set(constraints) & set("dis"):
            for e in "dis":
                constraints.setdefault(e, (0, 0))
        else:
            for e in "dis":
                constraints.setdefault(e, (0, None))

        # The maximum of the generic error type defaults to unlimited.
        constraints.setdefault("e", (0, None))

        # The cost equation defaults to equal costs. Also, the cost of any
        # error type not mentioned in the cost equation defaults to 0.
        if "cost" in constraints:
            for e in "dis":
                constraints["cost"].setdefault(e, 0)
        else:
            constraints["cost"] = {"d": 1, "i": 1, "s": 1, "max":
              constraints["e"][1]}

    def fix_groups(self, pattern, reverse, fuzzy):
        self.subpattern.fix_groups(pattern, reverse, True)

    def pack_characters(self, info):
        self.subpattern = self.subpattern.pack_characters(info)
        return self

    def remove_captures(self):
        self.subpattern = self.subpattern.remove_captures()
        return self

    def is_atomic(self):
        return self.subpattern.is_atomic()

    def contains_group(self):
        return self.subpattern.contains_group()

    def _compile(self, reverse, fuzzy):
        # The individual limits.
        arguments = []
        for e in "dise":
            v = self.constraints[e]
            arguments.append(v[0])
            arguments.append(UNLIMITED if v[1] is None else v[1])

        # The coeffs of the cost equation.
        for e in "dis":
            arguments.append(self.constraints["cost"][e])

        # The maximum of the cost equation.
        v = self.constraints["cost"]["max"]
        arguments.append(UNLIMITED if v is None else v)

        flags = 0
        if reverse:
            flags |= REVERSE_OP

        test = self.constraints.get("test")

        if test:
            return ([(OP.FUZZY_EXT, flags) + tuple(arguments)] +
              test.compile(reverse, True) + [(OP.NEXT,)] +
              self.subpattern.compile(reverse, True) + [(OP.END,)])

        return ([(OP.FUZZY, flags) + tuple(arguments)] +
          self.subpattern.compile(reverse, True) + [(OP.END,)])

    def dump(self, indent, reverse):
        constraints = self._constraints_to_string()
        if constraints:
            constraints = " " + constraints
        print("{}FUZZY{}".format(INDENT * indent, constraints))
        self.subpattern.dump(indent + 1, reverse)

    def is_empty(self):
        return self.subpattern.is_empty()

    def __eq__(self, other):
        return (type(self) is type(other) and self.subpattern ==
          other.subpattern and self.constraints == other.constraints)

    def max_width(self):
        return UNLIMITED

    def _constraints_to_string(self):
        constraints = []

        for name in "ids":
            min, max = self.constraints[name]
            if max == 0:
                continue

            con = ""

            if min > 0:
                con = "{}<=".format(min)

            con += name

            if max is not None:
                con += "<={}".format(max)

            constraints.append(con)

        cost = []
        for name in "ids":
            coeff = self.constraints["cost"][name]
            if coeff > 0:
                cost.append("{}{}".format(coeff, name))

        limit = self.constraints["cost"]["max"]
        if limit is not None and limit > 0:
            cost = "{}<={}".format("+".join(cost), limit)
            constraints.append(cost)

        return ",".join(constraints)

class Grapheme(RegexBase):
    def _compile(self, reverse, fuzzy):
        # Match at least 1 character until a grapheme boundary is reached. Note
        # that this is the same whether matching forwards or backwards.
        grapheme_matcher = Atomic(Sequence([LazyRepeat(AnyAll(), 1, None),
          GraphemeBoundary()]))

        return grapheme_matcher.compile(reverse, fuzzy)

    def dump(self, indent, reverse):
        print("{}GRAPHEME".format(INDENT * indent))

    def max_width(self):
        return UNLIMITED

class GraphemeBoundary:
    def compile(self, reverse, fuzzy):
        return [(OP.GRAPHEME_BOUNDARY, 1)]

class GreedyRepeat(RegexBase):
    _opcode = OP.GREEDY_REPEAT
    _op_name = "GREEDY_REPEAT"

    def __init__(self, subpattern, min_count, max_count):
        RegexBase.__init__(self)
        self.subpattern = subpattern
        self.min_count = min_count
        self.max_count = max_count

    def fix_groups(self, pattern, reverse, fuzzy):
        self.subpattern.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        subpattern = self.subpattern.optimise(info, reverse)

        return type(self)(subpattern, self.min_count, self.max_count)

    def pack_characters(self, info):
        self.subpattern = self.subpattern.pack_characters(info)
        return self

    def remove_captures(self):
        self.subpattern = self.subpattern.remove_captures()
        return self

    def is_atomic(self):
        return self.min_count == self.max_count and self.subpattern.is_atomic()

    def can_be_affix(self):
        return False

    def contains_group(self):
        return self.subpattern.contains_group()

    def get_firstset(self, reverse):
        fs = self.subpattern.get_firstset(reverse)
        if self.min_count == 0:
            fs.add(None)

        return fs

    def _compile(self, reverse, fuzzy):
        repeat = [self._opcode, self.min_count]
        if self.max_count is None:
            repeat.append(UNLIMITED)
        else:
            repeat.append(self.max_count)

        subpattern = self.subpattern.compile(reverse, fuzzy)
        if not subpattern:
            return []

        return ([tuple(repeat)] + subpattern + [(OP.END, )])

    def dump(self, indent, reverse):
        if self.max_count is None:
            limit = "INF"
        else:
            limit = self.max_count
        print("{}{} {} {}".format(INDENT * indent, self._op_name,
          self.min_count, limit))

        self.subpattern.dump(indent + 1, reverse)

    def is_empty(self):
        return self.subpattern.is_empty()

    def __eq__(self, other):
        return type(self) is type(other) and (self.subpattern, self.min_count,
          self.max_count) == (other.subpattern, other.min_count,
          other.max_count)

    def max_width(self):
        if self.max_count is None:
            return UNLIMITED

        return self.subpattern.max_width() * self.max_count

    def get_required_string(self, reverse):
        max_count = UNLIMITED if self.max_count is None else self.max_count
        if self.min_count == 0:
            w = self.subpattern.max_width() * max_count
            return min(w, UNLIMITED), None

        ofs, req = self.subpattern.get_required_string(reverse)
        if req:
            return ofs, req

        w = self.subpattern.max_width() * max_count
        return min(w, UNLIMITED), None

class PossessiveRepeat(GreedyRepeat):
    def is_atomic(self):
        return True

    def _compile(self, reverse, fuzzy):
        subpattern = self.subpattern.compile(reverse, fuzzy)
        if not subpattern:
            return []

        repeat = [self._opcode, self.min_count]
        if self.max_count is None:
            repeat.append(UNLIMITED)
        else:
            repeat.append(self.max_count)

        return ([(OP.ATOMIC, ), tuple(repeat)] + subpattern + [(OP.END, ),
          (OP.END, )])

    def dump(self, indent, reverse):
        print("{}ATOMIC".format(INDENT * indent))

        if self.max_count is None:
            limit = "INF"
        else:
            limit = self.max_count
        print("{}{} {} {}".format(INDENT * (indent + 1), self._op_name,
          self.min_count, limit))

        self.subpattern.dump(indent + 2, reverse)

class Group(RegexBase):
    def __init__(self, info, group, subpattern):
        RegexBase.__init__(self)
        self.info = info
        self.group = group
        self.subpattern = subpattern

        self.call_ref = None

    def fix_groups(self, pattern, reverse, fuzzy):
        self.info.defined_groups[self.group] = (self, reverse, fuzzy)
        self.subpattern.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        subpattern = self.subpattern.optimise(info, reverse)

        return Group(self.info, self.group, subpattern)

    def pack_characters(self, info):
        self.subpattern = self.subpattern.pack_characters(info)
        return self

    def remove_captures(self):
        return self.subpattern.remove_captures()

    def is_atomic(self):
        return self.subpattern.is_atomic()

    def can_be_affix(self):
        return False

    def contains_group(self):
        return True

    def get_firstset(self, reverse):
        return self.subpattern.get_firstset(reverse)

    def has_simple_start(self):
        return self.subpattern.has_simple_start()

    def _compile(self, reverse, fuzzy):
        code = []

        public_group = private_group = self.group
        if private_group < 0:
            public_group = self.info.private_groups[private_group]
            private_group = self.info.group_count - private_group

        key = self.group, reverse, fuzzy
        ref = self.info.call_refs.get(key)
        if ref is not None:
            code += [(OP.CALL_REF, ref)]

        code += [(OP.GROUP, int(not reverse), private_group, public_group)]
        code += self.subpattern.compile(reverse, fuzzy)
        code += [(OP.END, )]

        if ref is not None:
            code += [(OP.END, )]

        return code

    def dump(self, indent, reverse):
        group = self.group
        if group < 0:
            group = self.info.private_groups[group]
        print("{}GROUP {}".format(INDENT * indent, group))
        self.subpattern.dump(indent + 1, reverse)

    def __eq__(self, other):
        return (type(self) is type(other) and (self.group, self.subpattern) ==
          (other.group, other.subpattern))

    def max_width(self):
        return self.subpattern.max_width()

    def get_required_string(self, reverse):
        return self.subpattern.get_required_string(reverse)

    def __del__(self):
        self.info = None

class Keep(ZeroWidthBase):
    _opcode = OP.KEEP
    _op_name = "KEEP"

class LazyRepeat(GreedyRepeat):
    _opcode = OP.LAZY_REPEAT
    _op_name = "LAZY_REPEAT"

class LookAround(RegexBase):
    _dir_text = {False: "AHEAD", True: "BEHIND"}

    def __init__(self, behind, positive, subpattern):
        RegexBase.__init__(self)
        self.behind = bool(behind)
        self.positive = bool(positive)
        self.subpattern = subpattern

    def fix_groups(self, pattern, reverse, fuzzy):
        self.subpattern.fix_groups(pattern, self.behind, fuzzy)

    def optimise(self, info, reverse):
        subpattern = self.subpattern.optimise(info, self.behind)
        if self.positive and subpattern.is_empty():
            return subpattern

        return LookAround(self.behind, self.positive, subpattern)

    def pack_characters(self, info):
        self.subpattern = self.subpattern.pack_characters(info)
        return self

    def remove_captures(self):
        return self.subpattern.remove_captures()

    def is_atomic(self):
        return self.subpattern.is_atomic()

    def can_be_affix(self):
        return self.subpattern.can_be_affix()

    def contains_group(self):
        return self.subpattern.contains_group()

    def get_firstset(self, reverse):
        if self.positive and self.behind == reverse:
            return self.subpattern.get_firstset(reverse)

        return set([None])

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if fuzzy:
            flags |= FUZZY_OP
        if reverse:
            flags |= REVERSE_OP

        return ([(OP.LOOKAROUND, flags, int(not self.behind))] +
          self.subpattern.compile(self.behind) + [(OP.END, )])

    def dump(self, indent, reverse):
        print("{}LOOK{} {}".format(INDENT * indent,
          self._dir_text[self.behind], POS_TEXT[self.positive]))
        self.subpattern.dump(indent + 1, self.behind)

    def is_empty(self):
        return self.positive and self.subpattern.is_empty()

    def __eq__(self, other):
        return type(self) is type(other) and (self.behind, self.positive,
          self.subpattern) == (other.behind, other.positive, other.subpattern)

    def max_width(self):
        return 0

class LookAroundConditional(RegexBase):
    _dir_text = {False: "AHEAD", True: "BEHIND"}

    def __init__(self, behind, positive, subpattern, yes_item, no_item):
        RegexBase.__init__(self)
        self.behind = bool(behind)
        self.positive = bool(positive)
        self.subpattern = subpattern
        self.yes_item = yes_item
        self.no_item = no_item

    def fix_groups(self, pattern, reverse, fuzzy):
        self.subpattern.fix_groups(pattern, reverse, fuzzy)
        self.yes_item.fix_groups(pattern, reverse, fuzzy)
        self.no_item.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        subpattern = self.subpattern.optimise(info, self.behind)
        yes_item = self.yes_item.optimise(info, self.behind)
        no_item = self.no_item.optimise(info, self.behind)

        return LookAroundConditional(self.behind, self.positive, subpattern,
          yes_item, no_item)

    def pack_characters(self, info):
        self.subpattern = self.subpattern.pack_characters(info)
        self.yes_item = self.yes_item.pack_characters(info)
        self.no_item = self.no_item.pack_characters(info)
        return self

    def remove_captures(self):
        self.subpattern = self.subpattern.remove_captures()
        self.yes_item = self.yes_item.remove_captures()
        self.no_item = self.no_item.remove_captures()

    def is_atomic(self):
        return (self.subpattern.is_atomic() and self.yes_item.is_atomic() and
          self.no_item.is_atomic())

    def can_be_affix(self):
        return (self.subpattern.can_be_affix() and self.yes_item.can_be_affix()
          and self.no_item.can_be_affix())

    def contains_group(self):
        return (self.subpattern.contains_group() or
          self.yes_item.contains_group() or self.no_item.contains_group())

    def _compile(self, reverse, fuzzy):
        code = [(OP.CONDITIONAL, int(self.positive), int(not self.behind))]
        code.extend(self.subpattern.compile(self.behind, fuzzy))
        code.append((OP.NEXT, ))
        code.extend(self.yes_item.compile(reverse, fuzzy))
        add_code = self.no_item.compile(reverse, fuzzy)
        if add_code:
            code.append((OP.NEXT, ))
            code.extend(add_code)

        code.append((OP.END, ))

        return code

    def dump(self, indent, reverse):
        print("{}CONDITIONAL {} {}".format(INDENT * indent,
          self._dir_text[self.behind], POS_TEXT[self.positive]))
        self.subpattern.dump(indent + 1, self.behind)
        print("{}EITHER".format(INDENT * indent))
        self.yes_item.dump(indent + 1, reverse)
        if not self.no_item.is_empty():
            print("{}OR".format(INDENT * indent))
            self.no_item.dump(indent + 1, reverse)

    def is_empty(self):
        return (self.subpattern.is_empty() and self.yes_item.is_empty() or
          self.no_item.is_empty())

    def __eq__(self, other):
        return type(self) is type(other) and (self.subpattern, self.yes_item,
          self.no_item) == (other.subpattern, other.yes_item, other.no_item)

    def max_width(self):
        return max(self.yes_item.max_width(), self.no_item.max_width())

    def get_required_string(self, reverse):
        return self.max_width(), None

class PrecompiledCode(RegexBase):
    def __init__(self, code):
        self.code = code

    def _compile(self, reverse, fuzzy):
        return [tuple(self.code)]

class Property(RegexBase):
    _opcode = {(NOCASE, False): OP.PROPERTY, (IGNORECASE, False):
      OP.PROPERTY_IGN, (FULLCASE, False): OP.PROPERTY, (FULLIGNORECASE, False):
      OP.PROPERTY_IGN, (NOCASE, True): OP.PROPERTY_REV, (IGNORECASE, True):
      OP.PROPERTY_IGN_REV, (FULLCASE, True): OP.PROPERTY_REV, (FULLIGNORECASE,
      True): OP.PROPERTY_IGN_REV}

    def __init__(self, value, positive=True, case_flags=NOCASE,
      zerowidth=False, encoding=0):
        RegexBase.__init__(self)
        self.value = value
        self.positive = bool(positive)
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]
        self.zerowidth = bool(zerowidth)
        self.encoding = encoding

        self._key = (self.__class__, self.value, self.positive,
          self.case_flags, self.zerowidth)

    def rebuild(self, positive, case_flags, zerowidth):
        return Property(self.value, positive, case_flags, zerowidth,
          self.encoding)

    def optimise(self, info, reverse, in_set=False):
        return self

    def get_firstset(self, reverse):
        return set([self])

    def has_simple_start(self):
        return True

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if self.zerowidth:
            flags |= ZEROWIDTH_OP
        if fuzzy:
            flags |= FUZZY_OP
        flags |= self.encoding << ENCODING_OP_SHIFT
        return [(self._opcode[self.case_flags, reverse], flags, self.value)]

    def dump(self, indent, reverse):
        prop = PROPERTY_NAMES[self.value >> 16]
        name, value = prop[0], prop[1][self.value & 0xFFFF]
        print("{}PROPERTY {} {}:{}{}{}".format(INDENT * indent,
          POS_TEXT[self.positive], name, value, CASE_TEXT[self.case_flags],
          ["", " ASCII"][self.encoding]))

    def matches(self, ch):
        return _regex.has_property_value(self.value, ch) == self.positive

    def max_width(self):
        return 1

class Prune(ZeroWidthBase):
    _op_name = "PRUNE"

    def _compile(self, reverse, fuzzy):
        return [(OP.PRUNE, )]

class Range(RegexBase):
    _opcode = {(NOCASE, False): OP.RANGE, (IGNORECASE, False): OP.RANGE_IGN,
      (FULLCASE, False): OP.RANGE, (FULLIGNORECASE, False): OP.RANGE_IGN,
      (NOCASE, True): OP.RANGE_REV, (IGNORECASE, True): OP.RANGE_IGN_REV,
      (FULLCASE, True): OP.RANGE_REV, (FULLIGNORECASE, True): OP.RANGE_IGN_REV}
    _op_name = "RANGE"

    def __init__(self, lower, upper, positive=True, case_flags=NOCASE,
      zerowidth=False):
        RegexBase.__init__(self)
        self.lower = lower
        self.upper = upper
        self.positive = bool(positive)
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]
        self.zerowidth = bool(zerowidth)

        self._key = (self.__class__, self.lower, self.upper, self.positive,
          self.case_flags, self.zerowidth)

    def rebuild(self, positive, case_flags, zerowidth):
        return Range(self.lower, self.upper, positive, case_flags, zerowidth)

    def optimise(self, info, reverse, in_set=False):
        # Is the range case-sensitive?
        if not self.positive or not (self.case_flags & IGNORECASE) or in_set:
            return self

        # Is full case-folding possible?
        if (not (info.flags & UNICODE) or (self.case_flags & FULLIGNORECASE) !=
          FULLIGNORECASE):
            return self

        # Get the characters which expand to multiple codepoints on folding.
        expanding_chars = _regex.get_expand_on_folding()

        # Get the folded characters in the range.
        items = []
        for ch in expanding_chars:
            if self.lower <= ord(ch) <= self.upper:
                folded = _regex.fold_case(FULL_CASE_FOLDING, ch)
                items.append(String([ord(c) for c in folded],
                  case_flags=self.case_flags))

        if not items:
            # We can fall back to simple case-folding.
            return self

        if len(items) < self.upper - self.lower + 1:
            # Not all the characters are covered by the full case-folding.
            items.insert(0, self)

        return Branch(items)

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if self.zerowidth:
            flags |= ZEROWIDTH_OP
        if fuzzy:
            flags |= FUZZY_OP
        return [(self._opcode[self.case_flags, reverse], flags, self.lower,
          self.upper)]

    def dump(self, indent, reverse):
        display_lower = ascii(chr(self.lower)).lstrip("bu")
        display_upper = ascii(chr(self.upper)).lstrip("bu")
        print("{}RANGE {} {} {}{}".format(INDENT * indent,
          POS_TEXT[self.positive], display_lower, display_upper,
          CASE_TEXT[self.case_flags]))

    def matches(self, ch):
        return (self.lower <= ch <= self.upper) == self.positive

    def max_width(self):
        return 1

class RefGroup(RegexBase):
    _opcode = {(NOCASE, False): OP.REF_GROUP, (IGNORECASE, False):
      OP.REF_GROUP_IGN, (FULLCASE, False): OP.REF_GROUP, (FULLIGNORECASE,
      False): OP.REF_GROUP_FLD, (NOCASE, True): OP.REF_GROUP_REV, (IGNORECASE,
      True): OP.REF_GROUP_IGN_REV, (FULLCASE, True): OP.REF_GROUP_REV,
      (FULLIGNORECASE, True): OP.REF_GROUP_FLD_REV}

    def __init__(self, info, group, position, case_flags=NOCASE):
        RegexBase.__init__(self)
        self.info = info
        self.group = group
        self.position = position
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]

        self._key = self.__class__, self.group, self.case_flags

    def fix_groups(self, pattern, reverse, fuzzy):
        try:
            self.group = int(self.group)
        except ValueError:
            try:
                self.group = self.info.group_index[self.group]
            except KeyError:
                raise error("unknown group", pattern, self.position)

        if not 1 <= self.group <= self.info.group_count:
            raise error("invalid group reference", pattern, self.position)

        self._key = self.__class__, self.group, self.case_flags

    def remove_captures(self):
        raise error("group reference not allowed", self.pattern, self.position)

    def _compile(self, reverse, fuzzy):
        flags = 0
        if fuzzy:
            flags |= FUZZY_OP
        return [(self._opcode[self.case_flags, reverse], flags, self.group)]

    def dump(self, indent, reverse):
        print("{}REF_GROUP {}{}".format(INDENT * indent, self.group,
          CASE_TEXT[self.case_flags]))

    def max_width(self):
        return UNLIMITED

    def __del__(self):
        self.info = None

class SearchAnchor(ZeroWidthBase):
    _opcode = OP.SEARCH_ANCHOR
    _op_name = "SEARCH_ANCHOR"

class Sequence(RegexBase):
    def __init__(self, items=None):
        RegexBase.__init__(self)
        if items is None:
            items = []

        self.items = items

    def fix_groups(self, pattern, reverse, fuzzy):
        for s in self.items:
            s.fix_groups(pattern, reverse, fuzzy)

    def optimise(self, info, reverse):
        # Flatten the sequences.
        items = []
        for s in self.items:
            s = s.optimise(info, reverse)
            if isinstance(s, Sequence):
                items.extend(s.items)
            else:
                items.append(s)

        return make_sequence(items)

    def pack_characters(self, info):
        "Packs sequences of characters into strings."
        items = []
        characters = []
        case_flags = NOCASE
        for s in self.items:
            if type(s) is Character and s.positive and not s.zerowidth:
                if s.case_flags != case_flags:
                    # Different case sensitivity, so flush, unless neither the
                    # previous nor the new character are cased.
                    if s.case_flags or is_cased_i(info, s.value):
                        Sequence._flush_characters(info, characters,
                          case_flags, items)

                        case_flags = s.case_flags

                characters.append(s.value)
            elif type(s) is String or type(s) is Literal:
                if s.case_flags != case_flags:
                    # Different case sensitivity, so flush, unless the neither
                    # the previous nor the new string are cased.
                    if s.case_flags or any(is_cased_i(info, c) for c in
                      characters):
                        Sequence._flush_characters(info, characters,
                          case_flags, items)

                        case_flags = s.case_flags

                characters.extend(s.characters)
            else:
                Sequence._flush_characters(info, characters, case_flags, items)

                items.append(s.pack_characters(info))

        Sequence._flush_characters(info, characters, case_flags, items)

        return make_sequence(items)

    def remove_captures(self):
        self.items = [s.remove_captures() for s in self.items]
        return self

    def is_atomic(self):
        return all(s.is_atomic() for s in self.items)

    def can_be_affix(self):
        return False

    def contains_group(self):
        return any(s.contains_group() for s in self.items)

    def get_firstset(self, reverse):
        fs = set()
        items = self.items
        if reverse:
            items.reverse()
        for s in items:
            fs |= s.get_firstset(reverse)
            if None not in fs:
                return fs
            fs.discard(None)

        return fs | set([None])

    def has_simple_start(self):
        return bool(self.items) and self.items[0].has_simple_start()

    def _compile(self, reverse, fuzzy):
        seq = self.items
        if reverse:
            seq = seq[::-1]

        code = []
        for s in seq:
            code.extend(s.compile(reverse, fuzzy))

        return code

    def dump(self, indent, reverse):
        for s in self.items:
            s.dump(indent, reverse)

    @staticmethod
    def _flush_characters(info, characters, case_flags, items):
        if not characters:
            return

        # Disregard case_flags if all of the characters are case-less.
        if case_flags & IGNORECASE:
            if not any(is_cased_i(info, c) for c in characters):
                case_flags = NOCASE

        if (case_flags & FULLIGNORECASE) == FULLIGNORECASE:
            literals = Sequence._fix_full_casefold(characters)

            for item in literals:
                chars = item.characters

                if len(chars) == 1:
                    items.append(Character(chars[0], case_flags=item.case_flags))
                else:
                    items.append(String(chars, case_flags=item.case_flags))
        else:
            if len(characters) == 1:
                items.append(Character(characters[0], case_flags=case_flags))
            else:
                items.append(String(characters, case_flags=case_flags))

        characters[:] = []

    @staticmethod
    def _fix_full_casefold(characters):
        # Split a literal needing full case-folding into chunks that need it
        # and chunks that can use simple case-folding, which is faster.
        expanded = [_regex.fold_case(FULL_CASE_FOLDING, c) for c in
          _regex.get_expand_on_folding()]
        string = _regex.fold_case(FULL_CASE_FOLDING, ''.join(chr(c)
          for c in characters)).lower()
        chunks = []

        for e in expanded:
            found = string.find(e)

            while found >= 0:
                chunks.append((found, found + len(e)))
                found = string.find(e, found + 1)

        pos = 0
        literals = []

        for start, end in Sequence._merge_chunks(chunks):
            if pos < start:
                literals.append(Literal(characters[pos : start],
                  case_flags=IGNORECASE))

            literals.append(Literal(characters[start : end],
              case_flags=FULLIGNORECASE))
            pos = end

        if pos < len(characters):
            literals.append(Literal(characters[pos : ], case_flags=IGNORECASE))

        return literals

    @staticmethod
    def _merge_chunks(chunks):
        if len(chunks) < 2:
            return chunks

        chunks.sort()

        start, end = chunks[0]
        new_chunks = []

        for s, e in chunks[1 : ]:
            if s <= end:
                end = max(end, e)
            else:
                new_chunks.append((start, end))
                start, end = s, e

        new_chunks.append((start, end))

        return new_chunks

    def is_empty(self):
        return all(i.is_empty() for i in self.items)

    def __eq__(self, other):
        return type(self) is type(other) and self.items == other.items

    def max_width(self):
        return sum(s.max_width() for s in self.items)

    def get_required_string(self, reverse):
        seq = self.items
        if reverse:
            seq = seq[::-1]

        offset = 0

        for s in seq:
            ofs, req = s.get_required_string(reverse)
            offset += ofs
            if req:
                return offset, req

        return offset, None

class SetBase(RegexBase):
    def __init__(self, info, items, positive=True, case_flags=NOCASE,
      zerowidth=False):
        RegexBase.__init__(self)
        self.info = info
        self.items = tuple(items)
        self.positive = bool(positive)
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]
        self.zerowidth = bool(zerowidth)

        self.char_width = 1

        self._key = (self.__class__, self.items, self.positive,
          self.case_flags, self.zerowidth)

    def rebuild(self, positive, case_flags, zerowidth):
        return type(self)(self.info, self.items, positive, case_flags,
          zerowidth).optimise(self.info, False)

    def get_firstset(self, reverse):
        return set([self])

    def has_simple_start(self):
        return True

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if self.zerowidth:
            flags |= ZEROWIDTH_OP
        if fuzzy:
            flags |= FUZZY_OP
        code = [(self._opcode[self.case_flags, reverse], flags)]
        for m in self.items:
            code.extend(m.compile())

        code.append((OP.END, ))

        return code

    def dump(self, indent, reverse):
        print("{}{} {}{}".format(INDENT * indent, self._op_name,
          POS_TEXT[self.positive], CASE_TEXT[self.case_flags]))
        for i in self.items:
            i.dump(indent + 1, reverse)

    def _handle_case_folding(self, info, in_set):
        # Is the set case-sensitive?
        if not self.positive or not (self.case_flags & IGNORECASE) or in_set:
            return self

        # Is full case-folding possible?
        if (not (self.info.flags & UNICODE) or (self.case_flags &
          FULLIGNORECASE) != FULLIGNORECASE):
            return self

        # Get the characters which expand to multiple codepoints on folding.
        expanding_chars = _regex.get_expand_on_folding()

        # Get the folded characters in the set.
        items = []
        seen = set()
        for ch in expanding_chars:
            if self.matches(ord(ch)):
                folded = _regex.fold_case(FULL_CASE_FOLDING, ch)
                if folded not in seen:
                    items.append(String([ord(c) for c in folded],
                      case_flags=self.case_flags))
                    seen.add(folded)

        if not items:
            # We can fall back to simple case-folding.
            return self

        return Branch([self] + items)

    def max_width(self):
        # Is the set case-sensitive?
        if not self.positive or not (self.case_flags & IGNORECASE):
            return 1

        # Is full case-folding possible?
        if (not (self.info.flags & UNICODE) or (self.case_flags &
          FULLIGNORECASE) != FULLIGNORECASE):
            return 1

        # Get the characters which expand to multiple codepoints on folding.
        expanding_chars = _regex.get_expand_on_folding()

        # Get the folded characters in the set.
        seen = set()
        for ch in expanding_chars:
            if self.matches(ord(ch)):
                folded = _regex.fold_case(FULL_CASE_FOLDING, ch)
                seen.add(folded)

        if not seen:
            return 1

        return max(len(folded) for folded in seen)

    def __del__(self):
        self.info = None

class SetDiff(SetBase):
    _opcode = {(NOCASE, False): OP.SET_DIFF, (IGNORECASE, False):
      OP.SET_DIFF_IGN, (FULLCASE, False): OP.SET_DIFF, (FULLIGNORECASE, False):
      OP.SET_DIFF_IGN, (NOCASE, True): OP.SET_DIFF_REV, (IGNORECASE, True):
      OP.SET_DIFF_IGN_REV, (FULLCASE, True): OP.SET_DIFF_REV, (FULLIGNORECASE,
      True): OP.SET_DIFF_IGN_REV}
    _op_name = "SET_DIFF"

    def optimise(self, info, reverse, in_set=False):
        items = self.items
        if len(items) > 2:
            items = [items[0], SetUnion(info, items[1 : ])]

        if len(items) == 1:
            return items[0].with_flags(case_flags=self.case_flags,
              zerowidth=self.zerowidth).optimise(info, reverse, in_set)

        self.items = tuple(m.optimise(info, reverse, in_set=True) for m in
          items)

        return self._handle_case_folding(info, in_set)

    def matches(self, ch):
        m = self.items[0].matches(ch) and not self.items[1].matches(ch)
        return m == self.positive

class SetInter(SetBase):
    _opcode = {(NOCASE, False): OP.SET_INTER, (IGNORECASE, False):
      OP.SET_INTER_IGN, (FULLCASE, False): OP.SET_INTER, (FULLIGNORECASE,
      False): OP.SET_INTER_IGN, (NOCASE, True): OP.SET_INTER_REV, (IGNORECASE,
      True): OP.SET_INTER_IGN_REV, (FULLCASE, True): OP.SET_INTER_REV,
      (FULLIGNORECASE, True): OP.SET_INTER_IGN_REV}
    _op_name = "SET_INTER"

    def optimise(self, info, reverse, in_set=False):
        items = []
        for m in self.items:
            m = m.optimise(info, reverse, in_set=True)
            if isinstance(m, SetInter) and m.positive:
                # Intersection in intersection.
                items.extend(m.items)
            else:
                items.append(m)

        if len(items) == 1:
            return items[0].with_flags(case_flags=self.case_flags,
              zerowidth=self.zerowidth).optimise(info, reverse, in_set)

        self.items = tuple(items)

        return self._handle_case_folding(info, in_set)

    def matches(self, ch):
        m = all(i.matches(ch) for i in self.items)
        return m == self.positive

class SetSymDiff(SetBase):
    _opcode = {(NOCASE, False): OP.SET_SYM_DIFF, (IGNORECASE, False):
      OP.SET_SYM_DIFF_IGN, (FULLCASE, False): OP.SET_SYM_DIFF, (FULLIGNORECASE,
      False): OP.SET_SYM_DIFF_IGN, (NOCASE, True): OP.SET_SYM_DIFF_REV,
      (IGNORECASE, True): OP.SET_SYM_DIFF_IGN_REV, (FULLCASE, True):
      OP.SET_SYM_DIFF_REV, (FULLIGNORECASE, True): OP.SET_SYM_DIFF_IGN_REV}
    _op_name = "SET_SYM_DIFF"

    def optimise(self, info, reverse, in_set=False):
        items = []
        for m in self.items:
            m = m.optimise(info, reverse, in_set=True)
            if isinstance(m, SetSymDiff) and m.positive:
                # Symmetric difference in symmetric difference.
                items.extend(m.items)
            else:
                items.append(m)

        if len(items) == 1:
            return items[0].with_flags(case_flags=self.case_flags,
              zerowidth=self.zerowidth).optimise(info, reverse, in_set)

        self.items = tuple(items)

        return self._handle_case_folding(info, in_set)

    def matches(self, ch):
        m = False
        for i in self.items:
            m = m != i.matches(ch)

        return m == self.positive

class SetUnion(SetBase):
    _opcode = {(NOCASE, False): OP.SET_UNION, (IGNORECASE, False):
      OP.SET_UNION_IGN, (FULLCASE, False): OP.SET_UNION, (FULLIGNORECASE,
      False): OP.SET_UNION_IGN, (NOCASE, True): OP.SET_UNION_REV, (IGNORECASE,
      True): OP.SET_UNION_IGN_REV, (FULLCASE, True): OP.SET_UNION_REV,
      (FULLIGNORECASE, True): OP.SET_UNION_IGN_REV}
    _op_name = "SET_UNION"

    def optimise(self, info, reverse, in_set=False):
        items = []
        for m in self.items:
            m = m.optimise(info, reverse, in_set=True)
            if isinstance(m, SetUnion) and m.positive:
                # Union in union.
                items.extend(m.items)
            elif isinstance(m, AnyAll):
                return AnyAll()
            else:
                items.append(m)

        # Are there complementary properties?
        properties = (set(), set())

        for m in items:
            if isinstance(m, Property):
                properties[m.positive].add((m.value, m.case_flags, m.zerowidth))

        if properties[0] & properties[1]:
            return AnyAll()

        if len(items) == 1:
            i = items[0]
            return i.with_flags(positive=i.positive == self.positive,
              case_flags=self.case_flags,
              zerowidth=self.zerowidth).optimise(info, reverse, in_set)

        self.items = tuple(items)

        return self._handle_case_folding(info, in_set)

    def _compile(self, reverse, fuzzy):
        flags = 0
        if self.positive:
            flags |= POSITIVE_OP
        if self.zerowidth:
            flags |= ZEROWIDTH_OP
        if fuzzy:
            flags |= FUZZY_OP

        characters, others = defaultdict(list), []
        for m in self.items:
            if isinstance(m, Character):
                characters[m.positive].append(m.value)
            else:
                others.append(m)

        code = [(self._opcode[self.case_flags, reverse], flags)]

        for positive, values in characters.items():
            flags = 0
            if positive:
                flags |= POSITIVE_OP
            if len(values) == 1:
                code.append((OP.CHARACTER, flags, values[0]))
            else:
                code.append((OP.STRING, flags, len(values)) + tuple(values))

        for m in others:
            code.extend(m.compile())

        code.append((OP.END, ))

        return code

    def matches(self, ch):
        m = any(i.matches(ch) for i in self.items)
        return m == self.positive

class Skip(ZeroWidthBase):
    _op_name = "SKIP"
    _opcode = OP.SKIP

class StartOfLine(ZeroWidthBase):
    _opcode = OP.START_OF_LINE
    _op_name = "START_OF_LINE"

class StartOfLineU(StartOfLine):
    _opcode = OP.START_OF_LINE_U
    _op_name = "START_OF_LINE_U"

class StartOfString(ZeroWidthBase):
    _opcode = OP.START_OF_STRING
    _op_name = "START_OF_STRING"

class StartOfWord(ZeroWidthBase):
    _opcode = OP.START_OF_WORD
    _op_name = "START_OF_WORD"

class String(RegexBase):
    _opcode = {(NOCASE, False): OP.STRING, (IGNORECASE, False): OP.STRING_IGN,
      (FULLCASE, False): OP.STRING, (FULLIGNORECASE, False): OP.STRING_FLD,
      (NOCASE, True): OP.STRING_REV, (IGNORECASE, True): OP.STRING_IGN_REV,
      (FULLCASE, True): OP.STRING_REV, (FULLIGNORECASE, True):
      OP.STRING_FLD_REV}

    def __init__(self, characters, case_flags=NOCASE):
        self.characters = tuple(characters)
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]

        if (self.case_flags & FULLIGNORECASE) == FULLIGNORECASE:
            folded_characters = []
            for char in self.characters:
                folded = _regex.fold_case(FULL_CASE_FOLDING, chr(char))
                folded_characters.extend(ord(c) for c in folded)
        else:
            folded_characters = self.characters

        self.folded_characters = tuple(folded_characters)
        self.required = False

        self._key = self.__class__, self.characters, self.case_flags

    def get_firstset(self, reverse):
        if reverse:
            pos = -1
        else:
            pos = 0
        return set([Character(self.characters[pos],
          case_flags=self.case_flags)])

    def has_simple_start(self):
        return True

    def _compile(self, reverse, fuzzy):
        flags = 0
        if fuzzy:
            flags |= FUZZY_OP
        if self.required:
            flags |= REQUIRED_OP
        return [(self._opcode[self.case_flags, reverse], flags,
          len(self.folded_characters)) + self.folded_characters]

    def dump(self, indent, reverse):
        display = ascii("".join(chr(c) for c in self.characters)).lstrip("bu")
        print("{}STRING {}{}".format(INDENT * indent, display,
          CASE_TEXT[self.case_flags]))

    def max_width(self):
        return len(self.folded_characters)

    def get_required_string(self, reverse):
        return 0, self

class Literal(String):
    def dump(self, indent, reverse):
        literal = ''.join(chr(c) for c in self.characters)
        display = ascii(literal).lstrip("bu")
        print("{}LITERAL MATCH {}{}".format(INDENT * indent, display,
          CASE_TEXT[self.case_flags]))

class StringSet(Branch):
    def __init__(self, info, name, case_flags=NOCASE):
        self.info = info
        self.name = name
        self.case_flags = CASE_FLAGS_COMBINATIONS[case_flags]

        self._key = self.__class__, self.name, self.case_flags

        self.set_key = (name, self.case_flags)
        if self.set_key not in info.named_lists_used:
            info.named_lists_used[self.set_key] = len(info.named_lists_used)

        index = self.info.named_lists_used[self.set_key]
        items = self.info.kwargs[self.name]

        case_flags = self.case_flags

        encoding = self.info.flags & _ALL_ENCODINGS
        fold_flags = encoding | case_flags

        choices = []

        for string in items:
            if isinstance(string, str):
                string = [ord(c) for c in string]

            choices.append([Character(c, case_flags=case_flags) for c in
              string])

        # Sort from longest to shortest.
        choices.sort(key=len, reverse=True)

        self.branches = [Sequence(choice) for choice in choices]

    def dump(self, indent, reverse):
        print("{}STRING_SET {}{}".format(INDENT * indent, self.name,
          CASE_TEXT[self.case_flags]))

    def __del__(self):
        self.info = None

class Source:
    "Scanner for the regular expression source string."
    def __init__(self, string):
        if isinstance(string, str):
            self.string = string
            self.char_type = chr
        else:
            self.string = string.decode("latin-1")
            self.char_type = lambda c: bytes([c])

        self.pos = 0
        self.ignore_space = False
        self.sep = string[ : 0]

    def peek(self, override_ignore=False):
        string = self.string
        pos = self.pos

        try:
            if self.ignore_space and not override_ignore:
                while True:
                    if string[pos].isspace():
                        # Skip over the whitespace.
                        pos += 1
                    elif string[pos] == "#":
                        # Skip over the comment to the end of the line.
                        pos = string.index("\n", pos)
                    else:
                        break

            return string[pos]
        except IndexError:
            # We've reached the end of the string.
            return string[ : 0]
        except ValueError:
            # The comment extended to the end of the string.
            return string[ : 0]

    def get(self, override_ignore=False):
        string = self.string
        pos = self.pos

        try:
            if self.ignore_space and not override_ignore:
                while True:
                    if string[pos].isspace():
                        # Skip over the whitespace.
                        pos += 1
                    elif string[pos] == "#":
                        # Skip over the comment to the end of the line.
                        pos = string.index("\n", pos)
                    else:
                        break

            ch = string[pos]
            self.pos = pos + 1
            return ch
        except IndexError:
            # We've reached the end of the string.
            self.pos = pos
            return string[ : 0]
        except ValueError:
            # The comment extended to the end of the string.
            self.pos = len(string)
            return string[ : 0]

    def get_many(self, count=1):
        string = self.string
        pos = self.pos

        try:
            if self.ignore_space:
                substring = []

                while len(substring) < count:
                    while True:
                        if string[pos].isspace():
                            # Skip over the whitespace.
                            pos += 1
                        elif string[pos] == "#":
                            # Skip over the comment to the end of the line.
                            pos = string.index("\n", pos)
                        else:
                            break

                    substring.append(string[pos])
                    pos += 1

                substring = "".join(substring)
            else:
                substring = string[pos : pos + count]
                pos += len(substring)

            self.pos = pos
            return substring
        except IndexError:
            # We've reached the end of the string.
            self.pos = len(string)
            return "".join(substring)
        except ValueError:
            # The comment extended to the end of the string.
            self.pos = len(string)
            return "".join(substring)

    def get_while(self, test_set, include=True, keep_spaces=False):
        string = self.string
        pos = self.pos

        if self.ignore_space and not keep_spaces:
            try:
                substring = []

                while True:
                    if string[pos].isspace():
                        # Skip over the whitespace.
                        pos += 1
                    elif string[pos] == "#":
                        # Skip over the comment to the end of the line.
                        pos = string.index("\n", pos)
                    elif (string[pos] in test_set) == include:
                        substring.append(string[pos])
                        pos += 1
                    else:
                        break

                self.pos = pos
            except IndexError:
                # We've reached the end of the string.
                self.pos = len(string)
            except ValueError:
                # The comment extended to the end of the string.
                self.pos = len(string)

            return "".join(substring)
        else:
            try:
                while (string[pos] in test_set) == include:
                    pos += 1

                substring = string[self.pos : pos]

                self.pos = pos

                return substring
            except IndexError:
                # We've reached the end of the string.
                substring = string[self.pos : pos]

                self.pos = pos

                return substring

    def skip_while(self, test_set, include=True):
        string = self.string
        pos = self.pos

        try:
            if self.ignore_space:
                while True:
                    if string[pos].isspace():
                        # Skip over the whitespace.
                        pos += 1
                    elif string[pos] == "#":
                        # Skip over the comment to the end of the line.
                        pos = string.index("\n", pos)
                    elif (string[pos] in test_set) == include:
                        pos += 1
                    else:
                        break
            else:
                while (string[pos] in test_set) == include:
                    pos += 1

            self.pos = pos
        except IndexError:
            # We've reached the end of the string.
            self.pos = len(string)
        except ValueError:
            # The comment extended to the end of the string.
            self.pos = len(string)

    def match(self, substring):
        string = self.string
        pos = self.pos

        if self.ignore_space:
            try:
                for c in substring:
                    while True:
                        if string[pos].isspace():
                            # Skip over the whitespace.
                            pos += 1
                        elif string[pos] == "#":
                            # Skip over the comment to the end of the line.
                            pos = string.index("\n", pos)
                        else:
                            break

                    if string[pos] != c:
                        return False

                    pos += 1

                self.pos = pos

                return True
            except IndexError:
                # We've reached the end of the string.
                return False
            except ValueError:
                # The comment extended to the end of the string.
                return False
        else:
            if not string.startswith(substring, pos):
                return False

            self.pos = pos + len(substring)

            return True

    def expect(self, substring):
        if not self.match(substring):
            raise error("missing {}".format(substring), self.string, self.pos)

    def at_end(self):
        string = self.string
        pos = self.pos

        try:
            if self.ignore_space:
                while True:
                    if string[pos].isspace():
                        pos += 1
                    elif string[pos] == "#":
                        pos = string.index("\n", pos)
                    else:
                        break

            return pos >= len(string)
        except IndexError:
            # We've reached the end of the string.
            return True
        except ValueError:
            # The comment extended to the end of the string.
            return True

class Info:
    "Info about the regular expression."

    def __init__(self, flags=0, char_type=None, kwargs={}):
        flags |= DEFAULT_FLAGS[(flags & _ALL_VERSIONS) or DEFAULT_VERSION]
        self.flags = flags
        self.global_flags = flags
        self.inline_locale = False

        self.kwargs = kwargs

        self.group_count = 0
        self.group_index = {}
        self.group_name = {}
        self.char_type = char_type
        self.named_lists_used = {}
        self.open_groups = []
        self.open_group_count = {}
        self.defined_groups = {}
        self.group_calls = []
        self.private_groups = {}

    def open_group(self, name=None):
        group = self.group_index.get(name)
        if group is None:
            while True:
                self.group_count += 1
                if name is None or self.group_count not in self.group_name:
                    break

            group = self.group_count
            if name:
                self.group_index[name] = group
                self.group_name[group] = name

        if group in self.open_groups:
            # We have a nested named group. We'll assign it a private group
            # number, initially negative until we can assign a proper
            # (positive) number.
            group_alias = -(len(self.private_groups) + 1)
            self.private_groups[group_alias] = group
            group = group_alias

        self.open_groups.append(group)
        self.open_group_count[group] = self.open_group_count.get(group, 0) + 1

        return group

    def close_group(self):
        self.open_groups.pop()

    def is_open_group(self, name):
        # In version 1, a group reference can refer to an open group. We'll
        # just pretend the group isn't open.
        version = (self.flags & _ALL_VERSIONS) or DEFAULT_VERSION
        if version == VERSION1:
            return False

        if name.isdigit():
            group = int(name)
        else:
            group = self.group_index.get(name)

        return group in self.open_groups

def _check_group_features(info, parsed):
    """Checks whether the reverse and fuzzy features of the group calls match
    the groups which they call.
    """
    call_refs = {}
    additional_groups = []
    for call, reverse, fuzzy in info.group_calls:
        # Look up the reference of this group call.
        key = (call.group, reverse, fuzzy)
        ref = call_refs.get(key)
        if ref is None:
            # This group doesn't have a reference yet, so look up its features.
            if call.group == 0:
                # Calling the pattern as a whole.
                rev = bool(info.flags & REVERSE)
                fuz = isinstance(parsed, Fuzzy)
                if (rev, fuz) != (reverse, fuzzy):
                    # The pattern as a whole doesn't have the features we want,
                    # so we'll need to make a copy of it with the desired
                    # features.
                    additional_groups.append((CallRef(len(call_refs), parsed),
                      reverse, fuzzy))
            else:
                # Calling a capture group.
                def_info = info.defined_groups[call.group]
                group = def_info[0]
                if def_info[1 : ] != (reverse, fuzzy):
                    # The group doesn't have the features we want, so we'll
                    # need to make a copy of it with the desired features.
                    additional_groups.append((group, reverse, fuzzy))

            ref = len(call_refs)
            call_refs[key] = ref

        call.call_ref = ref

    info.call_refs = call_refs
    info.additional_groups = additional_groups

def _get_required_string(parsed, flags):
    "Gets the required string and related info of a parsed pattern."

    req_offset, required = parsed.get_required_string(bool(flags & REVERSE))
    if required:
        required.required = True
        if req_offset >= UNLIMITED:
            req_offset = -1

        req_flags = required.case_flags
        if not (flags & UNICODE):
            req_flags &= ~UNICODE

        req_chars = required.folded_characters
    else:
        req_offset = 0
        req_chars = ()
        req_flags = 0

    return req_offset, req_chars, req_flags

class Scanner:
    def __init__(self, lexicon, flags=0):
        self.lexicon = lexicon

        # Combine phrases into a compound pattern.
        patterns = []
        for phrase, action in lexicon:
            # Parse the regular expression.
            source = Source(phrase)
            info = Info(flags, source.char_type)
            source.ignore_space = bool(info.flags & VERBOSE)
            parsed = _parse_pattern(source, info)
            if not source.at_end():
                raise error("unbalanced parenthesis", source.string,
                  source.pos)

            # We want to forbid capture groups within each phrase.
            patterns.append(parsed.remove_captures())

        # Combine all the subpatterns into one pattern.
        info = Info(flags)
        patterns = [Group(info, g + 1, p) for g, p in enumerate(patterns)]
        parsed = Branch(patterns)

        # Optimise the compound pattern.
        reverse = bool(info.flags & REVERSE)
        parsed = parsed.optimise(info, reverse)
        parsed = parsed.pack_characters(info)

        # Get the required string.
        req_offset, req_chars, req_flags = _get_required_string(parsed,
          info.flags)

        # Check the features of the groups.
        _check_group_features(info, parsed)

        # Complain if there are any group calls. They are not supported by the
        # Scanner class.
        if info.call_refs:
            raise error("recursive regex not supported by Scanner",
              source.string, source.pos)

        reverse = bool(info.flags & REVERSE)

        # Compile the compound pattern. The result is a list of tuples.
        code = parsed.compile(reverse) + [(OP.SUCCESS, )]

        # Flatten the code into a list of ints.
        code = _flatten_code(code)

        if not parsed.has_simple_start():
            # Get the first set, if possible.
            try:
                fs_code = _compile_firstset(info, parsed.get_firstset(reverse))
                fs_code = _flatten_code(fs_code)
                code = fs_code + code
            except _FirstSetError:
                pass

        # Check the global flags for conflicts.
        version = (info.flags & _ALL_VERSIONS) or DEFAULT_VERSION
        if version not in (0, VERSION0, VERSION1):
            raise ValueError("VERSION0 and VERSION1 flags are mutually incompatible")

        # Create the PatternObject.
        #
        # Local flags like IGNORECASE affect the code generation, but aren't
        # needed by the PatternObject itself. Conversely, global flags like
        # LOCALE _don't_ affect the code generation but _are_ needed by the
        # PatternObject.
        self.scanner = _regex.compile(None, (flags & GLOBAL_FLAGS) | version,
          code, {}, {}, {}, [], req_offset, req_chars, req_flags,
          len(patterns))

    def scan(self, string):
        result = []
        append = result.append
        match = self.scanner.scanner(string).match
        i = 0
        while True:
            m = match()
            if not m:
                break
            j = m.end()
            if i == j:
                break
            action = self.lexicon[m.lastindex - 1][1]
            if hasattr(action, '__call__'):
                self.match = m
                action = action(self, m.group())
            if action is not None:
                append(action)
            i = j

        return result, string[i : ]

# Get the known properties dict.
PROPERTIES = _regex.get_properties()

# Build the inverse of the properties dict.
PROPERTY_NAMES = {}
for prop_name, (prop_id, values) in PROPERTIES.items():
    name, prop_values = PROPERTY_NAMES.get(prop_id, ("", {}))
    name = max(name, prop_name, key=len)
    PROPERTY_NAMES[prop_id] = name, prop_values

    for val_name, val_id in values.items():
        prop_values[val_id] = max(prop_values.get(val_id, ""), val_name,
          key=len)

# Character escape sequences.
CHARACTER_ESCAPES = {
    "a": "\a",
    "b": "\b",
    "f": "\f",
    "n": "\n",
    "r": "\r",
    "t": "\t",
    "v": "\v",
}

ASCII_ENCODING = 1
UNICODE_ENCODING = 2

# Predefined character set escape sequences.
CHARSET_ESCAPES = {
    "d": lookup_property(None, "Digit", True),
    "D": lookup_property(None, "Digit", False),
    "h": lookup_property(None, "Blank", True),
    "s": lookup_property(None, "Space", True),
    "S": lookup_property(None, "Space", False),
    "w": lookup_property(None, "Word", True),
    "W": lookup_property(None, "Word", False),
}

ASCII_CHARSET_ESCAPES = dict(CHARSET_ESCAPES)
ASCII_CHARSET_ESCAPES.update({
    "d": lookup_property(None, "Digit", True, encoding=ASCII_ENCODING),
    "D": lookup_property(None, "Digit", False, encoding=ASCII_ENCODING),
    "s": lookup_property(None, "Space", True, encoding=ASCII_ENCODING),
    "S": lookup_property(None, "Space", False, encoding=ASCII_ENCODING),
    "w": lookup_property(None, "Word", True, encoding=ASCII_ENCODING),
    "W": lookup_property(None, "Word", False, encoding=ASCII_ENCODING),
})
UNICODE_CHARSET_ESCAPES = dict(CHARSET_ESCAPES)
UNICODE_CHARSET_ESCAPES.update({
    "d": lookup_property(None, "Digit", True, encoding=UNICODE_ENCODING),
    "D": lookup_property(None, "Digit", False, encoding=UNICODE_ENCODING),
    "s": lookup_property(None, "Space", True, encoding=UNICODE_ENCODING),
    "S": lookup_property(None, "Space", False, encoding=UNICODE_ENCODING),
    "w": lookup_property(None, "Word", True, encoding=UNICODE_ENCODING),
    "W": lookup_property(None, "Word", False, encoding=UNICODE_ENCODING),
})

# Positional escape sequences.
POSITION_ESCAPES = {
    "A": StartOfString(),
    "b": Boundary(),
    "B": Boundary(False),
    "K": Keep(),
    "m": StartOfWord(),
    "M": EndOfWord(),
    "Z": EndOfString(),
    "z": EndOfString(),
}
ASCII_POSITION_ESCAPES = dict(POSITION_ESCAPES)
ASCII_POSITION_ESCAPES.update({
    "b": Boundary(encoding=ASCII_ENCODING),
    "B": Boundary(False, encoding=ASCII_ENCODING),
    "m": StartOfWord(encoding=ASCII_ENCODING),
    "M": EndOfWord(encoding=ASCII_ENCODING),
})
UNICODE_POSITION_ESCAPES = dict(POSITION_ESCAPES)
UNICODE_POSITION_ESCAPES.update({
    "b": Boundary(encoding=UNICODE_ENCODING),
    "B": Boundary(False, encoding=UNICODE_ENCODING),
    "m": StartOfWord(encoding=UNICODE_ENCODING),
    "M": EndOfWord(encoding=UNICODE_ENCODING),
})

# Positional escape sequences when WORD flag set.
WORD_POSITION_ESCAPES = dict(POSITION_ESCAPES)
WORD_POSITION_ESCAPES.update({
    "b": DefaultBoundary(),
    "B": DefaultBoundary(False),
    "m": DefaultStartOfWord(),
    "M": DefaultEndOfWord(),
})

# Regex control verbs.
VERBS = {
    "FAIL": Failure(),
    "F": Failure(),
    "PRUNE": Prune(),
    "SKIP": Skip(),
}
