#
# Copyright (c), 2018-2020, SISSA (International School for Advanced Studies).
# All rights reserved.
# This file is distributed under the terms of the MIT License.
# See the file 'LICENSE' in the root directory of the present
# distribution, or http://opensource.org/licenses/MIT.
#
# @author Davide Brunato <brunato@sissa.it>
#
"""
XSD atomic datatypes for XPath. Includes a class for UntypedAtomic data and some
classes for XSD datetime and duration types.
"""
from abc import ABCMeta, abstractmethod
import operator
import re
import decimal
import datetime
import base64
from collections import namedtuple
from calendar import isleap, leapdays

from .exceptions import ElementPathTypeError, ElementPathValueError

###
# Date/Time helpers
MONTH_DAYS = [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
MONTH_DAYS_LEAP = [0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]


def adjust_day(year, month, day):
    if month in {1, 3, 5, 7, 8, 10, 12}:
        return day
    elif month in {4, 6, 9, 11}:
        return min(day, 30)
    else:
        return min(day, 29) if isleap(year) else min(day, 28)


def days_from_common_era(year):
    """
    Returns the number of days from from 0001-01-01 to the provided year. For a
    common era year the days are counted until the last day of December, for a
    BCE year the days are counted down from the end to the 1st of January.
    """
    if year > 0:
        return year * 365 + year // 4 - year // 100 + year // 400
    elif year >= -1:
        return year * 366
    else:
        year = -year - 1
        return -(366 + year * 365 + year // 4 - year // 100 + year // 400)


DAYS_IN_4Y = days_from_common_era(4)
DAYS_IN_100Y = days_from_common_era(100)
DAYS_IN_400Y = days_from_common_era(400)


def months2days(year, month, months_delta):
    """
    Converts a delta of months to a delta of days, counting from the 1st day of the month,
    relative to the year and the month passed as arguments.

    :param year: the reference start year, a negative or zero value means a BCE year \
    (0 is 1 BCE, -1 is 2 BCE, -2 is 3 BCE, etc).
    :param month: the starting month (1-12).
    :param months_delta: the number of months, if negative count backwards.
    """
    if not months_delta:
        return 0

    total_months = month - 1 + months_delta
    target_year = year + total_months // 12
    target_month = total_months % 12 + 1

    if month <= 2:
        y_days = 365 * (target_year - year) + leapdays(year, target_year)
    else:
        y_days = 365 * (target_year - year) + leapdays(year + 1, target_year + 1)

    months_days = MONTH_DAYS_LEAP if isleap(target_year) else MONTH_DAYS
    if target_month >= month:
        m_days = sum(months_days[m] for m in range(month, target_month))
        return y_days + m_days if y_days >= 0 else y_days + m_days
    else:
        m_days = sum(months_days[m] for m in range(target_month, month))
        return y_days - m_days if y_days >= 0 else y_days - m_days


class Timezone(datetime.tzinfo):
    """
    A tzinfo implementation for XSD timezone offsets. Offsets must be specified
    between -14:00 and +14:00.

    :param offset: a timedelta instance or an XSD timezone formatted string.
    """
    _maxoffset = datetime.timedelta(hours=14, minutes=0)
    _minoffset = -_maxoffset

    def __init__(self, offset):
        super(Timezone, self).__init__()
        if not isinstance(offset, datetime.timedelta):
            raise ElementPathTypeError("offset must be a datetime.timedelta or "
                                       "an XSD timezone formatted string")
        if offset < self._minoffset or offset > self._maxoffset:
            raise ElementPathValueError("offset must be between -14:00 and +14:00")
        self.offset = offset

    @classmethod
    def fromstring(cls, text):
        if text == 'Z':
            return cls(datetime.timedelta(0))

        try:
            hours, minutes = text.split(':')
            hours = int(hours)
            minutes = int(minutes) if hours >= 0 else -int(minutes)
            return cls(datetime.timedelta(hours=hours, minutes=minutes))
        except ValueError:
            raise ElementPathValueError("%r: not an XSD timezone formatted string" % text)

    @classmethod
    def fromduration(cls, duration):
        return cls(datetime.timedelta(seconds=int(duration.seconds)))

    def __getinitargs__(self):
        return self.offset,

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

    def __eq__(self, other):
        return isinstance(other, Timezone) and self.offset == other.offset

    def __ne__(self, other):
        return not isinstance(other, Timezone) or self.offset != other.offset

    def __repr__(self):
        return "%s(%r)" % (self.__class__.__name__, self.offset)

    def __str__(self):
        return self.tzname(None)

    def utcoffset(self, dt):
        if not isinstance(dt, datetime.datetime) and dt is not None:
            raise ElementPathTypeError("utcoffset() argument must be a "
                                       "datetime.datetime instance or None")
        return self.offset

    def tzname(self, dt):
        if not isinstance(dt, datetime.datetime) and dt is not None:
            raise ElementPathTypeError("tzname() argument must be a "
                                       "datetime.datetime instance or None")

        if not self.offset:
            return 'Z'
        elif self.offset < datetime.timedelta(0):
            sign, offset = '-', -self.offset
        else:
            sign, offset = '+', self.offset

        hours, minutes = offset.seconds // 3600, offset.seconds // 60 % 60
        return '{}{:02d}:{:02d}'.format(sign, hours, minutes)

    def dst(self, dt):
        if not isinstance(dt, datetime.datetime) and dt is not None:
            raise ElementPathTypeError("dst() argument must be a "
                                       "datetime.datetime instance or None")

    def fromutc(self, dt):
        if isinstance(dt, datetime.datetime):
            return dt + self.offset
        elif dt is not None:
            raise TypeError("fromutc() argument must be a "
                            "datetime.datetime instance or None")


class AbstractDateTime(metaclass=ABCMeta):
    """
    A class for representing XSD date/time objects. It uses and internal datetime.datetime
    attribute and an integer attribute for processing BCE years or for years after 9999 CE.
    """
    version = '1.0'
    _pattern = re.compile(r'^$')
    _utc_timezone = Timezone(datetime.timedelta(0))
    _year = None

    def __init__(self, year=2000, month=1, day=1, hour=0, minute=0,
                 second=0, microsecond=0, tzinfo=None):
        if hour == 24 and minute == second == 0:
            delta = datetime.timedelta(days=1)
            hour = 0
        else:
            delta = 0

        if 1 <= year <= 9999:
            self._dt = datetime.datetime(year, month, day, hour, minute,
                                         second, microsecond, tzinfo)
        elif year == 0:
            raise ElementPathValueError('0 is an illegal value for year')
        elif not isinstance(year, int):
            raise ElementPathTypeError("wrong type %r for year" % type(year))
        else:
            self._year = year
            if isleap(year + bool(self.version != '1.0')):
                self._dt = datetime.datetime(4, month, day, hour, minute,
                                             second, microsecond, tzinfo)
            else:
                self._dt = datetime.datetime(6, month, day, hour, minute,
                                             second, microsecond, tzinfo)

        if delta:
            self._dt += delta

    def __repr__(self):
        fields = self._pattern.groupindex.keys()
        arg_string = ', '.join(
            str(getattr(self, k))
            for k in ['year', 'month', 'day', 'hour', 'minute'] if k in fields
        )
        if 'second' in fields:
            if self.microsecond:
                arg_string += ', %d.%06d' % (self.second, self.microsecond)
            else:
                arg_string += ', %d' % self.second

        if self.tzinfo is not None:
            arg_string += ', tzinfo=%r' % self.tzinfo
        return '%s(%s)' % (self.__class__.__name__, arg_string)

    @abstractmethod
    def __str__(self):
        raise NotImplementedError()

    @property
    def year(self):
        return self._year or self._dt.year

    @property
    def bce(self):
        return self._year is not None and self._year < 0

    @property
    def iso_year(self):
        """The ISO string representation of the year field."""
        year = self.year
        if -9999 <= year < -1:
            return '{:05}'.format(year if self.version == '1.0' else year + 1)
        elif year == -1:
            return '-0001' if self.version == '1.0' else '0000'
        elif 0 <= year <= 9999:
            return '{:04}'.format(year)
        else:
            return str(year)

    @property
    def month(self):
        return self._dt.month

    @property
    def day(self):
        return self._dt.day

    @property
    def hour(self):
        return self._dt.hour

    @property
    def minute(self):
        return self._dt.minute

    @property
    def second(self):
        return self._dt.second

    @property
    def microsecond(self):
        return self._dt.microsecond

    @property
    def tzinfo(self):
        return self._dt.tzinfo

    @tzinfo.setter
    def tzinfo(self, tz):
        self._dt = self._dt.replace(tzinfo=tz)

    @classmethod
    def fromstring(cls, datetime_string, tzinfo=None):
        """
        Creates an XSD date/time instance from a string formatted value.

        :param datetime_string: a string containing an XSD formatted date/time specification.
        :param tzinfo: optional implicit timezone information, must be a `Timezone` instance.
        :return: an AbstractDateTime concrete subclass instance.
        """
        if not isinstance(datetime_string, str):
            msg = '1st argument has an invalid type {!r}'
            raise ElementPathTypeError(msg.format(type(datetime_string)))
        elif tzinfo and not isinstance(tzinfo, Timezone):
            msg = '2nd argument has an invalid type {!r}'
            raise ElementPathTypeError(msg.format(type(tzinfo)))

        match = cls._pattern.match(datetime_string)
        if match is None:
            msg = 'Invalid datetime string {!r} for {!r}'
            raise ElementPathValueError(msg.format(datetime_string, cls))

        kwargs = {k: int(v) if k != 'tzinfo' else Timezone.fromstring(v)
                  for k, v in match.groupdict().items() if v is not None}

        if 'tzinfo' not in kwargs and tzinfo is not None:
            kwargs['tzinfo'] = tzinfo
        if 'microsecond' in kwargs:
            pow10 = 6 - len(match.groupdict()['microsecond'])
            kwargs['microsecond'] = 0 if pow10 < 0 else kwargs['microsecond'] * 10**pow10

        year = kwargs.get('year')
        if year is not None and year <= 0 and cls.version != '1.0':
            kwargs['year'] -= 1
        return cls(**kwargs)

    @classmethod
    def fromdatetime(cls, dt, year=None):
        """
        Creates an XSD date/time instance from a datetime.datetime/date/time instance.

        :param dt: the datetime, date or time instance that stores the XSD Date/Time value.
        :param year: if an year is provided the created instance refers to it and the \
        possibly present *dt.year* part is ignored.
        :return: an AbstractDateTime concrete subclass instance.
        """
        if not isinstance(dt, (datetime.datetime, datetime.date, datetime.time)):
            raise ElementPathTypeError('1st argument has an invalid type %r' % type(dt))
        elif year is not None and not isinstance(year, int):
            raise ElementPathTypeError('2nd argument has an invalid type %r' % type(year))

        kwargs = {k: getattr(dt, k) for k in cls._pattern.groupindex.keys() if hasattr(dt, k)}
        if year is not None:
            kwargs['year'] = year
        return cls(**kwargs)

    # Python can't compares offset-naive and offset-aware datetimes
    def _get_operands(self, other):
        if isinstance(other, (self.__class__, datetime.datetime)) or \
                isinstance(self, other.__class__):
            dt = getattr(other, '_dt', other)
            if self._dt.tzinfo is dt.tzinfo:
                return self._dt, dt
            elif self.tzinfo is None:
                return self._dt.replace(tzinfo=self._utc_timezone), dt
            elif dt.tzinfo is None:
                return self._dt, dt.replace(tzinfo=self._utc_timezone)
            else:
                return self._dt, dt
        else:
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))

    def __hash__(self):
        return hash((self._dt, self._year))

    def __eq__(self, other):
        try:
            return operator.eq(*self._get_operands(other)) and self.year == other.year
        except TypeError:
            return False

    def __ne__(self, other):
        try:
            return operator.ne(*self._get_operands(other)) or self.year != other.year
        except TypeError:
            return True


class OrderedDateTime(AbstractDateTime):
    @abstractmethod
    def __str__(self):
        raise NotImplementedError()

    @classmethod
    def fromdelta(cls, delta, adjust_timezone=False):
        """
        Creates an XSD dateTime/date instance from a datetime.timedelta related to
        0001-01-01T00:00:00 CE. In case of a date the time part is not counted.

        :param delta: a datetime.timedelta instance.
        :param adjust_timezone: if `True` adjusts the timezone of Date objects \
        with eventually present hours and minutes.
        """
        try:
            dt = datetime.datetime(1, 1, 1) + delta
        except OverflowError:
            days = delta.days
            if days > 0:
                y400, days = divmod(days, DAYS_IN_400Y)
                y100, days = divmod(days, DAYS_IN_100Y)
                y4, days = divmod(days, DAYS_IN_4Y)
                y1, days = divmod(days, 365)
                year = y400 * 400 + y100 * 100 + y4 * 4 + y1 + 1
                if y1 == 4 or y100 == 4:
                    year -= 1
                    days = 365

                td = datetime.timedelta(days=days, seconds=delta.seconds,
                                        microseconds=delta.microseconds)
                dt = datetime.datetime(4 if isleap(year) else 6, 1, 1) + td

            elif days >= -366:
                year = -1
                td = datetime.timedelta(days=days, seconds=delta.seconds,
                                        microseconds=delta.microseconds)
                dt = datetime.datetime(5, 1, 1) + td

            else:
                days = -days - 366
                y400, days = divmod(days, DAYS_IN_400Y)
                y100, days = divmod(days, DAYS_IN_100Y)
                y4, days = divmod(days, DAYS_IN_4Y)
                y1, days = divmod(days, 365)
                year = -y400 * 400 - y100 * 100 - y4 * 4 - y1 - 2
                if y1 == 4 or y100 == 4:
                    year += 1
                    days = 365

                td = datetime.timedelta(days=-days, seconds=delta.seconds,
                                        microseconds=delta.microseconds)
                if not td:
                    dt = datetime.datetime(4 if isleap(year + 1) else 6, 1, 1)
                    year += 1
                else:
                    dt = datetime.datetime(5 if isleap(year + 1) else 7, 1, 1) + td
        else:
            year = dt.year

        if issubclass(cls, Date10):
            if adjust_timezone and (dt.hour or dt.minute):
                assert dt.tzinfo is None
                hour, minute = dt.hour, dt.minute

                if hour < 14 or hour == 14 and minute == 0:
                    tz = Timezone(datetime.timedelta(hours=-hour, minutes=-minute))
                    dt = dt.replace(tzinfo=tz)
                else:
                    tz = Timezone(datetime.timedelta(hours=-dt.hour + 24, minutes=-minute))
                    dt = dt.replace(tzinfo=tz)
                    dt += datetime.timedelta(days=1)

            return cls(year, dt.month, dt.day, tzinfo=dt.tzinfo)
        return cls(year, dt.month, dt.day, dt.hour, dt.minute,
                   dt.second, dt.microsecond, dt.tzinfo)

    def todelta(self):
        """Returns the datetime.timedelta from 0001-01-01T00:00:00 CE."""
        if self._year is None:
            return operator.sub(*self._get_operands(datetime.datetime(1, 1, 1)))

        year, dt = self.year, self._dt
        tzinfo = None if dt.tzinfo is None else self._utc_timezone

        if year > 0:
            m_days = MONTH_DAYS_LEAP if isleap(year) else MONTH_DAYS
            days = days_from_common_era(year - 1) + sum(m_days[m] for m in range(1, dt.month))
        else:
            m_days = MONTH_DAYS_LEAP if isleap(year + 1) else MONTH_DAYS
            days = days_from_common_era(year) + sum(m_days[m] for m in range(1, dt.month))

        delta = (dt - datetime.datetime(dt.year, dt.month, day=1, tzinfo=tzinfo))
        return datetime.timedelta(days=days, seconds=delta.total_seconds())

    def _date_operator(self, op, other):
        if isinstance(other, self.__class__):
            dt1, dt2 = self._get_operands(other)
            if self._year is None and other._year is None:
                return DayTimeDuration.fromtimedelta(dt1 - dt2)
            return DayTimeDuration.fromtimedelta(self.todelta() - other.todelta())

        elif isinstance(other, datetime.timedelta):
            delta = op(self.todelta(), other)
            return type(self).fromdelta(delta, adjust_timezone=True)

        elif isinstance(other, DayTimeDuration):
            delta = op(self.todelta(), other.get_timedelta())
            return type(self).fromdelta(delta)

        elif isinstance(other, YearMonthDuration):
            month = op(self._dt.month - 1, other.months) % 12 + 1
            year = op(self.year, ((self._dt.month - 1) + other.months) // 12)
            day = adjust_day(year, month, self._dt.day)

            if year > 0:
                dt = self._dt.replace(year=year, month=month, day=day)
            elif isleap(year):
                dt = self._dt.replace(year=4, month=month, day=day)
            else:
                dt = self._dt.replace(year=6, month=month, day=day)

            kwargs = {k: getattr(dt, k) for k in self._pattern.groupindex.keys()}
            if year <= 0:
                kwargs['year'] = year
            return type(self)(**kwargs)

        else:
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))

    def __lt__(self, other):
        dt1, dt2 = self._get_operands(other)
        y1, y2 = self.year, other.year
        return y1 < y2 or y1 == y2 and dt1 < dt2

    def __le__(self, other):
        dt1, dt2 = self._get_operands(other)
        y1, y2 = self.year, other.year
        return y1 < y2 or y1 == y2 and dt1 <= dt2

    def __gt__(self, other):
        dt1, dt2 = self._get_operands(other)
        y1, y2 = self.year, other.year
        return y1 > y2 or y1 == y2 and dt1 > dt2

    def __ge__(self, other):
        dt1, dt2 = self._get_operands(other)
        y1, y2 = self.year, other.year
        return y1 > y2 or y1 == y2 and dt1 >= dt2

    def __add__(self, other):
        if isinstance(other, OrderedDateTime):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return self._date_operator(operator.add, other)

    def __sub__(self, other):
        return self._date_operator(operator.sub, other)


class DateTime10(OrderedDateTime):
    """XSD 1.0 xs:dateTime builtin type"""
    _pattern = re.compile(
        r'^(?P<year>(?:-)?[0-9]*[0-9]{4})-(?P<month>[0-9]{2})-(?P<day>[0-9]{2})'
        r'(T(?P<hour>[0-9]{2}):(?P<minute>[0-9]{2}):'
        r'(?P<second>[0-9]{2})(?:\.(?P<microsecond>[0-9]+))?)?'
        r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, year, month, day, hour=0, minute=0, second=0, microsecond=0, tzinfo=None):
        super(DateTime10, self).__init__(
            year, month, day, hour, minute, second, microsecond, tzinfo
        )

    def __str__(self):
        if self.microsecond:
            return '{}-{:02}-{:02}T{:02}:{:02}:{:02}.{:06}{}'.format(
                self.iso_year, self.month, self.day, self.hour, self.minute,
                self.second, self.microsecond, str(self.tzinfo or '')
            )
        return '{}-{:02}-{:02}T{:02}:{:02}:{:02}{}'.format(
            self.iso_year, self.month, self.day, self.hour,
            self.minute, self.second, str(self.tzinfo or '')
        )


class DateTime(DateTime10):
    """XSD 1.1 xs:dateTime builtin type"""
    version = '1.1'


class Date10(OrderedDateTime):
    """XSD 1.0 xs:date builtin type"""
    _pattern = re.compile(r'^(?P<year>(?:-)?[0-9]*[0-9]{4})-(?P<month>[0-9]{2})-(?P<day>[0-9]{2})'
                          r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, year, month, day, tzinfo=None):
        super(Date10, self).__init__(year, month, day, tzinfo=tzinfo)

    def __str__(self):
        return '{}-{:02}-{:02}{}'.format(
            self.iso_year, self.month, self.day, str(self.tzinfo or '')
        )


class Date(Date10):
    """XSD 1.1 xs:date builtin type"""
    version = '1.1'


class XPathGregorianDay(AbstractDateTime):
    """xs:gDay datatype for XPath expressions"""
    _pattern = re.compile(r'^---(?P<day>[0-9]{2})'
                          r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, day, tzinfo=None):
        super(XPathGregorianDay, self).__init__(day=day, tzinfo=tzinfo)

    def __str__(self):
        return '---{:02}{}'.format(self.day, str(self.tzinfo or ''))


class GregorianDay(XPathGregorianDay, OrderedDateTime):
    """XSD xs:gDay builtin type"""


class XPathGregorianMonth(AbstractDateTime):
    """xs:gMonth datatype for XPath expressions"""
    _pattern = re.compile(r'^--(?P<month>[0-9]{2})'
                          r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, month, tzinfo=None):
        super(XPathGregorianMonth, self).__init__(month=month, tzinfo=tzinfo)

    def __str__(self):
        return '--{:02}{}'.format(self.month, str(self.tzinfo or ''))


class GregorianMonth(XPathGregorianMonth, OrderedDateTime):
    """XSD xs:gMonth builtin type"""


class XPathGregorianMonthDay(AbstractDateTime):
    """xs:gMonthDay datatype for XPath expressions"""
    _pattern = re.compile(r'^--(?P<month>[0-9]{2})-(?P<day>[0-9]{2})'
                          r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, month, day, tzinfo=None):
        super(XPathGregorianMonthDay, self).__init__(month=month, day=day, tzinfo=tzinfo)

    def __str__(self):
        return '--{:02}-{:02}{}'.format(self.month, self.day, str(self.tzinfo or ''))


class GregorianMonthDay(XPathGregorianMonthDay, OrderedDateTime):
    """XSD xs:gMonthDay builtin type"""


class XPathGregorianYear(AbstractDateTime):
    """xs:gYear datatype for XPath expressions"""
    _pattern = re.compile(r'^(?P<year>(?:-)?[0-9]*[0-9]{4})'
                          r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, year, tzinfo=None):
        super(XPathGregorianYear, self).__init__(year, tzinfo=tzinfo)

    def __str__(self):
        return '{}{}'.format(self.iso_year, str(self.tzinfo or ''))


class GregorianYear10(XPathGregorianYear, OrderedDateTime):
    """XSD 1.0 xs:gYear builtin type"""


class GregorianYear(GregorianYear10):
    """XSD 1.1 xs:gYear builtin type"""
    version = '1.1'


class XPathGregorianYearMonth(AbstractDateTime):
    """xs:gYearMonth datatype for XPath expressions"""
    _pattern = re.compile(r'^(?P<year>(?:-)?[0-9]*[0-9]{4})-(?P<month>[0-9]{2})'
                          r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, year, month, tzinfo=None):
        super(XPathGregorianYearMonth, self).__init__(year, month, tzinfo=tzinfo)

    def __str__(self):
        return '{}-{:02}{}'.format(self.iso_year, self.month, str(self.tzinfo or ''))


class GregorianYearMonth10(XPathGregorianYearMonth, OrderedDateTime):
    """XSD 1.0 xs:gYearMonth builtin type"""


class GregorianYearMonth(GregorianYearMonth10):
    """XSD 1.1 xs:gYearMonth builtin type"""
    version = '1.1'


class Time(AbstractDateTime):
    """XSD xs:time builtin type"""
    _pattern = re.compile(
        r'^(?P<hour>[0-9]{2}):(?P<minute>[0-9]{2}):'
        r'(?P<second>[0-9]{2})(?:\.(?P<microsecond>[0-9]+))?'
        r'(?P<tzinfo>Z|[+-](?:(?:0[0-9]|1[0-3]):[0-5][0-9]|14:00))?$')

    def __init__(self, hour=0, minute=0, second=0, microsecond=0, tzinfo=None):
        if hour == 24 and minute == second == 0:
            hour = 0
        super(Time, self).__init__(
            hour=hour, minute=minute, second=second, microsecond=microsecond, tzinfo=tzinfo
        )

    def __str__(self):
        if self.microsecond:
            return '{:02}:{:02}:{:02}.{:06}{}'.format(
                self.hour, self.minute, self.second, self.microsecond, str(self.tzinfo or '')
            )
        return '{:02}:{:02}:{:02}{}'.format(
            self.hour, self.minute, self.second, str(self.tzinfo or '')
        )

    def __lt__(self, other):
        return operator.lt(*self._get_operands(other))

    def __le__(self, other):
        return operator.le(*self._get_operands(other))

    def __gt__(self, other):
        return operator.gt(*self._get_operands(other))

    def __ge__(self, other):
        return operator.ge(*self._get_operands(other))

    def __add__(self, other):
        if isinstance(other, DayTimeDuration):
            dt = self._dt + other.get_timedelta()
        elif isinstance(other, datetime.timedelta):
            dt = self._dt + other
        else:
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return Time(dt.hour, dt.minute, dt.second, dt.microsecond, dt.tzinfo)

    def __sub__(self, other):
        if isinstance(other, self.__class__):
            delta = operator.sub(*self._get_operands(other))
            return DayTimeDuration.fromtimedelta(delta)
        elif isinstance(other, DayTimeDuration):
            dt = self._dt - other.get_timedelta()
            return Time(dt.hour, dt.minute, dt.second, dt.microsecond, dt.tzinfo)
        elif isinstance(other, datetime.timedelta):
            dt = self._dt - other
            return Time(dt.hour, dt.minute, dt.second, dt.microsecond, dt.tzinfo)
        else:
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))


class Duration(object):
    """
    Base class for the XSD duration types.

    :param months: an integer value that represents years and months.
    :param seconds: a Decimal instance that represents days, hours, minutes, \
    seconds and fractions of seconds.
    """
    _pattern = re.compile(
        r'^(-)?P(?=(?:[0-9]|T))(?:([0-9]+)Y)?(?:([0-9]+)M)?(?:([0-9]+)D)?'
        r'(?:T(?=[0-9])(?:([0-9]+)H)?(?:([0-9]+)M)?(?:([0-9]+(?:\.[0-9]+)?)S)?)?$'
    )

    def __init__(self, months=0, seconds=0):
        if seconds < 0 < months or months < 0 < seconds:
            raise ElementPathValueError('signs differ: (months=%d, seconds=%d)' % (months, seconds))
        self.months = months
        self.seconds = decimal.Decimal(seconds)

    def __repr__(self):
        return '{}(months={!r}, seconds={})'.format(
            self.__class__.__name__, self.months, str(self.seconds)
        )

    def __str__(self):
        m = abs(self.months)
        years, months = m // 12, m % 12
        s = abs(self.seconds)
        days = int(s // 86400)
        hours = int(s // 3600 % 24)
        minutes = int(s // 60 % 60)
        seconds = s % 60

        value = '-P' if self.sign else 'P'
        if years or months or days:
            if years:
                value += '%dY' % years
            if months:
                value += '%dM' % months
            if days:
                value += '%dD' % days

        if hours or minutes or seconds:
            value += 'T'
            if hours:
                value += '%dH' % hours
            if minutes:
                value += '%dM' % minutes
            if seconds:
                value += '%sS' % seconds
        elif value[-1] == 'P':
            value += 'T0S'
        return value

    @classmethod
    def fromstring(cls, text):
        """
        Creates a Duration instance from a formatted XSD duration string.

        :param text: an ISO 8601 representation without week fragment and an optional decimal part \
        only for seconds fragment.
        """
        match = cls._pattern.match(text)
        if match is None:
            raise ElementPathValueError('%r is not an xs:duration value' % text)

        sign, years, months, days, hours, minutes, seconds = match.groups()
        seconds = decimal.Decimal(seconds or 0)
        minutes = int(minutes or 0) + int(seconds // 60)
        seconds = seconds % 60
        hours = int(hours or 0) + minutes // 60
        minutes = minutes % 60
        days = int(days or 0) + hours // 24
        hours = hours % 24
        months = int(months or 0) + 12 * int(years or 0)

        if sign is None:
            seconds = seconds + (days * 24 + hours) * 3600 + minutes * 60
        else:
            months = -months
            seconds = -seconds - (days * 24 + hours) * 3600 - minutes * 60

        if cls is DayTimeDuration:
            if months:
                raise ElementPathValueError('months must be 0 for %r' % cls.__name__)
            return cls(seconds=seconds)
        elif cls is YearMonthDuration:
            if seconds:
                raise ElementPathValueError('seconds must be 0 for %r' % cls.__name__)
            return cls(months=months)
        return cls(months=months, seconds=seconds)

    @property
    def sign(self):
        return '-' if self.months < 0 or self.seconds < 0 else ''

    def _compare_durations(self, other, op):
        """
        Ordering is defined through comparison of four datetime.datetime values.

        Ref: https://www.w3.org/TR/2012/REC-xmlschema11-2-20120405/#duration
        """
        if not isinstance(other, self.__class__):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))

        m1, s1 = self.months, int(self.seconds)
        m2, s2 = other.months, int(other.seconds)
        ms1, ms2 = int((self.seconds - s1) * 1000000), int((other.seconds - s2) * 1000000)
        return all([
            op(datetime.timedelta(months2days(1696, 9, m1), s1, ms1),
               datetime.timedelta(months2days(1696, 9, m2), s2, ms2)),
            op(datetime.timedelta(months2days(1697, 2, m1), s1, ms1),
               datetime.timedelta(months2days(1697, 2, m2), s2, ms2)),
            op(datetime.timedelta(months2days(1903, 3, m1), s1, ms1),
               datetime.timedelta(months2days(1903, 3, m2), s2, ms2)),
            op(datetime.timedelta(months2days(1903, 7, m1), s1, ms1),
               datetime.timedelta(months2days(1903, 7, m2), s2, ms2)),
        ])

    def __hash__(self):
        return hash((self.months, self.seconds))

    def __eq__(self, other):
        if isinstance(other, self.__class__):
            return self.months == other.months and self.seconds == other.seconds
        else:
            return other == (self.months, self.seconds)

    def __ne__(self, other):
        if isinstance(other, self.__class__):
            return self.months != other.months or self.seconds != other.seconds
        else:
            return other != (self.months, self.seconds)

    def __lt__(self, other):
        return self._compare_durations(other, operator.lt)

    def __le__(self, other):
        return self == other or self._compare_durations(other, operator.le)

    def __gt__(self, other):
        return self._compare_durations(other, operator.gt)

    def __ge__(self, other):
        return self == other or self._compare_durations(other, operator.ge)


class YearMonthDuration(Duration):

    def __init__(self, months=0):
        super(YearMonthDuration, self).__init__(months, 0)

    def __repr__(self):
        return '%s(months=%r)' % (self.__class__.__name__, self.months)

    def __add__(self, other):
        if not isinstance(other, self.__class__):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return YearMonthDuration(months=self.months + other.months)

    def __sub__(self, other):
        if not isinstance(other, self.__class__):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return YearMonthDuration(months=self.months - other.months)

    def __mul__(self, other):
        if not isinstance(other, (float, int, decimal.Decimal)):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return YearMonthDuration(months=int(float(self.months * other) + 0.5))

    def __truediv__(self, other):
        if isinstance(other, self.__class__):
            return self.months / other.months
        elif isinstance(other, (float, int, decimal.Decimal)):
            return YearMonthDuration(months=int(float(self.months / other) + 0.5))
        else:
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))


class DayTimeDuration(Duration):

    def __init__(self, seconds=0):
        super(DayTimeDuration, self).__init__(0, seconds)

    @classmethod
    def fromtimedelta(cls, td):
        return cls(seconds=decimal.Decimal(
            '{}.{:06}'.format(td.days * 86400 + td.seconds, td.microseconds)
        ))

    def get_timedelta(self):
        return datetime.timedelta(
            seconds=int(self.seconds), microseconds=int(self.seconds % 1 * 1000000)
        )

    def __repr__(self):
        return '%s(seconds=%s)' % (self.__class__.__name__, str(self.seconds))

    def __add__(self, other):
        if not isinstance(other, self.__class__):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return DayTimeDuration(seconds=self.seconds + other.seconds)

    def __sub__(self, other):
        if not isinstance(other, self.__class__):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return DayTimeDuration(seconds=self.seconds - other.seconds)

    def __mul__(self, other):
        if not isinstance(other, (float, int, decimal.Decimal)):
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))
        return DayTimeDuration(seconds=int(float(self.seconds * other) + 0.5))

    def __truediv__(self, other):
        if isinstance(other, self.__class__):
            return self.seconds / other.seconds
        elif isinstance(other, (float, int, decimal.Decimal)):
            return DayTimeDuration(seconds=int(float(self.seconds / other) + 0.5))
        else:
            raise ElementPathTypeError("wrong type %r for operand %r" % (type(other), other))


class UntypedAtomic(object):
    """
    Class for xs:untypedAtomic data. Provides special methods for comparing
    and converting to basic data types.

    :param value: the untyped value, usually a string.
    """
    def __init__(self, value):
        if not isinstance(value, (str, bytes, int, float, decimal.Decimal, bool)):
            raise ElementPathTypeError("{!r} is not an atomic value".format(value))
        self.value = value

    def __repr__(self):
        return '%s(value=%r)' % (self.__class__.__name__, self.value)

    def _get_operands(self, other, force_float=True):
        """
        Returns a couple of operands, applying a cast to the instance value based on
        the type of the *other* argument.

        :param other: The other operand, that determines the cast for the untyped instance.
        :param force_float: Force a conversion to float if *other* is an UntypedAtomic instance.
        :return: A couple of values.
        """
        if isinstance(other, UntypedAtomic):
            if force_float:
                return float(self.value), float(other.value)
            else:
                return self.value, other.value
        elif isinstance(other, int):
            return float(self.value), other
        else:
            return type(other)(self.value), other

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

    def __eq__(self, other):
        return operator.eq(*self._get_operands(other, force_float=False))

    def __ne__(self, other):
        return not operator.eq(*self._get_operands(other, force_float=False))

    def __lt__(self, other):
        return operator.lt(*self._get_operands(other))

    def __le__(self, other):
        return operator.le(*self._get_operands(other))

    def __gt__(self, other):
        return operator.gt(*self._get_operands(other))

    def __ge__(self, other):
        return operator.ge(*self._get_operands(other))

    def __add__(self, other):
        return operator.add(*self._get_operands(other))
    __radd__ = __add__

    def __sub__(self, other):
        return operator.sub(*self._get_operands(other))

    def __rsub__(self, other):
        return operator.sub(*reversed(self._get_operands(other)))

    def __mul__(self, other):
        return operator.mul(*self._get_operands(other))
    __rmul__ = __mul__

    def __truediv__(self, other):
        return operator.truediv(*self._get_operands(other))

    def __rtruediv__(self, other):
        return operator.truediv(*reversed(self._get_operands(other)))

    def __int__(self):
        return int(self.value)

    def __float__(self):
        return float(self.value)

    def __bool__(self):
        return bool(self.value)

    def __abs__(self):
        return abs(self.value)

    def __mod__(self, other):
        return operator.mod(*self._get_operands(other))

    def __str__(self):
        return str(self.value)

    def __bytes__(self):
        return bytes(self.value, encoding='utf-8')


####
# XSD atomic builtins validators and values

XsdBuiltin = namedtuple('XsdBuiltin', 'validator value')
"""A namedtuple-based type for describing XSD builtin types."""

WHITESPACES_PATTERN = re.compile(r'\s+')
NMTOKEN_PATTERN = re.compile(r'^[\w.\-:]+$')
NAME_PATTERN = re.compile(r'^(?:[^\d\W]|:)[\w.\-:]*$')
NCNAME_PATTERN = re.compile(r'^[^\d\W][\w.\-]*$')
QNAME_PATTERN = re.compile(
    r'^(?:(?P<prefix>[^\d\W][\w\-.\xb7\u0387\u06DD\u06DE]*):)?'
    r'(?P<local>[^\d\W][\w\-.\xb7\u0387\u06DD\u06DE]*)$',
)
HEX_BINARY_PATTERN = re.compile(r'^[0-9a-fA-F]+$')
NOT_BASE64_BINARY_PATTERN = re.compile(r'[^0-9a-zA-z+/= \t\n]')
LANGUAGE_CODE_PATTERN = re.compile(r'^[a-zA-Z]{1,8}(-[a-zA-Z0-9]{1,8})*$')
WRONG_ESCAPE_PATTERN = re.compile(r'%(?![a-eA-E\d]{2})')


class TypeProxyMeta(type):
    """
    A metaclass for creating type proxy classes, that can be used for instance
    and subclass checking and for building instances of related types. A type
    proxy class has to implement three methods as concrete class/static methods.
    """
    def __instancecheck__(cls, instance):
        return cls.instance_check(instance)

    def __subclasscheck__(cls, subclass):
        return cls.subclass_check(subclass)

    def __call__(cls, *args, **kwargs):
        return cls.instance_build(*args, **kwargs)

    def instance_check(cls, instance):
        """Checks the if the argument is an instance of one of related types."""
        raise NotImplementedError

    def subclass_check(cls, subclass):
        """Checks the if the argument is a subclass of one of related types."""
        raise NotImplementedError

    def instance_build(cls, *args, **kwargs):
        """Builds an instance belonging to one of related types."""
        raise NotImplementedError


class NumericTypeProxy(metaclass=TypeProxyMeta):
    """
    A type proxy class for xs:numeric related types (xs:float, xs:decimal and
    derived types). Builds xs:float instances.
    """
    @staticmethod
    def instance_check(other):
        return isinstance(other, (int, float, decimal.Decimal)) and \
            not isinstance(other, bool)

    @staticmethod
    def subclass_check(subclass):
        if issubclass(subclass, bool):
            return False
        return issubclass(subclass, int) or issubclass(subclass, float) \
            or issubclass(subclass, decimal.Decimal)

    @staticmethod
    def instance_build(x=0):
        return float(x)


class ArithmeticTypeProxy(metaclass=TypeProxyMeta):
    """
    A type proxy class for XSD types related to arithmetic operators, including
    types related to xs:numeric and datetime or duration types. Builds xs:float
    instances.
    """

    @staticmethod
    def instance_check(other):
        return isinstance(other, (int, float, decimal.Decimal, AbstractDateTime, Duration)) \
            and not isinstance(other, bool)

    @staticmethod
    def subclass_check(subclass):
        if issubclass(subclass, bool):
            return False
        return issubclass(subclass, int) or issubclass(subclass, float) or \
            issubclass(subclass, decimal.Decimal) or issubclass(subclass, Duration) \
            or issubclass(subclass, AbstractDateTime)

    @staticmethod
    def instance_build(x=0):
        return float(x)


def decimal_validator(x):
    return isinstance(x, (int, decimal.Decimal)) and not isinstance(x, bool)


def integer_validator(x):
    return isinstance(x, int) and not isinstance(x, bool)


def base64_binary_validator(x):
    if isinstance(x, bytes):
        x = x.decode()
    if not isinstance(x, str) or NOT_BASE64_BINARY_PATTERN.search(x) is not None:
        return False
    try:
        base64.standard_b64decode(x)
    except (ValueError, TypeError):
        return False
    else:
        return True


def hex_binary_validator(x):
    return isinstance(x, str) and not len(x) % 2 and HEX_BINARY_PATTERN.match(x) is not None


def ncname_validator(x):
    return isinstance(x, str) and NCNAME_PATTERN.match(x) is not None


XSD_BUILTIN_TYPES = {           # pragma: no cover
    'anyType': XsdBuiltin(
        lambda x: True,
        value=UntypedAtomic('1')
    ),
    'anySimpleType': XsdBuiltin(
        lambda x: isinstance(x, (str, int, float, bool, decimal.Decimal,
                                 AbstractDateTime, Duration, Timezone, UntypedAtomic)),
        value=UntypedAtomic('1')
    ),
    'anyAtomicType': XsdBuiltin(
        lambda x: False,
        value=None
    ),
    'string': XsdBuiltin(
        lambda x: isinstance(x, str),
        value='  alpha\t'
    ),
    'decimal': XsdBuiltin(
        decimal_validator,
        value=decimal.Decimal('1.0')
    ),
    'double': XsdBuiltin(
        lambda x: isinstance(x, float),
        value=1.0
    ),
    'float': XsdBuiltin(
        lambda x: isinstance(x, float),
        value=1.0
    ),
    'date': XsdBuiltin(
        lambda x: isinstance(x, Date),
        value=Date.fromstring('2000-01-01')
    ),
    'dateTime': XsdBuiltin(
        lambda x: isinstance(x, DateTime),
        value=DateTime.fromstring('2000-01-01T12:00:00')
    ),
    'gDay': XsdBuiltin(
        lambda x: isinstance(x, GregorianDay),
        value=GregorianDay.fromstring('---31')
    ),
    'gMonth': XsdBuiltin(
        lambda x: isinstance(x, GregorianMonth),
        value=GregorianMonth.fromstring('--12')
    ),
    'gMonthDay': XsdBuiltin(
        lambda x: isinstance(x, GregorianMonthDay),
        value=GregorianMonthDay.fromstring('--12-01')
    ),
    'gYear': XsdBuiltin(
        lambda x: isinstance(x, GregorianYear),
        value=GregorianYear.fromstring('1999')
    ),
    'gYearMonth': XsdBuiltin(
        lambda x: isinstance(x, GregorianYearMonth),
        value=GregorianYearMonth.fromstring('1999-09')
    ),
    'time': XsdBuiltin(
        lambda x: isinstance(x, Time),
        value=Time.fromstring('09:26:54')
    ),
    'duration': XsdBuiltin(
        lambda x: isinstance(x, Duration),
        value=Duration.fromstring('P1MT1S')
    ),
    'dayTimeDuration': XsdBuiltin(
        lambda x: isinstance(x, DayTimeDuration),
        value=DayTimeDuration.fromstring('P1DT1S')
    ),
    'yearMonthDuration': XsdBuiltin(
        lambda x: isinstance(x, YearMonthDuration),
        value=YearMonthDuration.fromstring('P1Y1M')
    ),
    'QName': XsdBuiltin(
        lambda x: isinstance(x, str) and QNAME_PATTERN.match(x) is not None,
        value='xs:element'
    ),
    'NOTATION': XsdBuiltin(
        lambda x: isinstance(x, str),
        value='alpha'
    ),
    'anyURI': XsdBuiltin(
        lambda x: isinstance(x, str),
        value='https://example.com'
    ),
    'normalizedString': XsdBuiltin(
        lambda x: isinstance(x, str) and '\t' not in x and '\r' not in x,
        value=' alpha  ',
    ),
    'token': XsdBuiltin(
        lambda x: isinstance(x, str) and WHITESPACES_PATTERN.match(x) is None,
        value='a token'
    ),
    'language': XsdBuiltin(
        lambda x: isinstance(x, str) and LANGUAGE_CODE_PATTERN.match(x) is not None,
        value='en-US'
    ),
    'Name': XsdBuiltin(
        lambda x: isinstance(x, str) and NAME_PATTERN.match(x) is not None,
        value='_a.name::'
    ),
    'NCName': XsdBuiltin(
        ncname_validator,
        value='nc-name'
    ),
    'ID': XsdBuiltin(
        ncname_validator,
        value='id1'
    ),
    'IDREF': XsdBuiltin(
        ncname_validator,
        value='id_ref1'
    ),
    'ENTITY': XsdBuiltin(
        ncname_validator,
        value='entity1'
    ),
    'NMTOKEN': XsdBuiltin(
        lambda x: isinstance(x, str) and NMTOKEN_PATTERN.match(x) is not None,
        value='a_token'
    ),
    'base64Binary': XsdBuiltin(
        base64_binary_validator,
        value=b'YWxwaGE='
    ),
    'hexBinary': XsdBuiltin(
        hex_binary_validator,
        value=b'31'
    ),
    'dateTimeStamp': XsdBuiltin(
        lambda x: isinstance(x, str),
        value='2000-01-01T12:00:00+01:00'
    ),
    'integer': XsdBuiltin(
        integer_validator,
        value=1
    ),
    'long': XsdBuiltin(
        lambda x: integer_validator(x) and (-2**63 <= x < 2**63),
        value=1
    ),
    'int': XsdBuiltin(
        lambda x: integer_validator(x) and (-2**31 <= x < 2**31),
        value=1
    ),
    'short': XsdBuiltin(
        lambda x: integer_validator(x) and (-2**15 <= x < 2**15),
        value=1
    ),
    'byte': XsdBuiltin(
        lambda x: integer_validator(x) and (-2**7 <= x < 2**7),
        value=1
    ),
    'positiveInteger': XsdBuiltin(
        lambda x: integer_validator(x) and x > 0,
        value=1
    ),
    'negativeInteger': XsdBuiltin(
        lambda x: integer_validator(x) and x < 0,
        value=-1
    ),
    'nonPositiveInteger': XsdBuiltin(
        lambda x: integer_validator(x) and x <= 0,
        value=0
    ),
    'nonNegativeInteger': XsdBuiltin(
        lambda x: integer_validator(x) and x >= 0,
        value=0
    ),
    'unsignedLong': XsdBuiltin(
        lambda x: integer_validator(x) and (0 <= x < 2**64),
        value=1
    ),
    'unsignedInt': XsdBuiltin(
        lambda x: integer_validator(x) and (0 <= x < 2**32),
        value=1
    ),
    'unsignedShort': XsdBuiltin(
        lambda x: integer_validator(x) and (0 <= x < 2**16),
        value=1
    ),
    'unsignedByte': XsdBuiltin(
        lambda x: integer_validator(x) and (0 <= x < 2**8),
        value=1
    ),
    'boolean': XsdBuiltin(
        lambda x: isinstance(x, bool),
        value=True
    ),
}
