python-cylc 7.6.0-1 / usr / lib / python2.7 / dist-packages / isodatetime / data.py

# -*- coding: utf-8 -*-
# ----------------------------------------------------------------------------
# (C) British Crown Copyright 2013-2017 Met Office.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
# ----------------------------------------------------------------------------

"""This provides ISO 8601 data model functionality."""


from . import dumpers
from . import timezone
from . import util


class Calendar(object):

    """Store constants for Gregorian calendar date-time calculation."""

    SECONDS_IN_MINUTE = 60
    MINUTES_IN_HOUR = 60
    HOURS_IN_DAY = 24
    DAYS_IN_WEEK = 7
    DAYS_IN_MONTHS = None  # This is set up in the set_* methods.
    DAYS_IN_MONTHS_LEAP = None  # This is set up in the set_* methods
    ROUGH_DAYS_IN_MONTH = 30  # Used for duration conversion, nowhere else.

    LEAP_YEAR_FACTOR_TRUTHS = [(4, True), (100, False), (400, True)]

    MODE_360 = "360day"
    MODE_365 = "365day"
    MODE_366 = "366day"
    MODE_GREGORIAN = "gregorian"

    # {mode: (days_in_months, days_in_months_leap), ...}
    MODES = {
        MODE_360: (12 * [30], None),
        MODE_365: ([31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31], None),
        MODE_366: ([31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31], None),
        MODE_GREGORIAN: (
            [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
            [31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
        ),
    }

    WEEK_DAY_START_REFERENCE = {"calendar": (2000, 1, 3),
                                "ordinal": (2000, 3)}
    UNIX_EPOCH_DATE_TIME_REFERENCE_PROPERTIES = {
        "year": 1970, "time_zone_hour": 0, "time_zone_minute": 0}

    _DEFAULT = None

    @classmethod
    def default(cls):
        if cls._DEFAULT is None:
            cls._DEFAULT = cls()
        return cls._DEFAULT

    def __init__(self):
        self.set_mode()

    def set_mode(self, mode=None):
        """Set calendar mode.

        mode -- calendar mode, which can be one of the keys in Calendar.MODES.
                If None, default to MODE_GREGORIAN.

        """
        if not mode:
            mode = self.MODE_GREGORIAN
        days_in_months, days_in_months_leap = self.MODES[mode.lower()]
        if days_in_months_leap is None:
            days_in_months_leap = days_in_months
        self.DAYS_IN_MONTHS = days_in_months
        self.DAYS_IN_MONTHS_LEAP = days_in_months_leap
        self.mode = mode

        # Recalculate
        self.SECONDS_IN_HOUR = self.SECONDS_IN_MINUTE * self.MINUTES_IN_HOUR
        self.SECONDS_IN_DAY = self.SECONDS_IN_HOUR * self.HOURS_IN_DAY
        self.MINUTES_IN_DAY = self.MINUTES_IN_HOUR * self.HOURS_IN_DAY
        self.INDEXED_DAYS_IN_MONTHS = [
            (i + 1, days) for i, days in enumerate(self.DAYS_IN_MONTHS)]
        self.INDEXED_DAYS_IN_MONTHS_LEAP = [
            (i + 1, days) for i, days in enumerate(self.DAYS_IN_MONTHS_LEAP)]
        self.REVERSED_INDEXED_DAYS_IN_MONTHS = (
            reversed(self.INDEXED_DAYS_IN_MONTHS))
        self.REVERSED_INDEXED_DAYS_IN_MONTHS_LEAP = (
            reversed(self.INDEXED_DAYS_IN_MONTHS))
        self.MONTHS_IN_YEAR = len(self.DAYS_IN_MONTHS)
        # No support for MONTHS_IN_YEAR_LEAP (some calendars...)
        self.DAYS_IN_YEAR = sum(self.DAYS_IN_MONTHS)
        self.ROUGH_DAYS_IN_YEAR = self.DAYS_IN_YEAR
        self.DAYS_IN_YEAR_LEAP = sum(self.DAYS_IN_MONTHS_LEAP)
        self.HOURS_IN_YEAR = self.DAYS_IN_YEAR * self.HOURS_IN_DAY
        self.MINUTES_IN_YEAR = self.DAYS_IN_YEAR * self.MINUTES_IN_DAY
        self.SECONDS_IN_YEAR = self.DAYS_IN_YEAR * self.SECONDS_IN_DAY
        self.HOURS_IN_YEAR_LEAP = self.DAYS_IN_YEAR_LEAP * self.HOURS_IN_DAY
        self.MINUTES_IN_YEAR_LEAP = (
            self.DAYS_IN_YEAR_LEAP * self.MINUTES_IN_DAY)
        self.SECONDS_IN_YEAR_LEAP = (
            self.DAYS_IN_YEAR_LEAP * self.SECONDS_IN_DAY)

    def __repr__(self):
        return "<%s-%s>" % (type(self).__name__, self.mode)


CALENDAR = Calendar.default()


TIMEPOINT_DUMPER_MAP = {
    0: dumpers.TimePointDumper(num_expanded_year_digits=0),
    2: dumpers.TimePointDumper(num_expanded_year_digits=2)
}


class BadInputError(ValueError):

    """An error raised when constructor inputs are invalid."""

    CONFLICT = "Conflicting input: {0} but have {1}"
    INT_CAST = "Invalid input for {0}: {1}: {2}"
    INT_REMAINDER = "Non-integer like number for {0}: {1}"
    MISSING = "Missing input: {0} needs {1}"
    OUT_OF_BOUNDS = "Invalid input (out of bounds): {0}: {1}"
    RECURRENCE = "Invalid recurrence info: {0}"
    TYPE = "Invalid type for {0}: {1}{2}"
    VALUES = "Invalid input for {0}: {1}: allowed: {2}"

    def __str__(self):
        format_string = self.args[0]
        format_args = self.args[1:]
        return format_string.format(*format_args)


class TimeRecurrence(object):

    """Represent a recurring duration."""

    __slots__ = ("repetitions", "start_point", "duration", "end_point",
                 "min_point", "max_point", "format_number")

    def __init__(self, repetitions=None, start_point=None,
                 duration=None, end_point=None, min_point=None,
                 max_point=None):
        inputs = (
            (repetitions, "repetitions", None, int),
            (start_point, "start_point", None, TimePoint),
            (duration, "duration", None, Duration),
            (end_point, "end_point", None, TimePoint),
            (min_point, "min_point", None, TimePoint),
            (max_point, "max_point", None, TimePoint)
        )
        _type_checker(*inputs)
        self.repetitions = repetitions
        self.start_point = start_point
        self.duration = duration
        self.end_point = end_point
        self.min_point = min_point
        self.max_point = max_point
        self.format_number = None
        if self.duration is None:
            # First form.
            self.format_number = 1
            start_year, start_days = self.start_point.get_ordinal_date()
            start_seconds = self.start_point.get_second_of_day()
            self.end_point.set_time_zone(self.start_point.time_zone)
            end_year, end_days = self.end_point.get_ordinal_date()
            end_seconds = self.end_point.get_second_of_day()
            diff_days = end_days - start_days
            if end_year > start_year:
                diff_days += get_days_in_year_range(start_year, end_year - 1)
            diff_seconds = end_seconds - start_seconds
            if diff_seconds < 0:
                diff_days -= 1
                diff_seconds += CALENDAR.SECONDS_IN_DAY
            if diff_seconds >= CALENDAR.SECONDS_IN_DAY:
                diff_days += 1
                diff_seconds -= CALENDAR.SECONDS_IN_DAY
            if self.repetitions == 1:
                self.duration = Duration(years=0)
            else:
                diff_days_float = diff_days / float(
                    self.repetitions - 1)
                diff_seconds_float = diff_seconds / float(
                    self.repetitions - 1)
                diff_days = int(diff_days_float)
                diff_seconds_float += (
                    diff_days_float - diff_days) * CALENDAR.SECONDS_IN_DAY
                self.duration = Duration(
                    days=diff_days, seconds=diff_seconds_float)
        elif self.end_point is None:
            # Third form.
            self.format_number = 3
            if self.repetitions is not None:
                point = self.start_point
                for i in range(self.repetitions - 1):
                    point += self.duration
                self.end_point = point
        elif self.start_point is None:
            # Fourth form.
            self.format_number = 4
            if self.repetitions is not None:
                point = self.end_point
                for i in range(self.repetitions - 1):
                    point -= self.duration
                self.start_point = point
        else:
            raise BadInputError(
                BadInputError.RECURRENCE,
                [i[:2] for i in inputs]
            )

    def get_is_valid(self, timepoint):
        """Return whether the timepoint is valid for this recurrence."""
        if not self._get_is_in_bounds(timepoint):
            return False
        for iter_timepoint in self.__iter__():
            if iter_timepoint == timepoint:
                return True
            if self.start_point is None and iter_timepoint < timepoint:
                return False
            if self.end_point is None and iter_timepoint > timepoint:
                return False
        return False

    def get_next(self, timepoint):
        """Return the next timepoint after this timepoint, or None."""
        if self.repetitions == 1 or timepoint is None:
            return None
        next_timepoint = timepoint + self.duration
        if self._get_is_in_bounds(next_timepoint):
            return next_timepoint
        if (self.format_number == 1 and next_timepoint > self.end_point):
            diff = next_timepoint - self.end_point
            if (2 * diff < self.duration and
                    self._get_is_in_bounds(self.end_point)):
                return self.end_point
        return None

    def get_prev(self, timepoint):
        """Return the previous timepoint before this timepoint, or None."""
        if self.repetitions == 1 or timepoint is None:
            return None
        prev_timepoint = timepoint - self.duration
        if self._get_is_in_bounds(prev_timepoint):
            return prev_timepoint
        return None

    def __getitem__(self, index):
        if index < 0 or not isinstance(index, int):
            raise IndexError(
                "Unsupported index for TimeRecurrence")
        for i, point in enumerate(self.__iter__()):
            if index == i:
                return point
        raise IndexError(
            "Invalid index for TimeRecurrence")

    def _get_is_in_bounds(self, timepoint):
        """Return whether the timepoint is within this recurrence series."""
        if timepoint is None:
            return False
        if self.start_point is not None and timepoint < self.start_point:
            return False
        if self.min_point is not None and timepoint < self.min_point:
            return False
        if self.max_point is not None and timepoint > self.max_point:
            return False
        if self.end_point is not None and timepoint > self.end_point:
            return False
        return True

    def __iter__(self):
        if self.start_point is None:
            point = self.end_point
            in_reverse = True
        else:
            point = self.start_point
            in_reverse = False

        if self.repetitions == 1 or not self.duration:
            if self._get_is_in_bounds(point):
                yield point
            point = None

        while point is not None:
            if self._get_is_in_bounds(point):
                yield point
            else:
                break
            if in_reverse:
                point = self.get_prev(point)
            else:
                point = self.get_next(point)

    def __str__(self):
        if self.repetitions is None:
            prefix = "R/"
        else:
            prefix = "R" + str(self.repetitions) + "/"
        if self.format_number == 1:
            return prefix + str(self.start_point) + "/" + str(self.end_point)
        elif self.format_number == 3:
            return prefix + str(self.start_point) + "/" + str(self.duration)
        elif self.format_number == 4:
            return prefix + str(self.duration) + "/" + str(self.end_point)
        return "R/?/?"

    def get_tests(self):
        """Return a series of self-tests."""
        for recur_expression, result_points in self.TEST_EXPRESSIONS:
            yield recur_expression, result_points


class Duration(object):

    """Represent a duration or period of time.

    Keyword arguments:
    years (default 0): number of calendar years in the duration (an
    inexact unit)
    months (default 0): number of calendar months in the duration (also
    an inexact unit)
    weeks (default 0): number of weeks in the duration - cannot be
    used in conjunction with other units (use multiples of 7 days
    instead)
    days (default 0): number of days in the duration
    hours (default 0): number of hours in the duration
    minutes (default 0): number of minutes in the duration
    seconds (default 0): number of seconds in the duration
    standardize (default False): boolean that, if True, switches on
    adjusting the attributes so that small units have minimal values.
    For example, 3664.4 seconds would become 1 hour, 1 minute, and 4.4
    seconds. Attributes will not adjust for units that are inexact
    (months and years).

    """

    DATA_ATTRIBUTES = [
        "years", "months", "weeks", "days", "hours", "minutes", "seconds"]

    __slots__ = DATA_ATTRIBUTES

    def __init__(self, years=0, months=0, weeks=0, days=0,
                 hours=0.0, minutes=0.0, seconds=0.0, standardize=False):
        _type_checker(
            (years, "years", int, float, None),
            (months, "months", int, float, None),
            (weeks, "weeks", int, float, None),
            (days, "days", int, float, None),
            (hours, "hours", int, float, None),
            (minutes, "minutes", int, float, None),
            (seconds, "seconds", int, float, None)
        )
        self.years = years
        self.months = months
        self.weeks = None
        self.days = days
        if weeks is not None:
            if days is None:
                self.days = CALENDAR.DAYS_IN_WEEK * weeks
            else:
                self.days += CALENDAR.DAYS_IN_WEEK * weeks
        self.hours = hours
        self.minutes = minutes
        self.seconds = seconds
        if (not self.years and not self.months and not self.hours and
                not self.minutes and not self.seconds and
                weeks and not days):
            self.weeks = self.days / CALENDAR.DAYS_IN_WEEK
            self.years, self.months, self.days = (None, None, None)
            self.hours, self.minutes, self.seconds = (None, None, None)
        if standardize:
            if self.seconds:
                num_minutes, self.seconds = divmod(
                    self.seconds, CALENDAR.SECONDS_IN_MINUTE)
                if self.minutes is None:
                    self.minutes = 0
                self.minutes += num_minutes
            if self.minutes:
                num_hours, self.minutes = divmod(
                    self.minutes, CALENDAR.MINUTES_IN_HOUR)
                if self.hours is None:
                    self.hours = 0
                self.hours += num_hours
            if self.hours:
                num_days, self.hours = divmod(
                    self.hours, CALENDAR.HOURS_IN_DAY)
                if self.days is None:
                    self.days = 0
                self.days += num_days

    def copy(self):
        """Return an unlinked copy of this instance."""
        return Duration(
            years=self.years, months=self.months, weeks=self.weeks,
            days=self.days, hours=self.hours, minutes=self.minutes,
            seconds=self.seconds)

    def get_days_and_seconds(self):
        """Return a roughly-converted duration in days and seconds.

        This cannot be accurate for non-uniform units such as years and
        months, and may yield incorrect results if used for comparisons
        derived from durations using these units.

        Seconds are returned in the range
        0 <= seconds < CALENDAR.SECONDS_IN_DAY, which means that a
        Duration which has self.seconds = CALENDAR.SECONDS_IN_DAY +
        100 will return 1 day, 100 seconds or (1, 100) from this
        method.

        """
        # TODO: Implement error calculation for the below quantities.
        new = self.copy()
        new.to_days()
        new_days = (new.years * CALENDAR.ROUGH_DAYS_IN_YEAR +
                    new.months * CALENDAR.ROUGH_DAYS_IN_MONTH +
                    new.days)
        new_seconds = (new.hours * CALENDAR.SECONDS_IN_HOUR +
                       new.minutes * CALENDAR.SECONDS_IN_MINUTE +
                       new.seconds)
        diff_days, new_seconds = divmod(new_seconds, CALENDAR.SECONDS_IN_DAY)
        new_days += diff_days
        return new_days, new_seconds

    def get_seconds(self):
        """Return a roughly-converted duration in seconds.

        This is not rigorous when converting from non-uniform units
        such as years and months.

        """
        days, seconds = self.get_days_and_seconds()
        return days * CALENDAR.SECONDS_IN_DAY + seconds

    def get_is_in_weeks(self):
        """Return whether we are in week representation."""
        return (self.weeks is not None)

    def to_days(self):
        """Convert to day representation rather than weeks."""
        if self.get_is_in_weeks():
            for attribute in ["years", "months", "hours",
                              "minutes", "seconds"]:
                if getattr(self, attribute) is None:
                    setattr(self, attribute, 0)
            self.days = self.weeks * CALENDAR.DAYS_IN_WEEK
            self.weeks = None

    def to_weeks(self):
        """Convert to week representation (warning: use with caution)."""
        if not self.get_is_in_weeks():
            self.weeks = self.days / CALENDAR.DAYS_IN_WEEK
            self.years, self.months, self.days = (None, None, None)
            self.hours, self.minutes, self.seconds = (None, None, None)

    def __abs__(self):
        new = self.copy()
        for attribute in new.DATA_ATTRIBUTES:
            attr_value = getattr(new, attribute)
            if attr_value is not None:
                setattr(new, attribute, abs(attr_value))
        return new

    def __add__(self, other):
        new = self.copy()
        if isinstance(other, Duration):
            if new.get_is_in_weeks():
                if other.get_is_in_weeks():
                    new.weeks += other.weeks
                    return new
                new.to_days()
            elif other.get_is_in_weeks():
                other = other.copy()
                other.to_days()
            new.years += other.years
            new.months += other.months
            new.days += other.days
            new.hours += other.hours
            new.minutes += other.minutes
            new.seconds += other.seconds
            return new
        if isinstance(other, TimePoint):
            return other + new
        raise TypeError(
            "Invalid type for addition: " +
            "'%s' should be Duration or TimePoint." %
            type(other).__name__
        )

    def __sub__(self, other):
        return self + -1 * other

    def __mul__(self, other):
        # TODO: support float multiplication?
        new = self.copy()
        if not isinstance(other, int):
            raise TypeError(
                "Invalid type for multiplication: " +
                "'%s' should be integer." %
                type(other).__name__
            )
        if self.get_is_in_weeks():
            new.weeks *= other
            return new
        new.years *= other
        new.months *= other
        new.days *= other
        new.hours *= other
        new.minutes *= other
        new.seconds *= other
        return new

    def __rmul__(self, other):
        return self.__mul__(other)

    def __floordiv__(self, other):
        # TODO: support float division?
        new = self.copy()
        if not isinstance(other, int):
            raise TypeError(
                "Invalid type for division: " +
                "'%s' should be integer." %
                type(other).__name__
            )
        if self.get_is_in_weeks():
            new.weeks //= other
            return new
        new.years //= other
        new.months //= other
        new.days //= other
        new.hours //= other
        new.minutes //= other
        new.seconds //= other

    def __cmp__(self, other):
        if not isinstance(other, Duration):
            raise TypeError(
                "Invalid type for comparison: " +
                "'%s' should be Duration." %
                type(other).__name__
            )
        my_data = self.get_days_and_seconds()
        other_data = other.get_days_and_seconds()
        return cmp(my_data, other_data)

    def __nonzero__(self):
        for attr in ["years", "months", "weeks", "days", "hours",
                     "minutes", "seconds"]:
            if getattr(self, attr, None):
                return True
        return False

    def __str__(self):
        start_string = "P"
        content_string = ""

        # Handle negative durations.
        is_fully_negative = False
        for attribute in self.DATA_ATTRIBUTES:
            attr_value = getattr(self, attribute)
            if attr_value is not None:
                if attr_value > 0:
                    is_fully_negative = False
                    break
                if attr_value < 0:
                    is_fully_negative = True
        if is_fully_negative:
            # Support negative durations as extensions to the standard.
            return "-" + str(abs(self))

        # Weeks are not combined with any other unit.
        if self.get_is_in_weeks():
            return (start_string + str(self.weeks) + "W").replace(".", ",")

        for prop_, unit in [("years", "Y"), ("months", "M"), ("days", "D"),
                            ("hours", "H"), ("minutes", "M"),
                            ("seconds", "S")]:
            prop_val = getattr(self, prop_)
            if prop_val:
                if int(prop_val) == prop_val:
                    content_string += str(int(prop_val)) + unit
                else:
                    content_string += str(prop_val) + unit
            if prop_ == "days":
                content_string += "T"

        if content_string == "T":
            # No content, zero duration.
            content_string = "0Y"
        elif content_string.endswith("T"):
            # No time unit information, so strip the delimiter.
            content_string = content_string[:-1]

        total_string = start_string + content_string
        return total_string.replace(".", ",")


class TimeZone(Duration):

    """Represent a time zone offset from UTC.

    Keyword arguments:
    hours, minutes: integers (default 0) denoting the hour and minute
    component of the offset from UTC. These may be positive, zero, or
    negative, as required. Note that a negative UTC offset should have
    both hours and minutes as zero or negative integers.
    unknown: a boolean that represents an unknown TimeZone. Some
    operations and comparisons may fail when this is True.

    """

    __slots__ = ['unknown'] + Duration.__slots__

    def __init__(self, hours=0, minutes=0, unknown=False):
        self.unknown = unknown
        super(TimeZone, self).__init__(hours=hours, minutes=minutes)

    def copy(self):
        """Return an unlinked copy of this instance."""
        return TimeZone(hours=self.hours, minutes=self.minutes,
                        unknown=self.unknown)

    def __str__(self):
        if self.unknown:
            return ""
        if self.hours == 0 and self.minutes == 0:
            return "Z"
        else:
            time_string = "+%02d:%02d"
            if self.hours < 0 or (self.hours == 0 and self.minutes < 0):
                time_string = "-%02d:%02d"
            return time_string % (abs(self.hours), abs(self.minutes))

    def __repr__(self):
        return "<isodatetime.data.TimeZone:" + repr(str(self)) + ">"


class TimePoint(object):

    """Represent an instant in time.

    An ISO 8601 date/time instant can be represented in three
    separate ways:
    Calendar date: calendar year, calendar month,
    calendar day of the month
    Ordinal date: calendar year, calendar day of the year
    Week date: calendar (week) year, calendar week,
    calendar day of the week (note: week years are not identical to
    calendar years).

    This class maintains a date/time instant in the original
    representation with which it was invoked - so it may be in any of
    these formats. See the TimePoint.to_*_date methods for internal
    conversions between formats.

    Where properties are not given (consistent with ISO 8601 reduced
    precision dates), they will be given the expected defaults if
    truncation is not specified. For example, if only the year and the
    month_of_year is given, the day_of_month will be set to 1.

    Time zone information defaults to UTC. It is essential to provide it
    unless you are happy with this behaviour. A date/time
    representation is ambiguous without it.

    Keyword arguments (usually default to None if not provided):
    expanded_year_digits (default 0) - an agreed-upon number of extra
    digits to represent the year, beyond the default of 4. For example,
    a value of 2 would suggest representing the year 2000 as 002000.
    year - a positive or negative integer. Note that ISO 8601 implies
    using non-zero expanded_year_digits when using negative integers.
    Remember we are using the proleptic Gregorian calendar, with a year
    zero which does not exist in standard 1 BC => 1 AD usage - so 2 BC
    should be represented as -1.
    month_of_year - an integer between 1 and 12 inclusive, if using the
    calendar date representation.
    week_of_year - an integer between 1 and 52/53 (depending on the
    year), if using the week date representation.
    day_of_year - an integer between 1 and 365/366 (depending on the
    year), if using the ordinal date representation.
    day_of_month - an integer between 1 and 28/29/30/31 (depending on
    the month), if using the calendar date representation.
    day_of_week - an integer between 1 and 7, if using the week date
    representation.
    hour_of_day - an integer between 1 and 24.
    hour_of_day_decimal - a float between 0 and 1, if using decimal
    accuracy for hours. Note that you should not provide lower units
    such as minute_of_hour or second_of_minute when using this.
    minute_of_hour - an integer between 0 and 59.
    minute_of_hour_decimal - a float between 0 and 1, if using decimal
    accuracy for minutes. Note that you should not provide lower units
    such as second_of_minute when using this.
    second_of_minute - an integer between 0 and 59 (note: no support
    for leap seconds at 60 yet)
    second_of_minute_decimal - a float between 0 and 1, if using decimal
    accuracy for seconds.
    time_zone_hour - (default 0) an integer denoting the hour time zone
    offset from UTC. Note that unless this is a truncated
    representation, 0 will be assumed if this is not provided.
    time_zone_minute - (default 0) an integer between 0 and 59 denoting
    the minute component of the time zone offset from UTC.
    dump_format - a custom format string to control the stringification
    of the timepoint. See isodatetime.parser_spec for more details.
    truncated - (default False) a boolean denoting whether the
    date/time instant has purposefully incomplete information
    (ISO 8601:2000 truncation).
    truncated_dump_format - a custom format string to control the
    stringification of the timepoint if it is truncated. See
    isodatetime.parser_spec for more details.
    truncated_property - a string that can either be "year_of_decade"
    or "year_of_century". This is used for truncated representations to
    distinguish between the two ways of truncating the year.
    is_empty_instance - if True, do not set any properties yet. These
    should be set as part of a copy operation.
    """

    DATA_ATTRIBUTES = [
        "expanded_year_digits", "year", "month_of_year",
        "day_of_year", "day_of_month", "day_of_week",
        "week_of_year", "hour_of_day", "minute_of_hour",
        "second_of_minute", "truncated", "truncated_property",
        "dump_format", "time_zone"
    ]

    __slots__ = DATA_ATTRIBUTES + ["truncated_dump_format"]

    def __init__(self, expanded_year_digits=0, year=None, month_of_year=None,
                 week_of_year=None, day_of_year=None, day_of_month=None,
                 day_of_week=None, hour_of_day=None, hour_of_day_decimal=None,
                 minute_of_hour=None, minute_of_hour_decimal=None,
                 second_of_minute=None, second_of_minute_decimal=None,
                 time_zone_hour=None, time_zone_minute=None,
                 dump_format=None, truncated=False,
                 truncated_dump_format=None, truncated_property=None,
                 is_empty_instance=False):
        if is_empty_instance:
            # This has been created for a copy - set properties later.
            return
        _type_checker(
            (expanded_year_digits, "expanded_year_digits", int),
            (year, "year", None, int),
            (month_of_year, "month_of_year", None, int),
            (week_of_year, "week_of_year", None, int),
            (day_of_year, "day_of_year", None, int),
            (day_of_month, "day_of_month", None, int),
            (day_of_week, "day_of_week", None, int),
            (hour_of_day, "hour_of_day", None, int, float),
            (hour_of_day_decimal, "hour_of_day_decimal", None, float),
            (minute_of_hour, "minute_of_hour", None, int, float),
            (minute_of_hour_decimal, "minute_of_hour_decimal", None, float),
            (second_of_minute, "second_of_minute", None, int, float),
            (second_of_minute_decimal, "second_of_minute_decimal", None,
             float),
            (time_zone_hour, "time_zone_hour", None, int),
            (time_zone_minute, "time_zone_minute", None, int)
        )
        if (dump_format is not None and not
                isinstance(dump_format, basestring)):
            raise BadInputError(
                BadInputError.TYPE,
                "dump_format", repr(dump_format), type(dump_format))
        if (truncated_dump_format is not None and not
                isinstance(truncated_dump_format, basestring)):
            raise BadInputError(
                BadInputError.TYPE,
                "truncated_dump_format", repr(truncated_dump_format),
                type(truncated_dump_format)
            )
        if (truncated_property is not None and
                truncated_property not in ["year_of_decade",
                                           "year_of_century"]):
            raise BadInputError(
                BadInputError.VALUES, "truncated_property",
                repr(truncated_property),
                "'year_of_decade' or 'year_of_century'")
        self.dump_format = dump_format
        self.expanded_year_digits = _int_caster(expanded_year_digits,
                                                "expanded_year_digits")
        self.truncated = truncated
        self.truncated_dump_format = truncated_dump_format
        self.truncated_property = truncated_property
        self.year = _int_caster(year, "year", allow_none=True)
        self.month_of_year = _int_caster(month_of_year, "year",
                                         allow_none=True)
        self.day_of_year = _int_caster(day_of_year, "day_of_year",
                                       allow_none=True)
        self.day_of_month = _int_caster(day_of_month, "day_of_month",
                                        allow_none=True)
        self.day_of_week = _int_caster(day_of_week, "day_of_week",
                                       allow_none=True)
        self.week_of_year = _int_caster(week_of_year, "week_of_year",
                                        allow_none=True)
        self.hour_of_day = _int_caster(hour_of_day, "hour_of_day",
                                       allow_none=True)
        if hour_of_day_decimal is not None:
            if self.hour_of_day is None:
                raise BadInputError(
                    BadInputError.MISSING, "hour_of_day_decimal",
                    "hour_of_day")
            self.hour_of_day += float(hour_of_day_decimal)
            if minute_of_hour is not None:
                raise BadInputError(
                    BadInputError.CONFLICT, "minute_of_hour",
                    "hour_of_day_decimal")
            if second_of_minute is not None:
                raise BadInputError(
                    BadInputError.CONFLICT, "second_of_minute",
                    "hour_of_day_decimal")
        if minute_of_hour_decimal is not None:
            if minute_of_hour is None:
                raise BadInputError(
                    BadInputError.MISSING, "minute_of_hour_decimal",
                    "minute_of_hour")
            self.minute_of_hour = _int_caster(
                minute_of_hour, "minute_of_hour")
            self.minute_of_hour += float(minute_of_hour_decimal)
            if second_of_minute is not None:
                raise BadInputError(
                    BadInputError.CONFLICT, "second_of_minute",
                    "minute_of_hour_decimal")
        else:
            self.minute_of_hour = _int_caster(
                minute_of_hour, "minute_of_hour", allow_none=True)
        if second_of_minute_decimal is not None:
            if second_of_minute is None:
                raise BadInputError(
                    BadInputError.MISSING,
                    "second_of_minute_decimal",
                    "second_of_minute")
            self.second_of_minute = _int_caster(second_of_minute,
                                                "second_of_minute")
            self.second_of_minute += float(second_of_minute_decimal)
        else:
            self.second_of_minute = _int_caster(second_of_minute,
                                                "second_of_minute",
                                                allow_none=True)
        if not self.truncated:
            if self.hour_of_day is None:
                self.hour_of_day = 0
            if hour_of_day_decimal is None and self.minute_of_hour is None:
                self.minute_of_hour = 0
            if (hour_of_day_decimal is None and
                    minute_of_hour_decimal is None and
                    self.second_of_minute is None):
                self.second_of_minute = 0
        self.time_zone = TimeZone()
        has_unknown_tz = True
        if time_zone_hour is not None:
            has_unknown_tz = False
            self.time_zone.hours = _int_caster(time_zone_hour,
                                               "time_zone_hour")
        if time_zone_minute is not None:
            has_unknown_tz = False
            self.time_zone.minutes = _int_caster(time_zone_minute,
                                                 "time_zone_minute")
        self.time_zone.unknown = self.truncated and has_unknown_tz
        if not self.truncated:
            # Reduced precision date - e.g. 1970 - assume Jan 1, etc.
            if (self.month_of_year is None and self.week_of_year is None and
                    self.day_of_year is None):
                self.month_of_year = 1
            if self.month_of_year is not None and self.day_of_month is None:
                self.day_of_month = 1
            if self.week_of_year is not None and self.day_of_week is None:
                self.day_of_week = 1

    def get_is_calendar_date(self):
        """Return whether this is in years, month-of-year, day-of-month."""
        return self.month_of_year is not None

    def get_is_ordinal_date(self):
        """Return whether this is in years, day-of-the year format."""
        return self.day_of_year is not None

    def get_is_week_date(self):
        """Return whether this is in years, week-of-year, day-of-week."""
        return self.week_of_year is not None

    def get_calendar_date(self):
        """Return the year, month-of-year and day-of-month for this date."""
        if self.get_is_calendar_date():
            return self.year, self.month_of_year, self.day_of_month
        if self.get_is_ordinal_date():
            return get_calendar_date_from_ordinal_date(self.year,
                                                       self.day_of_year)
        if self.get_is_week_date():
            return get_calendar_date_from_week_date(self.year,
                                                    self.week_of_year,
                                                    self.day_of_week)

    def get_hour_minute_second(self):
        """Return the time of day expressed in hours, minutes, seconds."""
        hour_of_day = self.hour_of_day
        minute_of_hour = self.minute_of_hour
        second_of_minute = self.second_of_minute
        if second_of_minute is None:
            if minute_of_hour is None:
                hour_decimals = hour_of_day - int(hour_of_day)
                hour_of_day = float(int(hour_of_day))
                minute_of_hour = CALENDAR.MINUTES_IN_HOUR * hour_decimals
            minute_decimals = minute_of_hour - int(minute_of_hour)
            minute_of_hour = float(int(minute_of_hour))
            second_of_minute = CALENDAR.SECONDS_IN_MINUTE * minute_decimals
        return hour_of_day, minute_of_hour, second_of_minute

    def get_ordinal_date(self):
        """Return the year, day-of-year for this date."""
        if self.get_is_calendar_date():
            return get_ordinal_date_from_calendar_date(self.year,
                                                       self.month_of_year,
                                                       self.day_of_month)
        if self.get_is_ordinal_date():
            return self.year, self.day_of_year
        if self.get_is_week_date():
            return get_ordinal_date_from_week_date(self.year,
                                                   self.week_of_year,
                                                   self.day_of_week)

    def get(self, property_name):
        """Return a calculated value for property name."""
        if property_name == "expanded_year_digits":
            return abs(self.year) / 10000
        if property_name == "year_sign":
            return "+" if self.year >= 0 else "-"
        if property_name == "century":
            return (abs(self.year) % 10000) // 100
        if property_name == "year_of_century":
            return abs(self.year) % 100
        if property_name == "month_of_year":
            if self.month_of_year is not None:
                return self.month_of_year
            return self.get_calendar_date()[1]
        if property_name == "day_of_year":
            if self.day_of_year is not None:
                return self.day_of_year
            return self.get_ordinal_date()[1]
        if property_name == "day_of_month":
            if self.day_of_month is not None:
                return self.day_of_month
            return self.get_calendar_date()[2]
        if property_name == "week_of_year":
            if self.week_of_year is not None:
                return self.week_of_year
            return self.get_week_date()[1]
        if property_name == "day_of_week":
            if self.day_of_week is not None:
                return self.day_of_week
            return self.get_week_date()[2]
        if property_name == "year_of_decade":
            return abs(self.year) % 10
        if property_name == "minute_of_hour":
            if self.minute_of_hour is None:
                return self.get_hour_minute_second()[1]
            return int(self.minute_of_hour)
        if property_name == "hour_of_day":
            return int(self.hour_of_day)
        if property_name == "hour_of_day_decimal_string":
            string = "%f" % (float(self.hour_of_day) - int(self.hour_of_day))
            string = string.replace("0.", "", 1).rstrip("0")
            if not string:
                return "0"
            return string
        if property_name == "minute_of_hour_decimal_string":
            string = "%f" % (float(self.minute_of_hour) -
                             int(self.minute_of_hour))
            string = string.replace("0.", "", 1).rstrip("0")
            if not string:
                return "0"
            return string
        if property_name == "second_of_minute":
            if self.second_of_minute is None:
                return self.get_hour_minute_second()[2]
            return int(self.second_of_minute)
        if property_name == "second_of_minute_decimal_string":
            string = "%f" % (float(self.second_of_minute) -
                             int(self.second_of_minute))
            string = string.replace("0.", "", 1).rstrip("0")
            if not string:
                return "0"
            return string
        if property_name == "time_zone_minute_abs":
            return abs(self.time_zone.minutes)
        if property_name == "time_zone_hour_abs":
            return abs(self.time_zone.hours)
        if property_name == "time_zone_sign":
            if self.time_zone.hours < 0 or self.time_zone.minutes < 0:
                return "-"
            return "+"
        if property_name == "seconds_since_unix_epoch":
            reference_timepoint = TimePoint(
                **CALENDAR.UNIX_EPOCH_DATE_TIME_REFERENCE_PROPERTIES)
            days, seconds = (
                self - reference_timepoint).get_days_and_seconds()
            # N.B. This needs altering if we implement leap seconds.
            return str(int(CALENDAR.SECONDS_IN_DAY * days + seconds))
        raise NotImplementedError(property_name)

    def get_second_of_day(self):
        """Return the seconds elapsed since the start of the day."""
        second_of_day = 0
        if self.second_of_minute is not None:
            second_of_day += self.second_of_minute
        if self.minute_of_hour is not None:
            second_of_day += self.minute_of_hour * CALENDAR.SECONDS_IN_MINUTE
        second_of_day += self.hour_of_day * CALENDAR.SECONDS_IN_HOUR
        return second_of_day

    def get_time_zone(self):
        """Return the time_zone offset from UTC as a duration."""
        return self.time_zone

    def get_time_zone_utc(self):
        """Return whether the time zone is explicitly in UTC."""
        if self.time_zone.unknown:
            return False
        return self.time_zone.hours == 0 and self.time_zone.minutes == 0

    def get_week_date(self):
        """Return the year, week-of-year, day-of-week for this date."""
        if self.get_is_calendar_date():
            return get_week_date_from_calendar_date(self.year,
                                                    self.month_of_year,
                                                    self.day_of_month)
        if self.get_is_ordinal_date():
            return get_week_date_from_ordinal_date(self.year,
                                                   self.day_of_year)
        if self.get_is_week_date():
            return self.year, self.week_of_year, self.day_of_week

    def apply_time_zone_offset(self, offset):
        """Apply a time zone shift represented by a Duration."""
        if offset.minutes:
            if self.minute_of_hour is None:
                self.hour_of_day += (
                    offset.minutes / float(CALENDAR.MINUTES_IN_HOUR))
            else:
                self.minute_of_hour += offset.minutes
            self._tick_over()
        if offset.hours:
            self.hour_of_day += offset.hours
            self._tick_over()

    def get_time_zone_offset(self, other):
        """Get the difference in hours and minutes between time zones."""
        if other.get_time_zone().unknown or self.get_time_zone().unknown:
            return Duration()
        return other.get_time_zone() - self.get_time_zone()

    def set_time_zone(self, dest_time_zone):
        """Adjust to the new time zone.

        dest_time_zone should be a TimeZone instance expressing difference
        from UTC, if any.

        """
        if dest_time_zone.unknown:
            return
        self.apply_time_zone_offset(dest_time_zone - self.get_time_zone())
        self.time_zone = dest_time_zone

    def set_time_zone_to_local(self):
        """Set the time zone to the local time zone, if it's not already."""
        local_hours, local_minutes = timezone.get_local_time_zone()
        self.set_time_zone(TimeZone(hours=local_hours, minutes=local_minutes))

    def set_time_zone_to_utc(self):
        """Set the time zone to UTC, if it's not already."""
        self.set_time_zone(TimeZone(hours=0, minutes=0))

    def to_calendar_date(self):
        """Reformat the date in years, month-of-year, day-of-month."""
        year, month, day = self.get_calendar_date()
        self.year, self.month_of_year, self.day_of_month = year, month, day
        self.day_of_year = None
        self.week_of_year = None
        self.day_of_week = None
        return self

    def to_hour_minute_second(self):
        """Expand time fractions into hours, minutes, seconds."""
        hour, minute, second = self.get_hour_minute_second()
        self.hour_of_day = hour
        self.minute_of_hour = minute
        self.second_of_minute = second

    def to_week_date(self):
        """Reformat the date in years, week-of-year, day-of-week."""
        self.year, self.week_of_year, self.day_of_week = self.get_week_date()
        self.day_of_year = None
        self.month_of_year = None
        self.day_of_month = None
        return self

    def to_ordinal_date(self):
        """Reformat the date in years and day-of-the-year."""
        self.year, self.day_of_year = self.get_ordinal_date()
        self.month_of_year = None
        self.day_of_month = None
        self.week_of_year = None
        self.day_of_week = None
        return self

    def get_largest_truncated_property_name(self):
        """Return the largest unit in a truncated representation."""
        if not self.truncated:
            return None
        prop_dict = self.get_truncated_properties()
        for attr in ["year_of_century", "year_of_decade", "month_of_year",
                     "week_of_year", "day_of_year", "day_of_month",
                     "day_of_week", "hour_of_day", "minute_of_hour",
                     "second_of_minute"]:
            if attr in prop_dict:
                return attr
        return None

    def get_truncated_properties(self):
        """Return a map of properties if this is a truncated representation."""
        if not self.truncated:
            return None
        props = {}
        if self.truncated_property == "year_of_decade":
            props.update({"year_of_decade": self.year % 10})
        if self.truncated_property == "year_of_century":
            props.update({"year_of_century": self.year % 100})
        for attr in ["month_of_year", "week_of_year", "day_of_year",
                     "day_of_month", "day_of_week", "hour_of_day",
                     "minute_of_hour", "second_of_minute"]:
            value = getattr(self, attr)
            if value is not None:
                props.update({attr: value})
        return props

    def add_truncated(self, year_of_century=None, year_of_decade=None,
                      month_of_year=None, week_of_year=None, day_of_year=None,
                      day_of_month=None, day_of_week=None, hour_of_day=None,
                      minute_of_hour=None, second_of_minute=None):
        """Combine this TimePoint with truncated time properties."""
        new = self.copy()
        if hour_of_day is not None and minute_of_hour is None:
            minute_of_hour = 0
        if ((hour_of_day is not None or minute_of_hour is not None) and
                second_of_minute is None):
            second_of_minute = 0
        if second_of_minute is not None or minute_of_hour is not None:
            new.to_hour_minute_second()
        if second_of_minute is not None:
            while new.second_of_minute != second_of_minute:
                new.second_of_minute += 1.0
                new._tick_over()
        if minute_of_hour is not None:
            while new.minute_of_hour != minute_of_hour:
                new.minute_of_hour += 1.0
                new._tick_over()
        if hour_of_day is not None:
            while new.hour_of_day != hour_of_day:
                new.hour_of_day += 1.0
                new._tick_over()
        if day_of_week is not None:
            new.to_week_date()
            while new.day_of_week != day_of_week:
                new.day_of_week += 1
                new._tick_over()
        if day_of_month is not None:
            new.to_calendar_date()
            while new.day_of_month != day_of_month:
                new.day_of_month += 1
                new._tick_over()
        if day_of_year is not None:
            new.to_ordinal_date()
            while new.day_of_year != day_of_year:
                new.day_of_year += 1
                new._tick_over()
        if week_of_year is not None:
            new.to_week_date()
            while new.week_of_year != week_of_year:
                new.week_of_year += 1
                new._tick_over()
        if month_of_year is not None:
            new.to_calendar_date()
            while new.month_of_year != month_of_year:
                new.month_of_year += 1
                new._tick_over()
        if year_of_decade is not None:
            new.to_calendar_date()
            new_year_of_decade = new.year % 10
            while new_year_of_decade != year_of_decade:
                new.year += 1
                new_year_of_decade = new.year % 10
        if year_of_century is not None:
            new.to_calendar_date()
            new_year_of_century = new.year % 100
            while new_year_of_century != year_of_century:
                new.year += 1
                new_year_of_century = new.year % 100
        return new

    def __add__(self, other, no_copy=False):
        if isinstance(other, TimePoint):
            if self.truncated and not other.truncated:
                new = self.copy()
                new_other = other.copy()
                prev_time_zone = new_other.get_time_zone()
                new_other.set_time_zone(new.get_time_zone())
                new_other = new_other.add_truncated(
                    **new.get_truncated_properties())
                new_other.set_time_zone(prev_time_zone)
                return new_other
            if other.truncated and not self.truncated:
                return other + self
        if not isinstance(other, Duration):
            raise TypeError(
                "Invalid addition: can only add Duration or "
                "truncated TimePoint to TimePoint.")
        duration = other
        if duration.get_is_in_weeks():
            duration = other.copy()
            duration.to_days()
        if no_copy:
            new = self
        else:
            new = self.copy()
        if duration.seconds:
            if new.second_of_minute is None:
                if new.minute_of_hour is None:
                    new.hour_of_day += (
                        duration.seconds / float(CALENDAR.SECONDS_IN_HOUR))
                else:
                    new.minute_of_hour += (
                        duration.seconds / float(CALENDAR.SECONDS_IN_MINUTE))
            else:
                new.second_of_minute += duration.seconds
            new._tick_over()
        if duration.minutes:
            if new.minute_of_hour is None:
                new.hour_of_day += (
                    duration.minutes / float(CALENDAR.MINUTES_IN_HOUR))
            else:
                new.minute_of_hour += duration.minutes
            new._tick_over()
        if duration.hours:
            new.hour_of_day += duration.hours
            new._tick_over()
        if duration.days:
            if new.get_is_calendar_date():
                new.day_of_month += duration.days
            elif new.get_is_ordinal_date():
                new.day_of_year += duration.days
            else:
                new.day_of_week += duration.days
            new._tick_over()
        if duration.months:
            # This is the dangerous one...
            new._add_months(duration.months)
        if duration.years:
            new.year += duration.years
            if new.get_is_calendar_date():
                month_index = (
                    (new.month_of_year - 1) % CALENDAR.MONTHS_IN_YEAR)
                if get_is_leap_year(new.year):
                    max_day_in_new_month = (
                        CALENDAR.DAYS_IN_MONTHS_LEAP[month_index])
                else:
                    max_day_in_new_month = (
                        CALENDAR.DAYS_IN_MONTHS[month_index])
                if new.day_of_month > max_day_in_new_month:
                    # For example, when Feb 29 - 1 year = Feb 28.
                    new.day_of_month = max_day_in_new_month
            elif new.get_is_ordinal_date():
                max_days_in_year = get_days_in_year(new.year)
                if max_days_in_year > new.day_of_year:
                    new.day_of_year = max_days_in_year
            elif new.get_is_week_date():
                max_weeks_in_year = get_weeks_in_year(new.year)
                if max_weeks_in_year > new.week_of_year:
                    new.week_of_year = max_weeks_in_year
        return new

    def copy(self):
        """Copy this TimePoint without leaving references."""
        dummy_timepoint = TimePoint(is_empty_instance=True)
        for attr in self.DATA_ATTRIBUTES:
            setattr(dummy_timepoint, attr, getattr(self, attr))
        dummy_timepoint.time_zone = self.time_zone.copy()
        return dummy_timepoint

    def get_props(self):
        """Return the data properties of this TimePoint."""
        hash_ = []
        for attr in self.DATA_ATTRIBUTES:
            value = getattr(self, attr, None)
            if callable(getattr(value, "copy", None)):
                value = value.copy()
            hash_.append((attr, value))
        return hash_

    def __cmp__(self, other):
        if not isinstance(other, TimePoint):
            raise TypeError(
                "Invalid comparison type '%s' - should be TimePoint." %
                type(other).__name__
            )
        if self.truncated != other.truncated:
            raise TypeError(
                "Cannot compare truncated to non-truncated " +
                "TimePoint: %s, %s" % (self, other))
        if self.get_props() == other.get_props():
            return 0
        if self.truncated:
            for attribute in self.DATA_ATTRIBUTES:
                other_attr = getattr(other, attribute)
                self_attr = getattr(self, attribute)
                if other_attr != self_attr:
                    return cmp(self_attr, other_attr)
            return 0
        other = other.copy()
        other.set_time_zone(self.get_time_zone())
        if self.get_is_calendar_date():
            my_date = self.get_calendar_date()
            other_date = other.get_calendar_date()
        else:
            my_date = self.get_ordinal_date()
            other_date = other.get_ordinal_date()
        my_datetime = list(my_date) + [self.get_second_of_day()]
        other_datetime = list(other_date) + [other.get_second_of_day()]
        return cmp(my_datetime, other_datetime)

    def __sub__(self, other):
        if isinstance(other, TimePoint):
            other = other.copy()
            other.set_time_zone(self.get_time_zone())
            my_year, my_day_of_year = self.get_ordinal_date()
            other_year, other_day_of_year = other.get_ordinal_date()
            diff_year = my_year - other_year
            diff_day = my_day_of_year - other_day_of_year
            if my_year > other_year:
                diff_day += get_days_in_year_range(other_year, my_year - 1)
            else:
                diff_day -= get_days_in_year_range(my_year, other_year - 1)
            if diff_day < 0:
                return -1 * (other - self)
            my_hour, my_minute, my_second = self.get_hour_minute_second()
            other_hour, other_minute, other_second = (
                other.get_hour_minute_second())
            diff_hour = my_hour - other_hour
            diff_minute = my_minute - other_minute
            diff_second = my_second - other_second
            if diff_second < 0:
                diff_minute -= 1
                diff_second += CALENDAR.SECONDS_IN_MINUTE
            if diff_minute < 0:
                diff_hour -= 1
                diff_minute += CALENDAR.MINUTES_IN_HOUR
            if diff_hour < 0:
                diff_day -= 1
                diff_hour += CALENDAR.HOURS_IN_DAY
            return Duration(
                days=diff_day, hours=diff_hour, minutes=diff_minute,
                seconds=diff_second)
        if not isinstance(other, Duration):
            raise TypeError(
                "Invalid subtraction type " +
                "'%s' - should be Duration." %
                type(other).__name__
            )
        duration = other
        return self.__add__(duration * -1)

    def _add_months(self, num_months):
        """Add an amount of months to the representation."""
        if num_months == 0:
            return
        was_ordinal_date = False
        was_week_date = False
        if not self.get_is_calendar_date():
            if self.get_is_ordinal_date():
                was_ordinal_date = True
            if self.get_is_week_date():
                was_week_date = True
            self.to_calendar_date()
        for i in range(abs(num_months)):
            if num_months > 0:
                self.month_of_year += 1
                if self.month_of_year > CALENDAR.MONTHS_IN_YEAR:
                    self.month_of_year -= CALENDAR.MONTHS_IN_YEAR
                    self.year += 1
            if num_months < 0:
                self.month_of_year -= 1
                if self.month_of_year < 1:
                    self.month_of_year += CALENDAR.MONTHS_IN_YEAR
                    self.year -= 1
            month_index = (self.month_of_year - 1) % CALENDAR.MONTHS_IN_YEAR
            if get_is_leap_year(self.year):
                max_day_in_new_month = (
                    CALENDAR.DAYS_IN_MONTHS_LEAP[month_index])
            else:
                max_day_in_new_month = (
                    CALENDAR.DAYS_IN_MONTHS[month_index])
            if self.day_of_month > max_day_in_new_month:
                # For example, when 31 March + 1 month = 30 April.
                self.day_of_month = max_day_in_new_month
        self._tick_over()
        if was_ordinal_date:
            self.to_ordinal_date()
        if was_week_date:
            self.to_week_date()

    def _tick_over(self):
        """Correct all the units going from smallest to largest."""
        if (self.hour_of_day is not None and
                self.minute_of_hour is not None):
            hours_remainder = self.hour_of_day - int(self.hour_of_day)
            self.hour_of_day -= hours_remainder
            self.minute_of_hour += (
                hours_remainder * CALENDAR.MINUTES_IN_HOUR)
        if (self.minute_of_hour is not None and
                self.second_of_minute is not None):
            minutes_remainder = self.minute_of_hour - int(self.minute_of_hour)
            self.minute_of_hour -= minutes_remainder
            self.second_of_minute += (
                minutes_remainder * CALENDAR.SECONDS_IN_MINUTE)
        if self.second_of_minute is not None:
            num_minutes, seconds = divmod(self.second_of_minute,
                                          CALENDAR.SECONDS_IN_MINUTE)
            self.minute_of_hour += num_minutes
            self.second_of_minute = seconds
        if self.minute_of_hour is not None:
            num_hours, minutes = divmod(self.minute_of_hour,
                                        CALENDAR.MINUTES_IN_HOUR)
            self.hour_of_day += num_hours
            self.minute_of_hour = minutes
        if self.hour_of_day is not None:
            num_days, hours = divmod(self.hour_of_day, CALENDAR.HOURS_IN_DAY)
            num_days = int(num_days)
            if self.day_of_week is not None:
                self.day_of_week += num_days
            elif self.day_of_month is not None:
                self.day_of_month += num_days
            elif self.day_of_year is not None:
                self.day_of_year += num_days
            self.hour_of_day = hours
        if self.day_of_week is not None:
            num_weeks, days = divmod(
                self.day_of_week - 1, CALENDAR.DAYS_IN_WEEK)
            self.week_of_year += num_weeks
            self.day_of_week = days + 1
        if self.day_of_month is not None:
            self._tick_over_day_of_month()
        if self.day_of_year is not None:
            while self.day_of_year < 1:
                days_in_last_year = get_days_in_year(self.year - 1)
                self.day_of_year += days_in_last_year
                self.year -= 1
            while self.day_of_year > get_days_in_year(self.year):
                days_in_next_year = get_days_in_year(self.year + 1)
                self.day_of_year -= days_in_next_year
                self.year += 1
        if self.week_of_year is not None:
            while self.week_of_year < 1:
                weeks_in_last_year = get_weeks_in_year(self.year - 1)
                self.week_of_year += weeks_in_last_year
                self.year -= 1
            while self.week_of_year > get_weeks_in_year(self.year):
                weeks_in_this_year = get_weeks_in_year(self.year)
                self.week_of_year -= weeks_in_this_year
                self.year += 1
        if self.month_of_year is not None:
            while self.month_of_year < 1:
                self.month_of_year += CALENDAR.MONTHS_IN_YEAR
                self.year -= 1
            while self.month_of_year > CALENDAR.MONTHS_IN_YEAR:
                self.month_of_year -= CALENDAR.MONTHS_IN_YEAR
                self.year += 1

    def _tick_over_day_of_month(self):
        if self.day_of_month < 1:
            num_days = 2
            for month, day in iter_months_days(
                    self.year,
                    month_of_year=self.month_of_year,
                    day_of_month=1, in_reverse=True):
                num_days -= 1
                if num_days == self.day_of_month:
                    self.month_of_year = month
                    self.day_of_month = day
                    break
            else:
                start_year = self.year
                while num_days != self.day_of_month:
                    start_year -= 1
                    for month, day in iter_months_days(
                            start_year, in_reverse=True):
                        num_days -= 1
                        if num_days == self.day_of_month:
                            break
                self.year = start_year
                self.month_of_year = month
                self.day_of_month = day
        else:
            month_index = (self.month_of_year - 1) % CALENDAR.MONTHS_IN_YEAR
            if get_is_leap_year(self.year):
                max_day_in_month = CALENDAR.DAYS_IN_MONTHS_LEAP[month_index]
            else:
                max_day_in_month = CALENDAR.DAYS_IN_MONTHS[month_index]
            if self.day_of_month > max_day_in_month:
                num_days = 0
                for month, day in iter_months_days(
                        self.year,
                        month_of_year=self.month_of_year,
                        day_of_month=1):
                    num_days += 1
                    if num_days == self.day_of_month:
                        self.month_of_year = month
                        self.day_of_month = day
                        break
                else:
                    start_year = self.year
                    while num_days != self.day_of_month:
                        start_year += 1
                        for month, day in iter_months_days(start_year):
                            num_days += 1
                            if num_days == self.day_of_month:
                                self.year = start_year
                                self.month_of_year = month
                                self.day_of_month = day
                                return

    def __str__(self, override_custom_dump_format=False,
                strftime_format=None):
        if self.expanded_year_digits not in TIMEPOINT_DUMPER_MAP:
            TIMEPOINT_DUMPER_MAP[self.expanded_year_digits] = (
                dumpers.TimePointDumper(
                    self.expanded_year_digits))
        dumper = TIMEPOINT_DUMPER_MAP[self.expanded_year_digits]
        if strftime_format is not None:
            return dumper.strftime(self, strftime_format)
        if self.truncated:
            if self.truncated_dump_format and not override_custom_dump_format:
                return dumper.dump(self, self.truncated_dump_format)
            return dumper.dump(self, self._get_truncated_dump_format())
        if self.dump_format and not override_custom_dump_format:
            return dumper.dump(self, self.dump_format)
        return dumper.dump(self, self._get_dump_format())

    def strftime(self, strftime_format):
        """Implement equivalent of Python 2's datetime.datetime.strftime.

        Dump based on the format given in the strftime_format string.

        """
        return self.__str__(strftime_format=strftime_format)

    def _get_dump_format(self):
        year_digits = 4 + self.expanded_year_digits
        year_string = "%0" + str(year_digits) + "d"
        if self.expanded_year_digits:
            if self.year < 0:
                year_string = "-" + year_string % abs(self.year)
            else:
                year_string = "+" + year_string % abs(self.year)
        elif self.year is not None and self.year < 0:
            raise OverflowError(
                "Year %s can only be represented in expanded format" %
                self.year
            )
        elif self.year is not None:
            year_string = year_string % self.year

        if self.get_is_calendar_date():
            date_string = year_string + "-MM-DD"
        if self.get_is_ordinal_date():
            date_string = year_string + "-DDD"
        if self.get_is_week_date():
            date_string = year_string + "-Www-D"
        time_string = "Thh"
        if self.minute_of_hour is None:
            time_string += ",ii"
        else:
            time_string += ":mm"
            if self.second_of_minute is None:
                time_string += ",nn"
            else:
                seconds_int = int(self.second_of_minute)
                time_string += ":ss"
                if seconds_int != self.second_of_minute:
                    time_string += ",tt"
        if time_string:
            if self.time_zone.hours == 0 and self.time_zone.minutes == 0:
                time_string += "Z"
            else:
                time_string += u"+hh:mm"
        return date_string + time_string

    def _get_truncated_dump_format(self):
        year_string = "-"
        if self.truncated_property == "year_of_decade":
            year_string = "-" + "z"
        elif self.truncated_property == "year_of_century":
            if self.day_of_month is None and self.month_of_year is not None:
                year_string = "-YY"
            else:
                year_string = "YY"
        date_string = year_string
        if self.month_of_year is not None:
            date_string = year_string + "-MM"
            if self.day_of_month is not None:
                date_string += "-DD"
        elif self.day_of_month is not None:
            if year_string == "-":
                date_string = year_string + "--DD"
            else:
                date_string = year_string + "-DD"
        if self.day_of_year is not None:
            day_string = "DDD"
            if year_string == "-":
                date_string = year_string + day_string
            else:
                date_string = year_string + "-" + day_string
        if self.week_of_year is not None:
            if year_string == "-":
                date_string = year_string + "Www"
            else:
                date_string = year_string + "-Www"
            if self.day_of_week is not None:
                date_string += "-D"
        elif self.day_of_week is not None:
            if year_string == "-":
                date_string = year_string + "W-D"
            else:
                date_string = year_string + "-W-D"
        time_string = ""
        if (self.hour_of_day is None and
                (self.minute_of_hour is not None or
                 self.second_of_minute is not None)):
            time_string = "T-"
        elif (self.hour_of_day is not None and
                int(self.hour_of_day) != self.hour_of_day):
            time_string = "Thh,ii"
        elif self.hour_of_day is not None:
            time_string = "Thh"
        if self.minute_of_hour is None and self.second_of_minute is not None:
            time_string += "-"
        elif (self.minute_of_hour is not None and
                int(self.minute_of_hour) != self.minute_of_hour):
            if self.hour_of_day is not None:
                time_string += ":"
            time_string += "mm,nn"
        elif self.minute_of_hour is not None:
            if self.hour_of_day is not None:
                time_string += ":"
            time_string += "mm"
        if self.second_of_minute is not None:
            seconds_int = int(self.second_of_minute)
            if self.minute_of_hour is not None:
                time_string += ":"
            time_string += "ss"
            if seconds_int != self.second_of_minute:
                time_string += ",tt"
        if time_string:
            if self.time_zone.hours == 0 and self.time_zone.minutes == 0:
                time_string += "Z"
            else:
                time_string += u"+hh:mm"
        if date_string == "YY":
            date_string = "-YY"
            time_string = time_string.replace(":", "")
        if date_string == "-":
            date_string = ""
        return date_string + time_string

    __repr__ = __str__


def _format_remainder(float_time_number):
    """Format a floating point remainder of a time unit."""
    string = "," + ("%f" % float_time_number)[2:].rstrip("0")
    if string == ",":
        return ""
    return string


@util.cache_results
def get_is_leap_year(year):
    """Return if year is a leap year."""
    year_is_leap = False
    for factor, is_leap_factor in CALENDAR.LEAP_YEAR_FACTOR_TRUTHS:
        if year % factor == 0:
            year_is_leap = is_leap_factor
    return year_is_leap


def get_days_in_year_range(start_year, end_year):
    """Return the number of days within this year range (inclusive)."""
    return _get_days_in_year_range(start_year, end_year,
                                   calendar_mode=CALENDAR.mode)


@util.cache_results
def _get_days_in_year_range(start_year, end_year, calendar_mode=None):
    """Return the number of days within this year range (inclusive).

    If end_year > start_year, return the days in start_year plus
    the days in the intervening years before end_year, plus the
    days in end_year.

    If end_year == start_year, return the days in start_year.

    If end_year < start_year, return 0.

    """
    # Get the number of days discounting leap years.
    if start_year == end_year:
        return get_days_in_year(start_year)
    if start_year > end_year:
        return 0
    days = (end_year + 1 - start_year) * CALENDAR.DAYS_IN_YEAR
    diff_days_leap = (CALENDAR.DAYS_IN_YEAR_LEAP - CALENDAR.DAYS_IN_YEAR)
    for factor, is_leap_factor in CALENDAR.LEAP_YEAR_FACTOR_TRUTHS:
        num_corrections = 0
        if start_year % factor == 0:
            num_corrections += 1
        if end_year != start_year and end_year % factor == 0:
            num_corrections += 1
        factor_start_year = start_year + 1
        while (factor_start_year % factor != 0 and
               factor_start_year < end_year):
            factor_start_year += 1
        if factor_start_year < end_year:
            num_corrections += 1
            num_corrections += (
                end_year - (factor_start_year + 1)) / factor
        if is_leap_factor:
            days += num_corrections * diff_days_leap
        else:
            days -= num_corrections * diff_days_leap
    return days


def get_days_in_year(year):
    """Return the number of days in this particular year."""
    return _get_days_in_year(year, calendar_mode=CALENDAR.mode)


@util.cache_results
def _get_days_in_year(year, calendar_mode=None):
    """Return the number of days in this particular year."""
    if get_is_leap_year(year):
        return CALENDAR.DAYS_IN_YEAR_LEAP
    return CALENDAR.DAYS_IN_YEAR


def get_weeks_in_year(year):
    """Return the number of calendar weeks in this week date year."""
    return _get_weeks_in_year(year, calendar_mode=CALENDAR.mode)


@util.cache_results
def _get_weeks_in_year(year, calendar_mode=None):
    """Return the number of calendar weeks in this week date year."""
    cal_year, cal_ord_days = get_ordinal_date_week_date_start(year)
    cal_year_next, cal_ord_days_next = get_ordinal_date_week_date_start(
        year + 1)
    diff_days = cal_ord_days_next - cal_ord_days
    for intervening_year in xrange(cal_year, cal_year_next):
        diff_days += get_days_in_year(intervening_year)
    return diff_days / CALENDAR.DAYS_IN_WEEK


def get_calendar_date_from_ordinal_date(year, day_of_year):
    """Translate an ordinal date into a calendar date.

    Returns the calendar year, calendar month, calendar day-of-month.

    Arguments:
    year is an integer that denotes the ordinal date year
    day_of_year is an integer that denotes the ordinal day in the year.

    """
    iter_num_days = 0
    for iter_month, iter_day in iter_months_days(year):
        iter_num_days += 1
        if iter_num_days == day_of_year:
            return year, iter_month, iter_day
    raise ValueError("Bad ordinal date: %s-%03d" % (year, day_of_year))


def get_calendar_date_from_week_date(year, week_of_year, day_of_week):
    """Translate a week date into a calendar date.

    Returns the calendar year, calendar month, calendar day-of-month.

    Arguments:
    year is an integer that denotes the week date year (may differ
    from calendar year)
    week_of_year is an integer that denotes the week number in the year
    day_of_week is an integer that denotes the day of the week (1-7).

    """
    num_days_week_year = (
        (week_of_year - 1) * CALENDAR.DAYS_IN_WEEK + day_of_week - 1)
    start_year, start_month, start_day = (
        get_calendar_date_week_date_start(year))
    if num_days_week_year == 0:
        return start_year, start_month, start_day
    total_iter_days = 0
    # Loop over the months and days left in the start year.
    for iter_month, iter_day in iter_months_days(
            start_year, month_of_year=start_month,
            day_of_month=start_day + 1):
        total_iter_days += 1
        if num_days_week_year == total_iter_days:
            return start_year, iter_month, iter_day
    if start_year < year:
        # We've only looped over the last year - now the current one.
        for iter_month, iter_day in iter_months_days(year):
            total_iter_days += 1
            if num_days_week_year == total_iter_days:
                return year, iter_month, iter_day
    for iter_month, iter_day in iter_months_days(year + 1):
        # Loop over the following year.
        total_iter_days += 1
        if num_days_week_year == total_iter_days:
            return year + 1, iter_month, iter_day
    raise ValueError("Bad week date: %s-W%02d-%s" % (year,
                                                     week_of_year,
                                                     day_of_week))


def get_ordinal_date_from_calendar_date(year, month_of_year, day_of_month):
    """Translate a calendar date into an ordinal date.

    Returns the ordinal year, calendar month, calendar day-of-month.

    Arguments:
    year is an integer that denotes the year
    month_of_year is an integer that denotes the month number in the
    year.
    day_of_month is an integer that denotes the day number in the
    month_of_year.

    """
    iter_num_days = 0
    for iter_month, iter_day in iter_months_days(year):
        iter_num_days += 1
        if iter_month == month_of_year and iter_day == day_of_month:
            return year, iter_num_days
    raise ValueError("Bad calendar date: %s-%02d-%02d" % (year,
                                                          month_of_year,
                                                          day_of_month))


def get_ordinal_date_from_week_date(year, week_of_year, day_of_week):
    """Translate a week date into an ordinal date.

    Returns the ordinal year, ordinal day-of-year.

    Arguments:
    year is an integer that denotes the week date year (which may
    differ from the ordinal or calendar year)
    week_of_year is an integer that denotes the week number in the
    year.
    day_of_week is an integer that denotes the day number in the
    week_of_year.

    """
    cal_year, cal_month, cal_day_of_month = get_calendar_date_from_week_date(
        year, week_of_year, day_of_week)
    return get_ordinal_date_from_calendar_date(
        cal_year, cal_month, cal_day_of_month)


def get_week_date_from_calendar_date(year, month_of_year, day_of_month):
    """Translate a calendar date into an week date.

    Returns the week date year, week-of-year, day-of-week.

    Arguments:
    year is an integer that denotes the calendar year, which may
    differ from the week date year.
    month_of_year is an integer that denotes the month number in the
    above year.
    day_of_month is an integer that denotes the day number in the
    above month_of_year.

    """
    prev_start = get_calendar_date_week_date_start(year - 1)
    this_start = get_calendar_date_week_date_start(year)
    next_start = get_calendar_date_week_date_start(year + 1)

    cal_date = (year, month_of_year, day_of_month)

    if prev_start <= cal_date < this_start:
        # This calendar date is in the previous week date year.
        start_year, start_month, start_day = prev_start
        week_date_start_year = year - 1
    elif this_start <= cal_date < next_start:
        # This calendar date is in the same week date year.
        start_year, start_month, start_day = this_start
        week_date_start_year = year
    else:
        # This calendar date is in the next week date year.
        start_year, start_month, start_day = next_start
        week_date_start_year = year + 1

    total_iter_days = -1
    # A week date year can theoretically span 3 calendar years...
    for iter_month, iter_day in iter_months_days(start_year,
                                                 month_of_year=start_month,
                                                 day_of_month=start_day):
        total_iter_days += 1
        if (start_year == year and
                iter_month == month_of_year and
                iter_day == day_of_month):
            week_of_year = (total_iter_days / CALENDAR.DAYS_IN_WEEK) + 1
            day_of_week = (total_iter_days % CALENDAR.DAYS_IN_WEEK) + 1
            return week_date_start_year, week_of_year, day_of_week

    for iter_start_year in [start_year + 1, start_year + 2]:
        # Look at following year when the calendar date is e.g. very early Jan.
        for iter_month, iter_day in iter_months_days(iter_start_year):
            total_iter_days += 1
            if (iter_start_year == year and
                    iter_month == month_of_year and
                    iter_day == day_of_month):
                week_of_year = (total_iter_days / CALENDAR.DAYS_IN_WEEK) + 1
                day_of_week = (total_iter_days % CALENDAR.DAYS_IN_WEEK) + 1
                return week_date_start_year, week_of_year, day_of_week
    raise ValueError("Bad calendar date: %s-%02d-%02d" % (year,
                                                          month_of_year,
                                                          day_of_month))


def get_week_date_from_ordinal_date(year, day_of_year):
    """Translate an ordinal date into a week date.

    Returns the week date year, week-of-year, day-of-week.

    Arguments:
    year is an integer that denotes the ordinal date year, which
    may differ from the week date year.
    day_of_year is an integer that denotes the ordinal day in the year.

    """
    year, month, day = get_calendar_date_from_ordinal_date(year, day_of_year)
    return get_week_date_from_calendar_date(year, month, day)


def get_calendar_date_week_date_start(year):
    """Return the calendar date of the start of (week date) year."""
    return _get_calendar_date_week_date_start(
        year, calendar_mode=CALENDAR.mode)


@util.cache_results
def _get_calendar_date_week_date_start(year, calendar_mode=None):
    """Return the calendar date of the start of (week date) year."""
    ref_year, ref_month, ref_day = (
        CALENDAR.WEEK_DAY_START_REFERENCE["calendar"])
    ref_year, ref_ordinal_day = (
        CALENDAR.WEEK_DAY_START_REFERENCE["ordinal"])
    if year == ref_year:
        return ref_year, ref_month, ref_day
    # Calculate the weekday for 1 January in this calendar year.
    days_diff = 0
    if year > ref_year:
        days_diff = 1 - ref_ordinal_day
        days_diff += get_days_in_year_range(ref_year, year - 1)
    elif ref_year > year:
        days_diff = ref_ordinal_day - 2
        days_diff += get_days_in_year_range(year, ref_year - 1)

    weekdays_diff = (days_diff) % CALENDAR.DAYS_IN_WEEK
    if year > ref_year:
        day_of_week_start_year = weekdays_diff + 1
    else:
        # Jan 1 as day of week.
        day_of_week_start_year = CALENDAR.DAYS_IN_WEEK - weekdays_diff
    if day_of_week_start_year == 1:
        return year, 1, 1
    if day_of_week_start_year > 4:
        # This week belongs to the previous year; get the next Monday.
        day = 1 + (8 - day_of_week_start_year)
        return year, 1, day
    # The week starts in the previous year - get the previous Monday.
    for month, day in iter_months_days(year - 1, in_reverse=True):
        day_of_week_start_year -= 1
        if day_of_week_start_year == 1:
            return year - 1, month, day


def get_days_since_1_ad(year):
    """Return the number of days since Jan 1, 1 A.D. to the year end."""
    return _get_days_since_1_ad(year, calendar_mode=CALENDAR.mode)


@util.cache_results
def _get_days_since_1_ad(year, calendar_mode=None):
    """Return the number of days since Jan 1, 1 A.D. to the year end."""
    if year == 1:
        return get_days_in_year(year)
    elif year < 1:
        return 0
    return get_days_in_year_range(1, year)


def get_ordinal_date_week_date_start(year):
    """Return the ordinal week date start for year (year, day-of-year)."""
    return _get_ordinal_date_week_date_start(
        year, calendar_mode=CALENDAR.mode)


@util.cache_results
def _get_ordinal_date_week_date_start(year, calendar_mode=None):
    """Return the ordinal week date start for year (year, day-of-year)."""
    cal_year, cal_month, cal_day = get_calendar_date_week_date_start(year)
    total_days = 0
    for iter_month, iter_day in iter_months_days(cal_year):
        total_days += 1
        if iter_month == cal_month and iter_day == cal_day:
            return cal_year, total_days


def get_timepoint_for_now():
    """Return a TimePoint at the current date/time."""
    import time
    return get_timepoint_from_seconds_since_unix_epoch(time.time())


def get_timepoint_from_seconds_since_unix_epoch(num_seconds):
    """Return a TimePoint at a date/time specified in Unix time.

    Note that Unix time always counts 1 day = 86400 seconds, so if
    we implement leap seconds we need to make the distinction.

    """
    reference_timepoint = TimePoint(
        **CALENDAR.UNIX_EPOCH_DATE_TIME_REFERENCE_PROPERTIES)
    return reference_timepoint + Duration(seconds=float(num_seconds))


def get_timepoint_properties_from_seconds_since_unix_epoch(num_seconds):
    """Translate Unix time into a dict of TimePoint constructor properties."""
    properties = dict(
        get_timepoint_from_seconds_since_unix_epoch(num_seconds).get_props())
    time_zone = properties.pop("time_zone")
    properties["time_zone_hour"] = time_zone.hours
    properties["time_zone_minute"] = time_zone.minutes
    return properties


def iter_months_days(year, month_of_year=None, day_of_month=None,
                     in_reverse=False):
    """Iterate over each day in each month of year.

    year is an integer specifying the year to use.
    month_of_year is an optional integer, specifying a start month.
    day_of_month is an optional integer, specifying a start day.
    in_reverse is an optional boolean that reverses the iteration if
    True (default False).

    """
    is_leap_year = get_is_leap_year(year)
    return _iter_months_days(
        is_leap_year, month_of_year, day_of_month, in_reverse=in_reverse,
        calendar_mode=CALENDAR.mode)


@util.cache_results
def _iter_months_days(is_leap_year, month_of_year, day_of_month,
                      in_reverse=False, calendar_mode=None):
    source = CALENDAR.INDEXED_DAYS_IN_MONTHS
    if is_leap_year:
        source = CALENDAR.INDEXED_DAYS_IN_MONTHS_LEAP
    if day_of_month is not None and month_of_year is None:
        raise ValueError("Need to specify start month as well as day.")
    results = []
    if in_reverse:
        if month_of_year is None:
            for month_num, days in reversed(source):
                day_range = range(days, 0, -1)
                for day in day_range:
                    results.append((month_num, day))
        else:
            for month_num, days in reversed(source):
                if month_num > month_of_year:
                    continue
                elif month_num == month_of_year and day_of_month is not None:
                    day_range = range(day_of_month, 0, -1)
                else:
                    day_range = range(days, 0, -1)
                for day in day_range:
                    results.append((month_num, day))
    else:
        if month_of_year is None:
            for month_num, days in source:
                day_range = range(1, days + 1)
                for day in day_range:
                    results.append((month_num, day))
        else:
            for month_num, days in source[month_of_year - 1:]:
                if month_num == month_of_year and day_of_month is not None:
                    day_range = range(day_of_month, days + 1)
                else:
                    day_range = range(1, days + 1)
                for day in day_range:
                    results.append((month_num, day))
    return results


def _int_caster(number, name="number", allow_none=False):
    if allow_none and number is None:
        return None
    try:
        int_number = int(number)
        float_number = float(number)
    except (TypeError, ValueError) as num_exc:
        raise BadInputError(
            BadInputError.INT_CAST, name, number, num_exc)
    if float(int_number) != float_number:
        raise BadInputError(
            BadInputError.INT_REMAINDER, name, number)
    return int_number


def _type_checker(*objects):
    for type_info in objects:
        value, name = type_info[:2]
        allowed_types = list(type_info[2:])
        none_is_allowed = False
        if None in allowed_types:
            if value is None:
                break
            none_is_allowed = True
            allowed_types.remove(None)
            allowed_types.append(type(None))
        if allowed_types and isinstance(value, allowed_types[0]):
            break
        if int in allowed_types and float not in allowed_types:
            value = _int_caster(value, name=name, allow_none=none_is_allowed)
        if any(isinstance(value, type_) for type_ in allowed_types):
            break
        values_string = ""
        if allowed_types:
            values_string = " should be: "
            values_string += " or ".join(
                [str(v) for v in allowed_types])
        raise BadInputError(
            BadInputError.TYPE, name, repr(value), values_string)


PARSE_PROPERTY_TRANSLATORS = {
    "seconds_since_unix_epoch":
    get_timepoint_properties_from_seconds_since_unix_epoch
}