_pydatetime.py

"""Pure Python implementation of the datetime module."""

__all__ = ("date", "datetime", "time", "timedelta", "timezone", "tzinfo",
           "MINYEAR", "MAXYEAR", "UTC")

__name__ = "datetime"


import time as _time
import math as _math
import sys
from operator import index as _index

def _cmp(x, y):
    return 0 if x == y else 1 if x > y else -1

def _get_class_module(self):
    module_name = self.__class__.__module__
    if module_name == 'datetime':
        return 'datetime.'
    else:
        return ''

MINYEAR = 1
MAXYEAR = 9999
_MAXORDINAL = 3652059  # date.max.toordinal()

# Utility functions, adapted from Python's Demo/classes/Dates.py, which
# also assumes the current Gregorian calendar indefinitely extended in
# both directions.  Difference:  Dates.py calls January 1 of year 0 day
# number 1.  The code here calls January 1 of year 1 day number 1.  This is
# to match the definition of the "proleptic Gregorian" calendar in Dershowitz
# and Reingold's "Calendrical Calculations", where it's the base calendar
# for all computations.  See the book for algorithms for converting between
# proleptic Gregorian ordinals and many other calendar systems.

# -1 is a placeholder for indexing purposes.
_DAYS_IN_MONTH = [-1, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

_DAYS_BEFORE_MONTH = [-1]  # -1 is a placeholder for indexing purposes.
dbm = 0
for dim in _DAYS_IN_MONTH[1:]:
    _DAYS_BEFORE_MONTH.append(dbm)
    dbm += dim
del dbm, dim

def _is_leap(year):
    "year -> 1 if leap year, else 0."
    return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0)

def _days_before_year(year):
    "year -> number of days before January 1st of year."
    y = year - 1
    return y*365 + y//4 - y//100 + y//400

def _days_in_month(year, month):
    "year, month -> number of days in that month in that year."
    assert 1 <= month <= 12, month
    if month == 2 and _is_leap(year):
        return 29
    return _DAYS_IN_MONTH[month]

def _days_before_month(year, month):
    "year, month -> number of days in year preceding first day of month."
    assert 1 <= month <= 12, f"month must be in 1..12, not {month}"
    return _DAYS_BEFORE_MONTH[month] + (month > 2 and _is_leap(year))

def _ymd2ord(year, month, day):
    "year, month, day -> ordinal, considering 01-Jan-0001 as day 1."
    assert 1 <= month <= 12, f"month must be in 1..12, not {month}"
    dim = _days_in_month(year, month)
    assert 1 <= day <= dim, f"day must be in 1..{dim}, not {day}"
    return (_days_before_year(year) +
            _days_before_month(year, month) +
            day)

_DI400Y = _days_before_year(401)    # number of days in 400 years
_DI100Y = _days_before_year(101)    #    "    "   "   " 100   "
_DI4Y   = _days_before_year(5)      #    "    "   "   "   4   "

# A 4-year cycle has an extra leap day over what we'd get from pasting
# together 4 single years.
assert _DI4Y == 4 * 365 + 1

# Similarly, a 400-year cycle has an extra leap day over what we'd get from
# pasting together 4 100-year cycles.
assert _DI400Y == 4 * _DI100Y + 1

# OTOH, a 100-year cycle has one fewer leap day than we'd get from
# pasting together 25 4-year cycles.
assert _DI100Y == 25 * _DI4Y - 1

def _ord2ymd(n):
    "ordinal -> (year, month, day), considering 01-Jan-0001 as day 1."

    # n is a 1-based index, starting at 1-Jan-1.  The pattern of leap years
    # repeats exactly every 400 years.  The basic strategy is to find the
    # closest 400-year boundary at or before n, then work with the offset
    # from that boundary to n.  Life is much clearer if we subtract 1 from
    # n first -- then the values of n at 400-year boundaries are exactly
    # those divisible by _DI400Y:
    #
    #     D  M   Y            n              n-1
    #     -- --- ----        ----------     ----------------
    #     31 Dec -400        -_DI400Y       -_DI400Y -1
    #      1 Jan -399         -_DI400Y +1   -_DI400Y      400-year boundary
    #     ...
    #     30 Dec  000        -1             -2
    #     31 Dec  000         0             -1
    #      1 Jan  001         1              0            400-year boundary
    #      2 Jan  001         2              1
    #      3 Jan  001         3              2
    #     ...
    #     31 Dec  400         _DI400Y        _DI400Y -1
    #      1 Jan  401         _DI400Y +1     _DI400Y      400-year boundary
    n -= 1
    n400, n = divmod(n, _DI400Y)
    year = n400 * 400 + 1   # ..., -399, 1, 401, ...

    # Now n is the (non-negative) offset, in days, from January 1 of year, to
    # the desired date.  Now compute how many 100-year cycles precede n.
    # Note that it's possible for n100 to equal 4!  In that case 4 full
    # 100-year cycles precede the desired day, which implies the desired
    # day is December 31 at the end of a 400-year cycle.
    n100, n = divmod(n, _DI100Y)

    # Now compute how many 4-year cycles precede it.
    n4, n = divmod(n, _DI4Y)

    # And now how many single years.  Again n1 can be 4, and again meaning
    # that the desired day is December 31 at the end of the 4-year cycle.
    n1, n = divmod(n, 365)

    year += n100 * 100 + n4 * 4 + n1
    if n1 == 4 or n100 == 4:
        assert n == 0
        return year-1, 12, 31

    # Now the year is correct, and n is the offset from January 1.  We find
    # the month via an estimate that's either exact or one too large.
    leapyear = n1 == 3 and (n4 != 24 or n100 == 3)
    assert leapyear == _is_leap(year)
    month = (n + 50) >> 5
    preceding = _DAYS_BEFORE_MONTH[month] + (month > 2 and leapyear)
    if preceding > n:  # estimate is too large
        month -= 1
        preceding -= _DAYS_IN_MONTH[month] + (month == 2 and leapyear)
    n -= preceding
    assert 0 <= n < _days_in_month(year, month)

    # Now the year and month are correct, and n is the offset from the
    # start of that month:  we're done!
    return year, month, n+1

# Month and day names.  For localized versions, see the calendar module.
_MONTHNAMES = [None, "Jan", "Feb", "Mar", "Apr", "May", "Jun",
                     "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
_DAYNAMES = [None, "Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]


def _build_struct_time(y, m, d, hh, mm, ss, dstflag):
    wday = (_ymd2ord(y, m, d) + 6) % 7
    dnum = _days_before_month(y, m) + d
    return _time.struct_time((y, m, d, hh, mm, ss, wday, dnum, dstflag))

def _format_time(hh, mm, ss, us, timespec='auto'):
    specs = {
        'hours': '{:02d}',
        'minutes': '{:02d}:{:02d}',
        'seconds': '{:02d}:{:02d}:{:02d}',
        'milliseconds': '{:02d}:{:02d}:{:02d}.{:03d}',
        'microseconds': '{:02d}:{:02d}:{:02d}.{:06d}'
    }

    if timespec == 'auto':
        # Skip trailing microseconds when us==0.
        timespec = 'microseconds' if us else 'seconds'
    elif timespec == 'milliseconds':
        us //= 1000
    try:
        fmt = specs[timespec]
    except KeyError:
        raise ValueError('Unknown timespec value')
    else:
        return fmt.format(hh, mm, ss, us)

def _format_offset(off, sep=':'):
    s = ''
    if off is not None:
        if off.days < 0:
            sign = "-"
            off = -off
        else:
            sign = "+"
        hh, mm = divmod(off, timedelta(hours=1))
        mm, ss = divmod(mm, timedelta(minutes=1))
        s += "%s%02d%s%02d" % (sign, hh, sep, mm)
        if ss or ss.microseconds:
            s += "%s%02d" % (sep, ss.seconds)

            if ss.microseconds:
                s += '.%06d' % ss.microseconds
    return s

_normalize_century = None
def _need_normalize_century():
    global _normalize_century
    if _normalize_century is None:
        try:
            _normalize_century = (
                _time.strftime("%Y", (99, 1, 1, 0, 0, 0, 0, 1, 0)) != "0099")
        except ValueError:
            _normalize_century = True
    return _normalize_century

_supports_c99 = None
def _can_support_c99():
    global _supports_c99
    if _supports_c99 is None:
        try:
            _supports_c99 = (
                _time.strftime("%F", (1900, 1, 1, 0, 0, 0, 0, 1, 0)) == "1900-01-01")
        except ValueError:
            _supports_c99 = False
    return _supports_c99

# Correctly substitute for %z and %Z escapes in strftime formats.
def _wrap_strftime(object, format, timetuple):
    # Don't call utcoffset() or tzname() unless actually needed.
    freplace = None  # the string to use for %f
    zreplace = None  # the string to use for %z
    colonzreplace = None  # the string to use for %:z
    Zreplace = None  # the string to use for %Z

    # Scan format for %z, %:z and %Z escapes, replacing as needed.
    newformat = []
    push = newformat.append
    i, n = 0, len(format)
    while i < n:
        ch = format[i]
        i += 1
        if ch == '%':
            if i < n:
                ch = format[i]
                i += 1
                if ch == 'f':
                    if freplace is None:
                        freplace = '%06d' % getattr(object,
                                                    'microsecond', 0)
                    newformat.append(freplace)
                elif ch == 'z':
                    if zreplace is None:
                        if hasattr(object, "utcoffset"):
                            zreplace = _format_offset(object.utcoffset(), sep="")
                        else:
                            zreplace = ""
                    assert '%' not in zreplace
                    newformat.append(zreplace)
                elif ch == ':':
                    if i < n:
                        ch2 = format[i]
                        i += 1
                        if ch2 == 'z':
                            if colonzreplace is None:
                                if hasattr(object, "utcoffset"):
                                    colonzreplace = _format_offset(object.utcoffset(), sep=":")
                                else:
                                    colonzreplace = ""
                            assert '%' not in colonzreplace
                            newformat.append(colonzreplace)
                        else:
                            push('%')
                            push(ch)
                            push(ch2)
                elif ch == 'Z':
                    if Zreplace is None:
                        Zreplace = ""
                        if hasattr(object, "tzname"):
                            s = object.tzname()
                            if s is not None:
                                # strftime is going to have at this: escape %
                                Zreplace = s.replace('%', '%%')
                    newformat.append(Zreplace)
                # Note that datetime(1000, 1, 1).strftime('%G') == '1000' so
                # year 1000 for %G can go on the fast path.
                elif ((ch in 'YG' or ch in 'FC' and _can_support_c99()) and
                        object.year < 1000 and _need_normalize_century()):
                    if ch == 'G':
                        year = int(_time.strftime("%G", timetuple))
                    else:
                        year = object.year
                    if ch == 'C':
                        push('{:02}'.format(year // 100))
                    else:
                        push('{:04}'.format(year))
                        if ch == 'F':
                            push('-{:02}-{:02}'.format(*timetuple[1:3]))
                else:
                    push('%')
                    push(ch)
            else:
                push('%')
        else:
            push(ch)
    newformat = "".join(newformat)
    return _time.strftime(newformat, timetuple)

# Helpers for parsing the result of isoformat()
def _is_ascii_digit(c):
    return c in "0123456789"

def _find_isoformat_datetime_separator(dtstr):
    # See the comment in _datetimemodule.c:_find_isoformat_datetime_separator
    len_dtstr = len(dtstr)
    if len_dtstr == 7:
        return 7

    assert len_dtstr > 7
    date_separator = "-"
    week_indicator = "W"

    if dtstr[4] == date_separator:
        if dtstr[5] == week_indicator:
            if len_dtstr < 8:
                raise ValueError("Invalid ISO string")
            if len_dtstr > 8 and dtstr[8] == date_separator:
                if len_dtstr == 9:
                    raise ValueError("Invalid ISO string")
                if len_dtstr > 10 and _is_ascii_digit(dtstr[10]):
                    # This is as far as we need to resolve the ambiguity for
                    # the moment - if we have YYYY-Www-##, the separator is
                    # either a hyphen at 8 or a number at 10.
                    #
                    # We'll assume it's a hyphen at 8 because it's way more
                    # likely that someone will use a hyphen as a separator than
                    # a number, but at this point it's really best effort
                    # because this is an extension of the spec anyway.
                    # TODO(pganssle): Document this
                    return 8
                return 10
            else:
                # YYYY-Www (8)
                return 8
        else:
            # YYYY-MM-DD (10)
            return 10
    else:
        if dtstr[4] == week_indicator:
            # YYYYWww (7) or YYYYWwwd (8)
            idx = 7
            while idx < len_dtstr:
                if not _is_ascii_digit(dtstr[idx]):
                    break
                idx += 1

            if idx < 9:
                return idx

            if idx % 2 == 0:
                # If the index of the last number is even, it's YYYYWwwd
                return 7
            else:
                return 8
        else:
            # YYYYMMDD (8)
            return 8


def _parse_isoformat_date(dtstr):
    # It is assumed that this is an ASCII-only string of lengths 7, 8 or 10,
    # see the comment on Modules/_datetimemodule.c:_find_isoformat_datetime_separator
    assert len(dtstr) in (7, 8, 10)
    year = int(dtstr[0:4])
    has_sep = dtstr[4] == '-'

    pos = 4 + has_sep
    if dtstr[pos:pos + 1] == "W":
        # YYYY-?Www-?D?
        pos += 1
        weekno = int(dtstr[pos:pos + 2])
        pos += 2

        dayno = 1
        if len(dtstr) > pos:
            if (dtstr[pos:pos + 1] == '-') != has_sep:
                raise ValueError("Inconsistent use of dash separator")

            pos += has_sep

            dayno = int(dtstr[pos:pos + 1])

        return list(_isoweek_to_gregorian(year, weekno, dayno))
    else:
        month = int(dtstr[pos:pos + 2])
        pos += 2
        if (dtstr[pos:pos + 1] == "-") != has_sep:
            raise ValueError("Inconsistent use of dash separator")

        pos += has_sep
        day = int(dtstr[pos:pos + 2])

        return [year, month, day]


_FRACTION_CORRECTION = [100000, 10000, 1000, 100, 10]


def _parse_hh_mm_ss_ff(tstr):
    # Parses things of the form HH[:?MM[:?SS[{.,}fff[fff]]]]
    len_str = len(tstr)

    time_comps = [0, 0, 0, 0]
    pos = 0
    for comp in range(0, 3):
        if (len_str - pos) < 2:
            raise ValueError("Incomplete time component")

        time_comps[comp] = int(tstr[pos:pos+2])

        pos += 2
        next_char = tstr[pos:pos+1]

        if comp == 0:
            has_sep = next_char == ':'

        if not next_char or comp >= 2:
            break

        if has_sep and next_char != ':':
            raise ValueError("Invalid time separator: %c" % next_char)

        pos += has_sep

    if pos < len_str:
        if tstr[pos] not in '.,':
            raise ValueError("Invalid microsecond separator")
        else:
            pos += 1
            if not all(map(_is_ascii_digit, tstr[pos:])):
                raise ValueError("Non-digit values in fraction")

            len_remainder = len_str - pos

            if len_remainder >= 6:
                to_parse = 6
            else:
                to_parse = len_remainder

            time_comps[3] = int(tstr[pos:(pos+to_parse)])
            if to_parse < 6:
                time_comps[3] *= _FRACTION_CORRECTION[to_parse-1]

    return time_comps

def _parse_isoformat_time(tstr):
    # Format supported is HH[:MM[:SS[.fff[fff]]]][+HH:MM[:SS[.ffffff]]]
    len_str = len(tstr)
    if len_str < 2:
        raise ValueError("Isoformat time too short")

    # This is equivalent to re.search('[+-Z]', tstr), but faster
    tz_pos = (tstr.find('-') + 1 or tstr.find('+') + 1 or tstr.find('Z') + 1)
    timestr = tstr[:tz_pos-1] if tz_pos > 0 else tstr

    time_comps = _parse_hh_mm_ss_ff(timestr)

    hour, minute, second, microsecond = time_comps
    became_next_day = False
    error_from_components = False
    if (hour == 24):
        if all(time_comp == 0 for time_comp in time_comps[1:]):
            hour = 0
            time_comps[0] = hour
            became_next_day = True
        else:
            error_from_components = True

    tzi = None
    if tz_pos == len_str and tstr[-1] == 'Z':
        tzi = timezone.utc
    elif tz_pos > 0:
        tzstr = tstr[tz_pos:]

        # Valid time zone strings are:
        # HH                  len: 2
        # HHMM                len: 4
        # HH:MM               len: 5
        # HHMMSS              len: 6
        # HHMMSS.f+           len: 7+
        # HH:MM:SS            len: 8
        # HH:MM:SS.f+         len: 10+

        if len(tzstr) in (0, 1, 3) or tstr[tz_pos-1] == 'Z':
            raise ValueError("Malformed time zone string")

        tz_comps = _parse_hh_mm_ss_ff(tzstr)

        if all(x == 0 for x in tz_comps):
            tzi = timezone.utc
        else:
            tzsign = -1 if tstr[tz_pos - 1] == '-' else 1

            td = timedelta(hours=tz_comps[0], minutes=tz_comps[1],
                           seconds=tz_comps[2], microseconds=tz_comps[3])

            tzi = timezone(tzsign * td)

    time_comps.append(tzi)

    return time_comps, became_next_day, error_from_components

# tuple[int, int, int] -> tuple[int, int, int] version of date.fromisocalendar
def _isoweek_to_gregorian(year, week, day):
    # Year is bounded this way because 9999-12-31 is (9999, 52, 5)
    if not MINYEAR <= year <= MAXYEAR:
        raise ValueError(f"year must be in {MINYEAR}..{MAXYEAR}, not {year}")

    if not 0 < week < 53:
        out_of_range = True

        if week == 53:
            # ISO years have 53 weeks in them on years starting with a
            # Thursday and leap years starting on a Wednesday
            first_weekday = _ymd2ord(year, 1, 1) % 7
            if (first_weekday == 4 or (first_weekday == 3 and
                                       _is_leap(year))):
                out_of_range = False

        if out_of_range:
            raise ValueError(f"Invalid week: {week}")

    if not 0 < day < 8:
        raise ValueError(f"Invalid weekday: {day} (range is [1, 7])")

    # Now compute the offset from (Y, 1, 1) in days:
    day_offset = (week - 1) * 7 + (day - 1)

    # Calculate the ordinal day for monday, week 1
    day_1 = _isoweek1monday(year)
    ord_day = day_1 + day_offset

    return _ord2ymd(ord_day)


# Just raise TypeError if the arg isn't None or a string.
def _check_tzname(name):
    if name is not None and not isinstance(name, str):
        raise TypeError("tzinfo.tzname() must return None or string, "
                        f"not {type(name).__name__!r}")

# name is the offset-producing method, "utcoffset" or "dst".
# offset is what it returned.
# If offset isn't None or timedelta, raises TypeError.
# If offset is None, returns None.
# Else offset is checked for being in range.
# If it is, its integer value is returned.  Else ValueError is raised.
def _check_utc_offset(name, offset):
    assert name in ("utcoffset", "dst")
    if offset is None:
        return
    if not isinstance(offset, timedelta):
        raise TypeError(f"tzinfo.{name}() must return None "
                        f"or timedelta, not {type(offset).__name__!r}")
    if not -timedelta(1) < offset < timedelta(1):
        raise ValueError("offset must be a timedelta "
                         "strictly between -timedelta(hours=24) and "
                         f"timedelta(hours=24), not {offset!r}")

def _check_date_fields(year, month, day):
    year = _index(year)
    month = _index(month)
    day = _index(day)
    if not MINYEAR <= year <= MAXYEAR:
        raise ValueError(f"year must be in {MINYEAR}..{MAXYEAR}, not {year}")
    if not 1 <= month <= 12:
        raise ValueError(f"month must be in 1..12, not {month}")
    dim = _days_in_month(year, month)
    if not 1 <= day <= dim:
        raise ValueError(f"day {day} must be in range 1..{dim} for month {month} in year {year}")
    return year, month, day

def _check_time_fields(hour, minute, second, microsecond, fold):
    hour = _index(hour)
    minute = _index(minute)
    second = _index(second)
    microsecond = _index(microsecond)
    if not 0 <= hour <= 23:
        raise ValueError(f"hour must be in 0..23, not {hour}")
    if not 0 <= minute <= 59:
        raise ValueError(f"minute must be in 0..59, not {minute}")
    if not 0 <= second <= 59:
        raise ValueError(f"second must be in 0..59, not {second}")
    if not 0 <= microsecond <= 999999:
        raise ValueError(f"microsecond must be in 0..999999, not {microsecond}")
    if fold not in (0, 1):
        raise ValueError(f"fold must be either 0 or 1, not {fold}")
    return hour, minute, second, microsecond, fold

def _check_tzinfo_arg(tz):
    if tz is not None and not isinstance(tz, tzinfo):
        raise TypeError(
            "tzinfo argument must be None or of a tzinfo subclass, "
            f"not {type(tz).__name__!r}"
        )

def _divide_and_round(a, b):
    """divide a by b and round result to the nearest integer

    When the ratio is exactly half-way between two integers,
    the even integer is returned.
    """
    # Based on the reference implementation for divmod_near
    # in Objects/longobject.c.
    q, r = divmod(a, b)
    # round up if either r / b > 0.5, or r / b == 0.5 and q is odd.
    # The expression r / b > 0.5 is equivalent to 2 * r > b if b is
    # positive, 2 * r < b if b negative.
    r *= 2
    greater_than_half = r > b if b > 0 else r < b
    if greater_than_half or r == b and q % 2 == 1:
        q += 1

    return q


class timedelta:
    """Represent the difference between two datetime objects.

    Supported operators:

    - add, subtract timedelta
    - unary plus, minus, abs
    - compare to timedelta
    - multiply, divide by int

    In addition, datetime supports subtraction of two datetime objects
    returning a timedelta, and addition or subtraction of a datetime
    and a timedelta giving a datetime.

    Representation: (days, seconds, microseconds).
    """
    # The representation of (days, seconds, microseconds) was chosen
    # arbitrarily; the exact rationale originally specified in the docstring
    # was "Because I felt like it."

    __slots__ = '_days', '_seconds', '_microseconds', '_hashcode'

    def __new__(cls, days=0, seconds=0, microseconds=0,
                milliseconds=0, minutes=0, hours=0, weeks=0):
        # Doing this efficiently and accurately in C is going to be difficult
        # and error-prone, due to ubiquitous overflow possibilities, and that
        # C double doesn't have enough bits of precision to represent
        # microseconds over 10K years faithfully.  The code here tries to make
        # explicit where go-fast assumptions can be relied on, in order to
        # guide the C implementation; it's way more convoluted than speed-
        # ignoring auto-overflow-to-long idiomatic Python could be.

        for name, value in (
            ("days", days),
            ("seconds", seconds),
            ("microseconds", microseconds),
            ("milliseconds", milliseconds),
            ("minutes", minutes),
            ("hours", hours),
            ("weeks", weeks)
        ):
            if not isinstance(value, (int, float)):
                raise TypeError(
                    f"unsupported type for timedelta {name} component: {type(value).__name__}"
                )

        # Final values, all integer.
        # s and us fit in 32-bit signed ints; d isn't bounded.
        d = s = us = 0

        # Normalize everything to days, seconds, microseconds.
        days += weeks*7
        seconds += minutes*60 + hours*3600
        microseconds += milliseconds*1000

        # Get rid of all fractions, and normalize s and us.
        # Take a deep breath <wink>.
        if isinstance(days, float):
            dayfrac, days = _math.modf(days)
            daysecondsfrac, daysecondswhole = _math.modf(dayfrac * (24.*3600.))
            assert daysecondswhole == int(daysecondswhole)  # can't overflow
            s = int(daysecondswhole)
            assert days == int(days)
            d = int(days)
        else:
            daysecondsfrac = 0.0
            d = days
        assert isinstance(daysecondsfrac, float)
        assert abs(daysecondsfrac) <= 1.0
        assert isinstance(d, int)
        assert abs(s) <= 24 * 3600
        # days isn't referenced again before redefinition

        if isinstance(seconds, float):
            secondsfrac, seconds = _math.modf(seconds)
            assert seconds == int(seconds)
            seconds = int(seconds)
            secondsfrac += daysecondsfrac
            assert abs(secondsfrac) <= 2.0
        else:
            secondsfrac = daysecondsfrac
        # daysecondsfrac isn't referenced again
        assert isinstance(secondsfrac, float)
        assert abs(secondsfrac) <= 2.0

        assert isinstance(seconds, int)
        days, seconds = divmod(seconds, 24*3600)
        d += days
        s += int(seconds)    # can't overflow
        assert isinstance(s, int)
        assert abs(s) <= 2 * 24 * 3600
        # seconds isn't referenced again before redefinition

        usdouble = secondsfrac * 1e6
        assert abs(usdouble) < 2.1e6    # exact value not critical
        # secondsfrac isn't referenced again

        if isinstance(microseconds, float):
            microseconds = round(microseconds + usdouble)
            seconds, microseconds = divmod(microseconds, 1000000)
            days, seconds = divmod(seconds, 24*3600)
            d += days
            s += seconds
        else:
            microseconds = int(microseconds)
            seconds, microseconds = divmod(microseconds, 1000000)
            days, seconds = divmod(seconds, 24*3600)
            d += days
            s += seconds
            microseconds = round(microseconds + usdouble)
        assert isinstance(s, int)
        assert isinstance(microseconds, int)
        assert abs(s) <= 3 * 24 * 3600
        assert abs(microseconds) < 3.1e6

        # Just a little bit of carrying possible for microseconds and seconds.
        seconds, us = divmod(microseconds, 1000000)
        s += seconds
        days, s = divmod(s, 24*3600)
        d += days

        assert isinstance(d, int)
        assert isinstance(s, int) and 0 <= s < 24*3600
        assert isinstance(us, int) and 0 <= us < 1000000

        if abs(d) > 999999999:
            raise OverflowError("timedelta # of days is too large: %d" % d)

        self = object.__new__(cls)
        self._days = d
        self._seconds = s
        self._microseconds = us
        self._hashcode = -1
        return self

    def __repr__(self):
        args = []
        if self._days:
            args.append("days=%d" % self._days)
        if self._seconds:
            args.append("seconds=%d" % self._seconds)
        if self._microseconds:
            args.append("microseconds=%d" % self._microseconds)
        if not args:
            args.append('0')
        return "%s%s(%s)" % (_get_class_module(self),
                             self.__class__.__qualname__,
                             ', '.join(args))

    def __str__(self):
        mm, ss = divmod(self._seconds, 60)
        hh, mm = divmod(mm, 60)
        s = "%d:%02d:%02d" % (hh, mm, ss)
        if self._days:
            def plural(n):
                return n, abs(n) != 1 and "s" or ""
            s = ("%d day%s, " % plural(self._days)) + s
        if self._microseconds:
            s = s + ".%06d" % self._microseconds
        return s

    def total_seconds(self):
        """Total seconds in the duration."""
        return ((self.days * 86400 + self.seconds) * 10**6 +
                self.microseconds) / 10**6

    # Read-only field accessors
    @property
    def days(self):
        """days"""
        return self._days

    @property
    def seconds(self):
        """seconds"""
        return self._seconds

    @property
    def microseconds(self):
        """microseconds"""
        return self._microseconds

    def __add__(self, other):
        if isinstance(other, timedelta):
            # for CPython compatibility, we cannot use
            # our __class__ here, but need a real timedelta
            return timedelta(self._days + other._days,
                             self._seconds + other._seconds,
                             self._microseconds + other._microseconds)
        return NotImplemented

    __radd__ = __add__

    def __sub__(self, other):
        if isinstance(other, timedelta):
            # for CPython compatibility, we cannot use
            # our __class__ here, but need a real timedelta
            return timedelta(self._days - other._days,
                             self._seconds - other._seconds,
                             self._microseconds - other._microseconds)
        return NotImplemented

    def __rsub__(self, other):
        if isinstance(other, timedelta):
            return -self + other
        return NotImplemented

    def __neg__(self):
        # for CPython compatibility, we cannot use
        # our __class__ here, but need a real timedelta
        return timedelta(-self._days,
                         -self._seconds,
                         -self._microseconds)

    def __pos__(self):
        return self

    def __abs__(self):
        if self._days < 0:
            return -self
        else:
            return self

    def __mul__(self, other):
        if isinstance(other, int):
            # for CPython compatibility, we cannot use
            # our __class__ here, but need a real timedelta
            return timedelta(self._days * other,
                             self._seconds * other,
                             self._microseconds * other)
        if isinstance(other, float):
            usec = self._to_microseconds()
            a, b = other.as_integer_ratio()
            return timedelta(0, 0, _divide_and_round(usec * a, b))
        return NotImplemented

    __rmul__ = __mul__

    def _to_microseconds(self):
        return ((self._days * (24*3600) + self._seconds) * 1000000 +
                self._microseconds)

    def __floordiv__(self, other):
        if not isinstance(other, (int, timedelta)):
            return NotImplemented
        usec = self._to_microseconds()
        if isinstance(other, timedelta):
            return usec // other._to_microseconds()
        if isinstance(other, int):
            return timedelta(0, 0, usec // other)

    def __truediv__(self, other):
        if not isinstance(other, (int, float, timedelta)):
            return NotImplemented
        usec = self._to_microseconds()
        if isinstance(other, timedelta):
            return usec / other._to_microseconds()
        if isinstance(other, int):
            return timedelta(0, 0, _divide_and_round(usec, other))
        if isinstance(other, float):
            a, b = other.as_integer_ratio()
            return timedelta(0, 0, _divide_and_round(b * usec, a))

    def __mod__(self, other):
        if isinstance(other, timedelta):
            r = self._to_microseconds() % other._to_microseconds()
            return timedelta(0, 0, r)
        return NotImplemented

    def __divmod__(self, other):
        if isinstance(other, timedelta):
            q, r = divmod(self._to_microseconds(),
                          other._to_microseconds())
            return q, timedelta(0, 0, r)
        return NotImplemented

    # Comparisons of timedelta objects with other.

    def __eq__(self, other):
        if isinstance(other, timedelta):
            return self._cmp(other) == 0
        else:
            return NotImplemented

    def __le__(self, other):
        if isinstance(other, timedelta):
            return self._cmp(other) <= 0
        else:
            return NotImplemented

    def __lt__(self, other):
        if isinstance(other, timedelta):
            return self._cmp(other) < 0
        else:
            return NotImplemented

    def __ge__(self, other):
        if isinstance(other, timedelta):
            return self._cmp(other) >= 0
        else:
            return NotImplemented

    def __gt__(self, other):
        if isinstance(other, timedelta):
            return self._cmp(other) > 0
        else:
            return NotImplemented

    def _cmp(self, other):
        assert isinstance(other, timedelta)
        return _cmp(self._getstate(), other._getstate())

    def __hash__(self):
        if self._hashcode == -1:
            self._hashcode = hash(self._getstate())
        return self._hashcode

    def __bool__(self):
        return (self._days != 0 or
                self._seconds != 0 or
                self._microseconds != 0)

    # Pickle support.

    def _getstate(self):
        return (self._days, self._seconds, self._microseconds)

    def __reduce__(self):
        return (self.__class__, self._getstate())

timedelta.min = timedelta(-999999999)
timedelta.max = timedelta(days=999999999, hours=23, minutes=59, seconds=59,
                          microseconds=999999)
timedelta.resolution = timedelta(microseconds=1)

class date:
    """Concrete date type.

    Constructors:

    __new__()
    fromtimestamp()
    today()
    fromordinal()
    strptime()

    Operators:

    __repr__, __str__
    __eq__, __le__, __lt__, __ge__, __gt__, __hash__
    __add__, __radd__, __sub__ (add/radd only with timedelta arg)

    Methods:

    timetuple()
    toordinal()
    weekday()
    isoweekday(), isocalendar(), isoformat()
    ctime()
    strftime()

    Properties (readonly):
    year, month, day
    """
    __slots__ = '_year', '_month', '_day', '_hashcode'

    def __new__(cls, year, month=None, day=None):
        """Constructor.

        Arguments:

        year, month, day (required, base 1)
        """
        if (month is None and
            isinstance(year, (bytes, str)) and len(year) == 4 and