datetime.py 82.4 KB
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"""Concrete date/time and related types.
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See http://www.iana.org/time-zones/repository/tz-link.html for
time zone and DST data sources.
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"""

import time as _time
import math as _math

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

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

Benjamin Peterson's avatar
Benjamin Peterson committed
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# -1 is a placeholder for indexing purposes.
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_DAYS_IN_MONTH = [-1, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
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_DAYS_BEFORE_MONTH = [-1]  # -1 is a placeholder for indexing purposes.
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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):
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    "year, month -> number of days in year preceding first day of month."
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    assert 1 <= month <= 12, 'month must be in 1..12'
    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, 'month must be in 1..12'
    dim = _days_in_month(year, month)
    assert 1 <= day <= dim, ('day must be in 1..%d' % dim)
    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))

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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)
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def _format_offset(off):
    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:%02d" % (sign, hh, mm)
        if ss or ss.microseconds:
            s += ":%02d" % ss.seconds

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

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# 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.
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    freplace = None  # the string to use for %f
    zreplace = None  # the string to use for %z
    Zreplace = None  # the string to use for %Z
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    # Scan format for %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:
                        zreplace = ""
                        if hasattr(object, "utcoffset"):
                            offset = object.utcoffset()
                            if offset is not None:
                                sign = '+'
                                if offset.days < 0:
                                    offset = -offset
                                    sign = '-'
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                                h, rest = divmod(offset, timedelta(hours=1))
                                m, rest = divmod(rest, timedelta(minutes=1))
                                s = rest.seconds
                                u = offset.microseconds
                                if u:
                                    zreplace = '%c%02d%02d%02d.%06d' % (sign, h, m, s, u)
                                elif s:
                                    zreplace = '%c%02d%02d%02d' % (sign, h, m, s)
                                else:
                                    zreplace = '%c%02d%02d' % (sign, h, m)
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                    assert '%' not in zreplace
                    newformat.append(zreplace)
                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)
                else:
                    push('%')
                    push(ch)
            else:
                push('%')
        else:
            push(ch)
    newformat = "".join(newformat)
    return _time.strftime(newformat, timetuple)

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# Helpers for parsing the result of isoformat()
def _parse_isoformat_date(dtstr):
    # It is assumed that this function will only be called with a
    # string of length exactly 10, and (though this is not used) ASCII-only
    year = int(dtstr[0:4])
    if dtstr[4] != '-':
        raise ValueError('Invalid date separator: %s' % dtstr[4])

    month = int(dtstr[5:7])

    if dtstr[7] != '-':
        raise ValueError('Invalid date separator')

    day = int(dtstr[8:10])

    return [year, month, day]

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 not next_char or comp >= 2:
            break

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

        pos += 1

    if pos < len_str:
        if tstr[pos] != '.':
            raise ValueError('Invalid microsecond component')
        else:
            pos += 1

            len_remainder = len_str - pos
            if len_remainder not in (3, 6):
                raise ValueError('Invalid microsecond component')

            time_comps[3] = int(tstr[pos:])
            if len_remainder == 3:
                time_comps[3] *= 1000

    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('[+-]', tstr), but faster
    tz_pos = (tstr.find('-') + 1 or tstr.find('+') + 1)
    timestr = tstr[:tz_pos-1] if tz_pos > 0 else tstr

    time_comps = _parse_hh_mm_ss_ff(timestr)

    tzi = None
    if tz_pos > 0:
        tzstr = tstr[tz_pos:]

        # Valid time zone strings are:
        # HH:MM               len: 5
        # HH:MM:SS            len: 8
        # HH:MM:SS.ffffff     len: 15

        if len(tzstr) not in (5, 8, 15):
            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


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# 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, "
                        "not '%s'" % type(name))

# 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.
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# Else offset is checked for being in range.
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# 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("tzinfo.%s() must return None "
                        "or timedelta, not '%s'" % (name, type(offset)))
    if not -timedelta(1) < offset < timedelta(1):
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        raise ValueError("%s()=%s, must be strictly between "
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                         "-timedelta(hours=24) and timedelta(hours=24)" %
                         (name, offset))

def _check_int_field(value):
    if isinstance(value, int):
        return value
    if not isinstance(value, float):
        try:
            value = value.__int__()
        except AttributeError:
            pass
        else:
            if isinstance(value, int):
                return value
            raise TypeError('__int__ returned non-int (type %s)' %
                            type(value).__name__)
        raise TypeError('an integer is required (got type %s)' %
                        type(value).__name__)
    raise TypeError('integer argument expected, got float')
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def _check_date_fields(year, month, day):
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    year = _check_int_field(year)
    month = _check_int_field(month)
    day = _check_int_field(day)
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    if not MINYEAR <= year <= MAXYEAR:
        raise ValueError('year must be in %d..%d' % (MINYEAR, MAXYEAR), year)
    if not 1 <= month <= 12:
        raise ValueError('month must be in 1..12', month)
    dim = _days_in_month(year, month)
    if not 1 <= day <= dim:
        raise ValueError('day must be in 1..%d' % dim, day)
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    return year, month, day
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def _check_time_fields(hour, minute, second, microsecond, fold):
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    hour = _check_int_field(hour)
    minute = _check_int_field(minute)
    second = _check_int_field(second)
    microsecond = _check_int_field(microsecond)
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    if not 0 <= hour <= 23:
        raise ValueError('hour must be in 0..23', hour)
    if not 0 <= minute <= 59:
        raise ValueError('minute must be in 0..59', minute)
    if not 0 <= second <= 59:
        raise ValueError('second must be in 0..59', second)
    if not 0 <= microsecond <= 999999:
        raise ValueError('microsecond must be in 0..999999', microsecond)
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    if fold not in (0, 1):
        raise ValueError('fold must be either 0 or 1', fold)
    return hour, minute, second, microsecond, fold
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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")

def _cmperror(x, y):
    raise TypeError("can't compare '%s' to '%s'" % (
                    type(x).__name__, type(y).__name__))

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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

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

    Supported operators:

    - add, subtract timedelta
    - unary plus, minus, abs
    - compare to timedelta
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    - multiply, divide by int
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    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).  Why?  Because I
    felt like it.
    """
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    __slots__ = '_days', '_seconds', '_microseconds', '_hashcode'
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    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.

        # XXX Check that all inputs are ints or floats.

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

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

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        if abs(d) > 999999999:
            raise OverflowError("timedelta # of days is too large: %d" % d)
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        self = object.__new__(cls)
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        self._days = d
        self._seconds = s
        self._microseconds = us
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        self._hashcode = -1
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        return self

    def __repr__(self):
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        args = []
        if self._days:
            args.append("days=%d" % self._days)
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        if self._seconds:
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            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)" % (self.__class__.__module__,
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                              self.__class__.__qualname__,
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                              ', '.join(args))
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    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."""
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        return ((self.days * 86400 + self.seconds) * 10**6 +
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                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):
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            # 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)
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        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):
669
            usec = self._to_microseconds()
670
            a, b = other.as_integer_ratio()
671
            return timedelta(0, 0, _divide_and_round(usec * a, b))
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        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):
696
            return timedelta(0, 0, _divide_and_round(usec, other))
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        if isinstance(other, float):
            a, b = other.as_integer_ratio()
699
            return timedelta(0, 0, _divide_and_round(b * usec, a))
700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750

    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 False

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

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

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

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

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

    def __hash__(self):
751 752 753
        if self._hashcode == -1:
            self._hashcode = hash(self._getstate())
        return self._hashcode
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    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()

    Operators:

    __repr__, __str__
786
    __eq__, __le__, __lt__, __ge__, __gt__, __hash__
787 788 789 790 791 792 793 794 795 796 797 798 799 800
    __add__, __radd__, __sub__ (add/radd only with timedelta arg)

    Methods:

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

    Properties (readonly):
    year, month, day
    """
801
    __slots__ = '_year', '_month', '_day', '_hashcode'
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    def __new__(cls, year, month=None, day=None):
        """Constructor.

        Arguments:

        year, month, day (required, base 1)
        """
810 811
        if month is None and isinstance(year, bytes) and len(year) == 4 and \
                1 <= year[2] <= 12:
812 813 814
            # Pickle support
            self = object.__new__(cls)
            self.__setstate(year)
815
            self._hashcode = -1
816
            return self
817
        year, month, day = _check_date_fields(year, month, day)
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        self = object.__new__(cls)
        self._year = year
        self._month = month
        self._day = day
822
        self._hashcode = -1
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        return self

    # Additional constructors

    @classmethod
    def fromtimestamp(cls, t):
        "Construct a date from a POSIX timestamp (like time.time())."
        y, m, d, hh, mm, ss, weekday, jday, dst = _time.localtime(t)
        return cls(y, m, d)

    @classmethod
    def today(cls):
        "Construct a date from time.time()."
        t = _time.time()
        return cls.fromtimestamp(t)

    @classmethod
    def fromordinal(cls, n):
841
        """Construct a date from a proleptic Gregorian ordinal.
842 843 844 845 846 847 848

        January 1 of year 1 is day 1.  Only the year, month and day are
        non-zero in the result.
        """
        y, m, d = _ord2ymd(n)
        return cls(y, m, d)

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    @classmethod
    def fromisoformat(cls, date_string):
        """Construct a date from the output of date.isoformat()."""
        if not isinstance(date_string, str):
            raise TypeError('fromisoformat: argument must be str')

        try:
            assert len(date_string) == 10
            return cls(*_parse_isoformat_date(date_string))
        except Exception:
            raise ValueError('Invalid isoformat string: %s' % date_string)


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    # Conversions to string

    def __repr__(self):
        """Convert to formal string, for repr().

        >>> dt = datetime(2010, 1, 1)
        >>> repr(dt)
        'datetime.datetime(2010, 1, 1, 0, 0)'

        >>> dt = datetime(2010, 1, 1, tzinfo=timezone.utc)
        >>> repr(dt)
        'datetime.datetime(2010, 1, 1, 0, 0, tzinfo=datetime.timezone.utc)'
        """
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        return "%s.%s(%d, %d, %d)" % (self.__class__.__module__,
                                      self.__class__.__qualname__,
                                      self._year,
                                      self._month,
                                      self._day)
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    # XXX These shouldn't depend on time.localtime(), because that
    # clips the usable dates to [1970 .. 2038).  At least ctime() is
    # easily done without using strftime() -- that's better too because
    # strftime("%c", ...) is locale specific.


    def ctime(self):
        "Return ctime() style string."
        weekday = self.toordinal() % 7 or 7
        return "%s %s %2d 00:00:00 %04d" % (
            _DAYNAMES[weekday],
            _MONTHNAMES[self._month],
            self._day, self._year)

    def strftime(self, fmt):
        "Format using strftime()."
        return _wrap_strftime(self, fmt, self.timetuple())

    def __format__(self, fmt):
899 900
        if not isinstance(fmt, str):
            raise TypeError("must be str, not %s" % type(fmt).__name__)
901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933
        if len(fmt) != 0:
            return self.strftime(fmt)
        return str(self)

    def isoformat(self):
        """Return the date formatted according to ISO.

        This is 'YYYY-MM-DD'.

        References:
        - http://www.w3.org/TR/NOTE-datetime
        - http://www.cl.cam.ac.uk/~mgk25/iso-time.html
        """
        return "%04d-%02d-%02d" % (self._year, self._month, self._day)

    __str__ = isoformat

    # Read-only field accessors
    @property
    def year(self):
        """year (1-9999)"""
        return self._year

    @property
    def month(self):
        """month (1-12)"""
        return self._month

    @property
    def day(self):
        """day (1-31)"""
        return self._day

934 935
    # Standard conversions, __eq__, __le__, __lt__, __ge__, __gt__,
    # __hash__ (and helpers)
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    def timetuple(self):
        "Return local time tuple compatible with time.localtime()."
        return _build_struct_time(self._year, self._month, self._day,
                                  0, 0, 0, -1)

    def toordinal(self):
        """Return proleptic Gregorian ordinal for the year, month and day.

        January 1 of year 1 is day 1.  Only the year, month and day values
        contribute to the result.
        """
        return _ymd2ord(self._year, self._month, self._day)

    def replace(self, year=None, month=None, day=None):
        """Return a new date with new values for the specified fields."""
        if year is None:
            year = self._year
        if month is None:
            month = self._month
        if day is None:
            day = self._day
958
        return type(self)(year, month, day)
959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994

    # Comparisons of date objects with other.

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

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

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

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

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

    def _cmp(self, other):
        assert isinstance(other, date)
        y, m, d = self._year, self._month, self._day
        y2, m2, d2 = other._year, other._month, other._day
        return _cmp((y, m, d), (y2, m2, d2))

    def __hash__(self):
        "Hash."
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        if self._hashcode == -1:
            self._hashcode = hash(self._getstate())
        return self._hashcode
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    # Computations

    def __add__(self, other):
        "Add a date to a timedelta."
        if isinstance(other, timedelta):
            o = self.toordinal() + other.days
            if 0 < o <= _MAXORDINAL:
                return date.fromordinal(o)
            raise OverflowError("result out of range")
        return NotImplemented

    __radd__ = __add__

    def __sub__(self, other):
        """Subtract two dates, or a date and a timedelta."""
        if isinstance(other, timedelta):
            return self + timedelta(-other.days)
        if isinstance(other, date):
            days1 = self.toordinal()
            days2 = other.toordinal()
            return timedelta(days1 - days2)
        return NotImplemented

    def weekday(self):
        "Return day of the week, where Monday == 0 ... Sunday == 6."
        return (self.toordinal() + 6) % 7

    # Day-of-the-week and week-of-the-year, according to ISO

    def isoweekday(self):
        "Return day of the week, where Monday == 1 ... Sunday == 7."
        # 1-Jan-0001 is a Monday
        return self.toordinal() % 7 or 7

    def isocalendar(self):
        """Return a 3-tuple containing ISO year, week number, and weekday.

        The first ISO week of the year is the (Mon-Sun) week
        containing the year's first Thursday; everything else derives
        from that.

        The first week is 1; Monday is 1 ... Sunday is 7.

        ISO calendar algorithm taken from
        http://www.phys.uu.nl/~vgent/calendar/isocalendar.htm
1044
        (used with permission)
1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062
        """
        year = self._year
        week1monday = _isoweek1monday(year)
        today = _ymd2ord(self._year, self._month, self._day)
        # Internally, week and day have origin 0
        week, day = divmod(today - week1monday, 7)
        if week < 0:
            year -= 1
            week1monday = _isoweek1monday(year)
            week, day = divmod(today - week1monday, 7)
        elif week >= 52:
            if today >= _isoweek1monday(year+1):
                year += 1
                week = 0
        return year, week+1, day+1

    # Pickle support.

1063
    def _getstate(self):
1064 1065 1066 1067 1068 1069 1070
        yhi, ylo = divmod(self._year, 256)
        return bytes([yhi, ylo, self._month, self._day]),

    def __setstate(self, string):
        yhi, ylo, self._month, self._day = string
        self._year = yhi * 256 + ylo

1071 1072
    def __reduce__(self):
        return (self.__class__, self._getstate())
1073 1074 1075 1076 1077 1078 1079

_date_class = date  # so functions w/ args named "date" can get at the class

date.min = date(1, 1, 1)
date.max = date(9999, 12, 31)
date.resolution = timedelta(days=1)

1080

1081 1082 1083 1084 1085 1086
class tzinfo:
    """Abstract base class for time zone info classes.

    Subclasses must override the name(), utcoffset() and dst() methods.
    """
    __slots__ = ()
1087

1088 1089 1090 1091 1092
    def tzname(self, dt):
        "datetime -> string name of time zone."
        raise NotImplementedError("tzinfo subclass must override tzname()")

    def utcoffset(self, dt):
1093
        "datetime -> timedelta, positive for east of UTC, negative for west of UTC"
1094 1095 1096
        raise NotImplementedError("tzinfo subclass must override utcoffset()")

    def dst(self, dt):
1097
        """datetime -> DST offset as timedelta, positive for east of UTC.
1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160

        Return 0 if DST not in effect.  utcoffset() must include the DST
        offset.
        """
        raise NotImplementedError("tzinfo subclass must override dst()")

    def fromutc(self, dt):
        "datetime in UTC -> datetime in local time."

        if not isinstance(dt, datetime):
            raise TypeError("fromutc() requires a datetime argument")
        if dt.tzinfo is not self:
            raise ValueError("dt.tzinfo is not self")

        dtoff = dt.utcoffset()
        if dtoff is None:
            raise ValueError("fromutc() requires a non-None utcoffset() "
                             "result")

        # See the long comment block at the end of this file for an
        # explanation of this algorithm.
        dtdst = dt.dst()
        if dtdst is None:
            raise ValueError("fromutc() requires a non-None dst() result")
        delta = dtoff - dtdst
        if delta:
            dt += delta
            dtdst = dt.dst()
            if dtdst is None:
                raise ValueError("fromutc(): dt.dst gave inconsistent "
                                 "results; cannot convert")
        return dt + dtdst

    # Pickle support.

    def __reduce__(self):
        getinitargs = getattr(self, "__getinitargs__", None)
        if getinitargs:
            args = getinitargs()
        else:
            args = ()
        getstate = getattr(self, "__getstate__", None)
        if getstate:
            state = getstate()
        else:
            state = getattr(self, "__dict__", None) or None
        if state is None:
            return (self.__class__, args)
        else:
            return (self.__class__, args, state)

_tzinfo_class = tzinfo

class time:
    """Time with time zone.

    Constructors:

    __new__()

    Operators:

    __repr__, __str__
1161
    __eq__, __le__, __lt__, __ge__, __gt__, __hash__
1162 1163 1164 1165 1166 1167 1168 1169 1170 1171

    Methods:

    strftime()
    isoformat()
    utcoffset()
    tzname()
    dst()

    Properties (readonly):
1172
    hour, minute, second, microsecond, tzinfo, fold
1173
    """
1174
    __slots__ = '_hour', '_minute', '_second', '_microsecond', '_tzinfo', '_hashcode', '_fold'
1175

1176
    def __new__(cls, hour=0, minute=0, second=0, microsecond=0, tzinfo=None, *, fold=0):
1177 1178 1179 1180 1181 1182 1183
        """Constructor.

        Arguments:

        hour, minute (required)
        second, microsecond (default to zero)
        tzinfo (default to None)
1184
        fold (keyword only, default to zero)
1185
        """
1186
        if isinstance(hour, bytes) and len(hour) == 6 and hour[0]&0x7F < 24:
1187
            # Pickle support
1188
            self = object.__new__(cls)
1189
            self.__setstate(hour, minute or None)
1190
            self._hashcode = -1
1191
            return self
1192 1193
        hour, minute, second, microsecond, fold = _check_time_fields(
            hour, minute, second, microsecond, fold)
1194
        _check_tzinfo_arg(tzinfo)
1195
        self = object.__new__(cls)
1196 1197 1198 1199 1200
        self._hour = hour
        self._minute = minute
        self._second = second
        self._microsecond = microsecond
        self._tzinfo = tzinfo
1201
        self._hashcode = -1
1202
        self._fold = fold
1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230
        return self

    # Read-only field accessors
    @property
    def hour(self):
        """hour (0-23)"""
        return self._hour

    @property
    def minute(self):
        """minute (0-59)"""
        return self._minute

    @property
    def second(self):
        """second (0-59)"""
        return self._second

    @property
    def microsecond(self):
        """microsecond (0-999999)"""
        return self._microsecond

    @property
    def tzinfo(self):
        """timezone info object"""
        return self._tzinfo

1231 1232 1233 1234
    @property
    def fold(self):
        return self._fold

1235 1236 1237 1238 1239 1240
    # Standard conversions, __hash__ (and helpers)

    # Comparisons of time objects with other.

    def __eq__(self, other):
        if isinstance(other, time):
1241
            return self._cmp(other, allow_mixed=True) == 0
1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268
        else:
            return False

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

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

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

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

1269
    def _cmp(self, other, allow_mixed=False):
1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284
        assert isinstance(other, time)
        mytz = self._tzinfo
        ottz = other._tzinfo
        myoff = otoff = None

        if mytz is ottz:
            base_compare = True
        else:
            myoff = self.utcoffset()
            otoff = other.utcoffset()
            base_compare = myoff == otoff

        if base_compare:
            return _cmp((self._hour, self._minute, self._second,
                         self._microsecond),
1285 1286
                        (other._hour, other._minute, other._second,
                         other._microsecond))
1287
        if myoff is None or otoff is None:
1288 1289 1290 1291
            if allow_mixed:
                return 2 # arbitrary non-zero value
            else:
                raise TypeError("cannot compare naive and aware times")
1292 1293 1294 1295 1296 1297 1298
        myhhmm = self._hour * 60 + self._minute - myoff//timedelta(minutes=1)
        othhmm = other._hour * 60 + other._minute - otoff//timedelta(minutes=1)
        return _cmp((myhhmm, self._second, self._microsecond),
                    (othhmm, other._second, other._microsecond))

    def __hash__(self):
        """Hash."""
1299
        if self._hashcode == -1:
1300 1301 1302 1303 1304
            if self.fold:
                t = self.replace(fold=0)
            else:
                t = self
            tzoff = t.utcoffset()
1305
            if not tzoff:  # zero or None
1306
                self._hashcode = hash(t._getstate()[0])
1307 1308 1309 1310 1311 1312 1313 1314 1315 1316
            else:
                h, m = divmod(timedelta(hours=self.hour, minutes=self.minute) - tzoff,
                              timedelta(hours=1))
                assert not m % timedelta(minutes=1), "whole minute"
                m //= timedelta(minutes=1)
                if 0 <= h < 24:
                    self._hashcode = hash(time(h, m, self.second, self.microsecond))
                else:
                    self._hashcode = hash((h, m, self.second, self.microsecond))
        return self._hashcode
1317 1318 1319

    # Conversion to string

1320 1321
    def _tzstr(self):
        """Return formatted timezone offset (+xx:xx) or an empty string."""
1322
        off = self.utcoffset()
1323
        return _format_offset(off)
1324 1325 1326 1327 1328 1329 1330 1331 1332

    def __repr__(self):
        """Convert to formal string, for repr()."""
        if self._microsecond != 0:
            s = ", %d, %d" % (self._second, self._microsecond)
        elif self._second != 0:
            s = ", %d" % self._second
        else:
            s = ""
1333 1334 1335
        s= "%s.%s(%d, %d%s)" % (self.__class__.__module__,
                                self.__class__.__qualname__,
                                self._hour, self._minute, s)
1336 1337 1338
        if self._tzinfo is not None:
            assert s[-1:] == ")"
            s = s[:-1] + ", tzinfo=%r" % self._tzinfo + ")"
1339 1340 1341
        if self._fold:
            assert s[-1:] == ")"
            s = s[:-1] + ", fold=1)"
1342 1343
        return s

1344
    def isoformat(self, timespec='auto'):
1345 1346
        """Return the time formatted according to ISO.

1347 1348 1349 1350 1351
        The full format is 'HH:MM:SS.mmmmmm+zz:zz'. By default, the fractional
        part is omitted if self.microsecond == 0.

        The optional argument timespec specifies the number of additional
        terms of the time to include.
1352 1353
        """
        s = _format_time(self._hour, self._minute, self._second,
1354
                          self._microsecond, timespec)
1355 1356 1357 1358 1359 1360 1361
        tz = self._tzstr()
        if tz:
            s += tz
        return s

    __str__ = isoformat

1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373
    @classmethod
    def fromisoformat(cls, time_string):
        """Construct a time from the output of isoformat()."""
        if not isinstance(time_string, str):
            raise TypeError('fromisoformat: argument must be str')

        try:
            return cls(*_parse_isoformat_time(time_string))
        except Exception:
            raise ValueError('Invalid isoformat string: %s' % time_string)


1374 1375 1376 1377
    def strftime(self, fmt):
        """Format using strftime().  The date part of the timestamp passed
        to underlying strftime should not be used.
        """
1378
        # The year must be >= 1000 else Python's strftime implementation
1379 1380 1381 1382 1383 1384 1385
        # can raise a bogus exception.
        timetuple = (1900, 1, 1,
                     self._hour, self._minute, self._second,
                     0, 1, -1)
        return _wrap_strftime(self, fmt, timetuple)

    def __format__(self, fmt):
1386 1387
        if not isinstance(fmt, str):
            raise TypeError("must be str, not %s" % type(fmt).__name__)
1388 1389 1390 1391 1392 1393 1394
        if len(fmt) != 0:
            return self.strftime(fmt)
        return str(self)

    # Timezone functions

    def utcoffset(self):
1395 1396
        """Return the timezone offset as timedelta, positive east of UTC
         (negative west of UTC)."""
1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416
        if self._tzinfo is None:
            return None
        offset = self._tzinfo.utcoffset(None)
        _check_utc_offset("utcoffset", offset)
        return offset

    def tzname(self):
        """Return the timezone name.

        Note that the name is 100% informational -- there's no requirement that
        it mean anything in particular. For example, "GMT", "UTC", "-500",
        "-5:00", "EDT", "US/Eastern", "America/New York" are all valid replies.
        """
        if self._tzinfo is None:
            return None
        name = self._tzinfo.tzname(None)
        _check_tzname(name)
        return name

    def dst(self):
1417 1418
        """Return 0 if DST is not in effect, or the DST offset (as timedelta
        positive eastward) if DST is in effect.
1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431

        This is purely informational; the DST offset has already been added to
        the UTC offset returned by utcoffset() if applicable, so there's no
        need to consult dst() unless you're interested in displaying the DST
        info.
        """
        if self._tzinfo is None:
            return None
        offset = self._tzinfo.dst(None)
        _check_utc_offset("dst", offset)
        return offset

    def replace(self, hour=None, minute=None, second=None, microsecond=None,
1432
                tzinfo=True, *, fold=None):
1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443
        """Return a new time with new values for the specified fields."""
        if hour is None:
            hour = self.hour
        if minute is None:
            minute = self.minute
        if second is None:
            second = self.second
        if microsecond is None:
            microsecond = self.microsecond
        if tzinfo is True:
            tzinfo = self.tzinfo
1444 1445
        if fold is None:
            fold = self._fold
1446
        return type(self)(hour, minute, second, microsecond, tzinfo, fold=fold)
1447 1448 1449

    # Pickle support.

1450
    def _getstate(self, protocol=3):
1451 1452
        us2, us3 = divmod(self._microsecond, 256)
        us1, us2 = divmod(us2, 256)
1453 1454 1455 1456
        h = self._hour
        if self._fold and protocol > 3:
            h += 128
        basestate = bytes([h, self._minute, self._second,
1457 1458 1459 1460 1461 1462 1463
                           us1, us2, us3])
        if self._tzinfo is None:
            return (basestate,)
        else:
            return (basestate, self._tzinfo)

    def __setstate(self, string, tzinfo):
1464 1465
        if tzinfo is not None and not isinstance(tzinfo, _tzinfo_class):
            raise TypeError("bad tzinfo state arg")
1466 1467 1468 1469 1470 1471 1472
        h, self._minute, self._second, us1, us2, us3 = string
        if h > 127:
            self._fold = 1
            self._hour = h - 128
        else:
            self._fold = 0
            self._hour = h
1473
        self._microsecond = (((us1 << 8) | us2) << 8) | us3
1474
        self._tzinfo = tzinfo
1475

1476 1477
    def __reduce_ex__(self, protocol):
        return (time, self._getstate(protocol))
1478

1479 1480 1481
    def __reduce__(self):
        return self.__reduce_ex__(2)

1482 1483 1484 1485 1486 1487 1488 1489 1490 1491
_time_class = time  # so functions w/ args named "time" can get at the class

time.min = time(0, 0, 0)
time.max = time(23, 59, 59, 999999)
time.resolution = timedelta(microseconds=1)

class datetime(date):
    """datetime(year, month, day[, hour[, minute[, second[, microsecond[,tzinfo]]]]])

    The year, month and day arguments are required. tzinfo may be None, or an
1492
    instance of a tzinfo subclass. The remaining arguments may be ints.
1493
    """
1494
    __slots__ = date.__slots__ + time.__slots__
1495 1496

    def __new__(cls, year, month=None, day=None, hour=0, minute=0, second=0,
1497 1498
                microsecond=0, tzinfo=None, *, fold=0):
        if isinstance(year, bytes) and len(year) == 10 and 1 <= year[2]&0x7F <= 12:
1499
            # Pickle support
1500
            self = object.__new__(cls)
1501
            self.__setstate(year, month)
1502
            self._hashcode = -1
1503
            return self
1504
        year, month, day = _check_date_fields(year, month, day)
1505 1506
        hour, minute, second, microsecond, fold = _check_time_fields(
            hour, minute, second, microsecond, fold)
1507
        _check_tzinfo_arg(tzinfo)
1508 1509 1510 1511
        self = object.__new__(cls)
        self._year = year
        self._month = month
        self._day = day
1512 1513 1514 1515 1516
        self._hour = hour
        self._minute = minute
        self._second = second
        self._microsecond = microsecond
        self._tzinfo = tzinfo
1517
        self._hashcode = -1
1518
        self._fold = fold
1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546
        return self

    # Read-only field accessors
    @property
    def hour(self):
        """hour (0-23)"""
        return self._hour

    @property
    def minute(self):
        """minute (0-59)"""
        return self._minute

    @property
    def second(self):
        """second (0-59)"""
        return self._second

    @property
    def microsecond(self):
        """microsecond (0-999999)"""
        return self._microsecond

    @property
    def tzinfo(self):
        """timezone info object"""
        return self._tzinfo

1547 1548 1549 1550
    @property
    def fold(self):
        return self._fold

1551
    @classmethod
1552
    def _fromtimestamp(cls, t, utc, tz):
1553 1554 1555 1556
        """Construct a datetime from a POSIX timestamp (like time.time()).

        A timezone info object may be passed in as well.
        """
1557
        frac, t = _math.modf(t)
1558
        us = round(frac * 1e6)
1559
        if us >= 1000000:
1560
            t += 1
1561 1562 1563 1564 1565 1566
            us -= 1000000
        elif us < 0:
            t -= 1
            us += 1000000

        converter = _time.gmtime if utc else _time.localtime
1567 1568
        y, m, d, hh, mm, ss, weekday, jday, dst = converter(t)
        ss = min(ss, 59)    # clamp out leap seconds if the platform has them
1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585
        result = cls(y, m, d, hh, mm, ss, us, tz)
        if tz is None:
            # As of version 2015f max fold in IANA database is
            # 23 hours at 1969-09-30 13:00:00 in Kwajalein.
            # Let's probe 24 hours in the past to detect a transition:
            max_fold_seconds = 24 * 3600
            y, m, d, hh, mm, ss = converter(t - max_fold_seconds)[:6]
            probe1 = cls(y, m, d, hh, mm, ss, us, tz)
            trans = result - probe1 - timedelta(0, max_fold_seconds)
            if trans.days < 0:
                y, m, d, hh, mm, ss = converter(t + trans // timedelta(0, 1))[:6]
                probe2 = cls(y, m, d, hh, mm, ss, us, tz)
                if probe2 == result:
                    result._fold = 1
        else:
            result = tz.fromutc(result)
        return result
1586 1587 1588 1589 1590 1591 1592 1593 1594

    @classmethod
    def fromtimestamp(cls, t, tz=None):
        """Construct a datetime from a POSIX timestamp (like time.time()).

        A timezone info object may be passed in as well.
        """
        _check_tzinfo_arg(tz)

1595
        return cls._fromtimestamp(t, tz is not None, tz)
1596 1597 1598

    @classmethod
    def utcfromtimestamp(cls, t):
1599
        """Construct a naive UTC datetime from a POSIX timestamp."""
1600
        return cls._fromtimestamp(t, True, None)
1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614

    @classmethod
    def now(cls, tz=None):
        "Construct a datetime from time.time() and optional time zone info."
        t = _time.time()
        return cls.fromtimestamp(t, tz)

    @classmethod
    def utcnow(cls):
        "Construct a UTC datetime from time.time()."
        t = _time.time()
        return cls.utcfromtimestamp(t)

    @classmethod
1615
    def combine(cls, date, time, tzinfo=True):
1616 1617 1618 1619 1620
        "Construct a datetime from a given date and a given time."
        if not isinstance(date, _date_class):
            raise TypeError("date argument must be a date instance")
        if not isinstance(time, _time_class):
            raise TypeError("time argument must be a time instance")
1621 1622
        if tzinfo is True:
            tzinfo = time.tzinfo
1623 1624
        return cls(date.year, date.month, date.day,
                   time.hour, time.minute, time.second, time.microsecond,
1625
                   tzinfo, fold=time.fold)
1626

1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651
    @classmethod
    def fromisoformat(cls, date_string):
        """Construct a datetime from the output of datetime.isoformat()."""
        if not isinstance(date_string, str):
            raise TypeError('fromisoformat: argument must be str')

        # Split this at the separator
        dstr = date_string[0:10]
        tstr = date_string[11:]

        try:
            date_components = _parse_isoformat_date(dstr)
        except ValueError:
            raise ValueError('Invalid isoformat string: %s' % date_string)

        if tstr:
            try:
                time_components = _parse_isoformat_time(tstr)
            except ValueError:
                raise ValueError('Invalid isoformat string: %s' % date_string)
        else:
            time_components = [0, 0, 0, 0, None]

        return cls(*(date_components + time_components))

1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664
    def timetuple(self):
        "Return local time tuple compatible with time.localtime()."
        dst = self.dst()
        if dst is None:
            dst = -1
        elif dst:
            dst = 1
        else:
            dst = 0
        return _build_struct_time(self.year, self.month, self.day,
                                  self.hour, self.minute, self.second,
                                  dst)

1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699
    def _mktime(self):
        """Return integer POSIX timestamp."""
        epoch = datetime(1970, 1, 1)
        max_fold_seconds = 24 * 3600
        t = (self - epoch) // timedelta(0, 1)
        def local(u):
            y, m, d, hh, mm, ss = _time.localtime(u)[:6]
            return (datetime(y, m, d, hh, mm, ss) - epoch) // timedelta(0, 1)

        # Our goal is to solve t = local(u) for u.
        a = local(t) - t
        u1 = t - a
        t1 = local(u1)
        if t1 == t:
            # We found one solution, but it may not be the one we need.
            # Look for an earlier solution (if `fold` is 0), or a
            # later one (if `fold` is 1).
            u2 = u1 + (-max_fold_seconds, max_fold_seconds)[self.fold]
            b = local(u2) - u2
            if a == b:
                return u1
        else:
            b = t1 - u1
            assert a != b
        u2 = t - b
        t2 = local(u2)
        if t2 == t:
            return u2
        if t1 == t:
            return u1
        # We have found both offsets a and b, but neither t - a nor t - b is
        # a solution.  This means t is in the gap.
        return (max, min)[self.fold](u1, u2)


1700 1701 1702
    def timestamp(self):
        "Return POSIX timestamp as float"
        if self._tzinfo is None:
1703 1704
            s = self._mktime()
            return s + self.microsecond / 1e6
1705 1706 1707
        else:
            return (self - _EPOCH).total_seconds()

1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722
    def utctimetuple(self):
        "Return UTC time tuple compatible with time.gmtime()."
        offset = self.utcoffset()
        if offset:
            self -= offset
        y, m, d = self.year, self.month, self.day
        hh, mm, ss = self.hour, self.minute, self.second
        return _build_struct_time(y, m, d, hh, mm, ss, 0)

    def date(self):
        "Return the date part."
        return date(self._year, self._month, self._day)

    def time(self):
        "Return the time part, with tzinfo None."
1723
        return time(self.hour, self.minute, self.second, self.microsecond, fold=self.fold)
1724 1725 1726 1727

    def timetz(self):
        "Return the time part, with same tzinfo."
        return time(self.hour, self.minute, self.second, self.microsecond,
1728
                    self._tzinfo, fold=self.fold)
1729 1730

    def replace(self, year=None, month=None, day=None, hour=None,
1731 1732
                minute=None, second=None, microsecond=None, tzinfo=True,
                *, fold=None):
1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749
        """Return a new datetime with new values for the specified fields."""
        if year is None:
            year = self.year
        if month is None:
            month = self.month
        if day is None:
            day = self.day
        if hour is None:
            hour = self.hour
        if minute is None:
            minute = self.minute
        if second is None:
            second = self.second
        if microsecond is None:
            microsecond = self.microsecond
        if tzinfo is True:
            tzinfo = self.tzinfo
1750 1751
        if fold is None:
            fold = self.fold
1752
        return type(self)(year, month, day, hour, minute, second,
1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772
                          microsecond, tzinfo, fold=fold)

    def _local_timezone(self):
        if self.tzinfo is None:
            ts = self._mktime()
        else:
            ts = (self - _EPOCH) // timedelta(seconds=1)
        localtm = _time.localtime(ts)
        local = datetime(*localtm[:6])
        try:
            # Extract TZ data if available
            gmtoff = localtm.tm_gmtoff
            zone = localtm.tm_zone
        except AttributeError:
            delta = local - datetime(*_time.gmtime(ts)[:6])
            zone = _time.strftime('%Z', localtm)
            tz = timezone(delta, zone)
        else:
            tz = timezone(timedelta(seconds=gmtoff), zone)
        return tz
1773

1774 1775
    def astimezone(self, tz=None):
        if tz is None:
1776
            tz = self._local_timezone()
1777
        elif not isinstance(tz, tzinfo):
1778 1779 1780 1781
            raise TypeError("tz argument must be an instance of tzinfo")

        mytz = self.tzinfo
        if mytz is None:
1782
            mytz = self._local_timezone()
1783 1784 1785 1786 1787

        if tz is mytz:
            return self

        # Convert self to UTC, and attach the new time zone object.
1788
        myoffset = mytz.utcoffset(self)
1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807
        if myoffset is None:
            raise ValueError("astimezone() requires an aware datetime")
        utc = (self - myoffset).replace(tzinfo=tz)

        # Convert from UTC to tz's local time.
        return tz.fromutc(utc)

    # Ways to produce a string.

    def ctime(self):
        "Return ctime() style string."
        weekday = self.toordinal() % 7 or 7
        return "%s %s %2d %02d:%02d:%02d %04d" % (
            _DAYNAMES[weekday],
            _MONTHNAMES[self._month],
            self._day,
            self._hour, self._minute, self._second,
            self._year)

1808
    def isoformat(self, sep='T', timespec='auto'):
1809 1810
        """Return the time formatted according to ISO.

1811 1812
        The full format looks like 'YYYY-MM-DD HH:MM:SS.mmmmmm'.
        By default, the fractional part is omitted if self.microsecond == 0.
1813 1814

        If self.tzinfo is not None, the UTC offset is also attached, giving
1815
        giving a full format of 'YYYY-MM-DD HH:MM:SS.mmmmmm+HH:MM'.
1816 1817 1818

        Optional argument sep specifies the separator between date and
        time, default 'T'.
1819 1820 1821

        The optional argument timespec specifies the number of additional
        terms of the time to include.
1822
        """
1823 1824
        s = ("%04d-%02d-%02d%c" % (self._year, self._month, self._day, sep) +
             _format_time(self._hour, self._minute, self._second,
1825 1826
                          self._microsecond, timespec))

1827
        off = self.utcoffset()
1828 1829 1830 1831
        tz = _format_offset(off)
        if tz:
            s += tz

1832 1833 1834 1835
        return s

    def __repr__(self):
        """Convert to formal string, for repr()."""
1836
        L = [self._year, self._month, self._day,  # These are never zero
1837 1838 1839 1840 1841
             self._hour, self._minute, self._second, self._microsecond]
        if L[-1] == 0:
            del L[-1]
        if L[-1] == 0:
            del L[-1]
1842 1843 1844
        s = "%s.%s(%s)" % (self.__class__.__module__,
                           self.__class__.__qualname__,
                           ", ".join(map(str, L)))
1845 1846 1847
        if self._tzinfo is not None:
            assert s[-1:] == ")"
            s = s[:-1] + ", tzinfo=%r" % self._tzinfo + ")"
1848 1849 1850
        if self._fold:
            assert s[-1:] == ")"
            s = s[:-1] + ", fold=1)"
1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863
        return s

    def __str__(self):
        "Convert to string, for str()."
        return self.isoformat(sep=' ')

    @classmethod
    def strptime(cls, date_string, format):
        'string, format -> new datetime parsed from a string (like time.strptime()).'
        import _strptime
        return _strptime._strptime_datetime(cls, date_string, format)

    def utcoffset(self):
1864
        """Return the timezone offset as timedelta positive east of UTC (negative west of
1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878
        UTC)."""
        if self._tzinfo is None:
            return None
        offset = self._tzinfo.utcoffset(self)
        _check_utc_offset("utcoffset", offset)
        return offset

    def tzname(self):
        """Return the timezone name.

        Note that the name is 100% informational -- there's no requirement that
        it mean anything in particular. For example, "GMT", "UTC", "-500",
        "-5:00", "EDT", "US/Eastern", "America/New York" are all valid replies.
        """
1879 1880 1881
        if self._tzinfo is None:
            return None
        name = self._tzinfo.tzname(self)
1882 1883 1884 1885
        _check_tzname(name)
        return name

    def dst(self):
1886 1887
        """Return 0 if DST is not in effect, or the DST offset (as timedelta
        positive eastward) if DST is in effect.
1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903

        This is purely informational; the DST offset has already been added to
        the UTC offset returned by utcoffset() if applicable, so there's no
        need to consult dst() unless you're interested in displaying the DST
        info.
        """
        if self._tzinfo is None:
            return None
        offset = self._tzinfo.dst(self)
        _check_utc_offset("dst", offset)
        return offset

    # Comparisons of datetime objects with other.

    def __eq__(self, other):
        if isinstance(other, datetime):
1904
            return self._cmp(other, allow_mixed=True) == 0
1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941
        elif not isinstance(other, date):
            return NotImplemented
        else:
            return False

    def __le__(self, other):
        if isinstance(other, datetime):
            return self._cmp(other) <= 0
        elif not isinstance(other, date):
            return NotImplemented
        else:
            _cmperror(self, other)

    def __lt__(self, other):
        if isinstance(other, datetime):
            return self._cmp(other) < 0
        elif not isinstance(other, date):
            return NotImplemented
        else:
            _cmperror(self, other)

    def __ge__(self, other):
        if isinstance(other, datetime):
            return self._cmp(other) >= 0
        elif not isinstance(other, date):
            return NotImplemented
        else:
            _cmperror(self, other)

    def __gt__(self, other):
        if isinstance(other, datetime):
            return self._cmp(other) > 0
        elif not isinstance(other, date):
            return NotImplemented
        else:
            _cmperror(self, other)

1942
    def _cmp(self, other, allow_mixed=False):
1943 1944 1945 1946 1947 1948 1949 1950
        assert isinstance(other, datetime)
        mytz = self._tzinfo
        ottz = other._tzinfo
        myoff = otoff = None

        if mytz is ottz:
            base_compare = True
        else:
1951 1952
            myoff = self.utcoffset()
            otoff = other.utcoffset()
1953 1954 1955 1956 1957 1958
            # Assume that allow_mixed means that we are called from __eq__
            if allow_mixed:
                if myoff != self.replace(fold=not self.fold).utcoffset():
                    return 2
                if otoff != other.replace(fold=not other.fold).utcoffset():
                    return 2
1959 1960 1961 1962 1963 1964
            base_compare = myoff == otoff

        if base_compare:
            return _cmp((self._year, self._month, self._day,
                         self._hour, self._minute, self._second,
                         self._microsecond),
1965 1966 1967
                        (other._year, other._month, other._day,
                         other._hour, other._minute, other._second,
                         other._microsecond))
1968
        if myoff is None or otoff is None:
1969 1970 1971 1972
            if allow_mixed:
                return 2 # arbitrary non-zero value
            else:
                raise TypeError("cannot compare naive and aware datetimes")
1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024
        # XXX What follows could be done more efficiently...
        diff = self - other     # this will take offsets into account
        if diff.days < 0:
            return -1
        return diff and 1 or 0

    def __add__(self, other):
        "Add a datetime and a timedelta."
        if not isinstance(other, timedelta):
            return NotImplemented
        delta = timedelta(self.toordinal(),
                          hours=self._hour,
                          minutes=self._minute,
                          seconds=self._second,
                          microseconds=self._microsecond)
        delta += other
        hour, rem = divmod(delta.seconds, 3600)
        minute, second = divmod(rem, 60)
        if 0 < delta.days <= _MAXORDINAL:
            return datetime.combine(date.fromordinal(delta.days),
                                    time(hour, minute, second,
                                         delta.microseconds,
                                         tzinfo=self._tzinfo))
        raise OverflowError("result out of range")

    __radd__ = __add__

    def __sub__(self, other):
        "Subtract two datetimes, or a datetime and a timedelta."
        if not isinstance(other, datetime):
            if isinstance(other, timedelta):
                return self + -other
            return NotImplemented

        days1 = self.toordinal()
        days2 = other.toordinal()
        secs1 = self._second + self._minute * 60 + self._hour * 3600
        secs2 = other._second + other._minute * 60 + other._hour * 3600
        base = timedelta(days1 - days2,
                         secs1 - secs2,
                         self._microsecond - other._microsecond)
        if self._tzinfo is other._tzinfo:
            return base
        myoff = self.utcoffset()
        otoff = other.utcoffset()
        if myoff == otoff:
            return base
        if myoff is None or otoff is None:
            raise TypeError("cannot mix naive and timezone-aware time")
        return base + otoff - myoff

    def __hash__(self):
2025
        if self._hashcode == -1:
2026 2027 2028 2029 2030
            if self.fold:
                t = self.replace(fold=0)
            else:
                t = self
            tzoff = t.utcoffset()
2031
            if tzoff is None:
2032
                self._hashcode = hash(t._getstate()[0])
2033 2034 2035 2036 2037
            else:
                days = _ymd2ord(self.year, self.month, self.day)
                seconds = self.hour * 3600 + self.minute * 60 + self.second
                self._hashcode = hash(timedelta(days, seconds, self.microsecond) - tzoff)
        return self._hashcode
2038 2039 2040

    # Pickle support.

2041
    def _getstate(self, protocol=3):
2042 2043 2044
        yhi, ylo = divmod(self._year, 256)
        us2, us3 = divmod(self._microsecond, 256)
        us1, us2 = divmod(us2, 256)
2045 2046 2047 2048
        m = self._month
        if self._fold and protocol > 3:
            m += 128
        basestate = bytes([yhi, ylo, m, self._day,
2049 2050 2051 2052 2053 2054 2055 2056
                           self._hour, self._minute, self._second,
                           us1, us2, us3])
        if self._tzinfo is None:
            return (basestate,)
        else:
            return (basestate, self._tzinfo)

    def __setstate(self, string, tzinfo):
2057 2058
        if tzinfo is not None and not isinstance(tzinfo, _tzinfo_class):
            raise TypeError("bad tzinfo state arg")
2059
        (yhi, ylo, m, self._day, self._hour,
2060
         self._minute, self._second, us1, us2, us3) = string
2061 2062 2063 2064 2065 2066
        if m > 127:
            self._fold = 1
            self._month = m - 128
        else:
            self._fold = 0
            self._month = m
2067 2068
        self._year = yhi * 256 + ylo
        self._microsecond = (((us1 << 8) | us2) << 8) | us3
2069
        self._tzinfo = tzinfo
2070

2071 2072
    def __reduce_ex__(self, protocol):
        return (self.__class__, self._getstate(protocol))
2073

2074 2075 2076
    def __reduce__(self):
        return self.__reduce_ex__(2)

2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087

datetime.min = datetime(1, 1, 1)
datetime.max = datetime(9999, 12, 31, 23, 59, 59, 999999)
datetime.resolution = timedelta(microseconds=1)


def _isoweek1monday(year):
    # Helper to calculate the day number of the Monday starting week 1
    # XXX This could be done more efficiently
    THURSDAY = 3
    firstday = _ymd2ord(year, 1, 1)
2088
    firstweekday = (firstday + 6) % 7  # See weekday() above
2089 2090 2091 2092 2093 2094 2095 2096 2097 2098
    week1monday = firstday - firstweekday
    if firstweekday > THURSDAY:
        week1monday += 7
    return week1monday

class timezone(tzinfo):
    __slots__ = '_offset', '_name'

    # Sentinel value to disallow None
    _Omitted = object()
2099 2100 2101 2102 2103 2104
    def __new__(cls, offset, name=_Omitted):
        if not isinstance(offset, timedelta):
            raise TypeError("offset must be a timedelta")
        if name is cls._Omitted:
            if not offset:
                return cls.utc
2105 2106 2107
            name = None
        elif not isinstance(name, str):
            raise TypeError("name must be a string")
2108
        if not cls._minoffset <= offset <= cls._maxoffset:
2109 2110 2111
            raise ValueError("offset must be a timedelta "
                             "strictly between -timedelta(hours=24) and "
                             "timedelta(hours=24).")
2112
        return cls._create(offset, name)
2113

2114 2115 2116 2117
    @classmethod
    def _create(cls, offset, name=None):
        self = tzinfo.__new__(cls)
        self._offset = offset
2118
        self._name = name
2119
        return self
2120 2121 2122 2123 2124 2125 2126 2127

    def __getinitargs__(self):
        """pickle support"""
        if self._name is None:
            return (self._offset,)
        return (self._offset, self._name)

    def __eq__(self, other):
2128 2129
        if type(other) != timezone:
            return False
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        return self._offset == other._offset

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

    def __repr__(self):
        """Convert to formal string, for repr().

        >>> tz = timezone.utc
        >>> repr(tz)
        'datetime.timezone.utc'
        >>> tz = timezone(timedelta(hours=-5), 'EST')
        >>> repr(tz)
        "datetime.timezone(datetime.timedelta(-1, 68400), 'EST')"
        """
        if self is self.utc:
            return 'datetime.timezone.utc'
        if self._name is None:
2148 2149 2150 2151 2152 2153
            return "%s.%s(%r)" % (self.__class__.__module__,
                                  self.__class__.__qualname__,
                                  self._offset)
        return "%s.%s(%r, %r)" % (self.__class__.__module__,
                                  self.__class__.__qualname__,
                                  self._offset, self._name)
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    def __str__(self):
        return self.tzname(None)

    def utcoffset(self, dt):
        if isinstance(dt, datetime) or dt is None:
            return self._offset
        raise TypeError("utcoffset() argument must be a datetime instance"
                        " or None")

    def tzname(self, dt):
        if isinstance(dt, datetime) or dt is None:
            if self._name is None:
                return self._name_from_offset(self._offset)
            return self._name
        raise TypeError("tzname() argument must be a datetime instance"
                        " or None")

    def dst(self, dt):
        if isinstance(dt, datetime) or dt is None:
            return None
        raise TypeError("dst() argument must be a datetime instance"
                        " or None")

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

    _maxoffset = timedelta(hours=23, minutes=59)
    _minoffset = -_maxoffset

    @staticmethod
    def _name_from_offset(delta):
2192 2193
        if not delta:
            return 'UTC'
2194 2195 2196 2197 2198 2199
        if delta < timedelta(0):
            sign = '-'
            delta = -delta
        else:
            sign = '+'
        hours, rest = divmod(delta, timedelta(hours=1))
2200 2201 2202 2203 2204 2205 2206 2207 2208
        minutes, rest = divmod(rest, timedelta(minutes=1))
        seconds = rest.seconds
        microseconds = rest.microseconds
        if microseconds:
            return (f'UTC{sign}{hours:02d}:{minutes:02d}:{seconds:02d}'
                    f'.{microseconds:06d}')
        if seconds:
            return f'UTC{sign}{hours:02d}:{minutes:02d}:{seconds:02d}'
        return f'UTC{sign}{hours:02d}:{minutes:02d}'
2209

2210 2211 2212
timezone.utc = timezone._create(timedelta(0))
timezone.min = timezone._create(timezone._minoffset)
timezone.max = timezone._create(timezone._maxoffset)
2213
_EPOCH = datetime(1970, 1, 1, tzinfo=timezone.utc)
2214

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# Some time zone algebra.  For a datetime x, let
#     x.n = x stripped of its timezone -- its naive time.
#     x.o = x.utcoffset(), and assuming that doesn't raise an exception or
#           return None
#     x.d = x.dst(), and assuming that doesn't raise an exception or
#           return None
#     x.s = x's standard offset, x.o - x.d
#
# Now some derived rules, where k is a duration (timedelta).
#
# 1. x.o = x.s + x.d
#    This follows from the definition of x.s.
#
# 2. If x and y have the same tzinfo member, x.s = y.s.
#    This is actually a requirement, an assumption we need to make about
#    sane tzinfo classes.
#
# 3. The naive UTC time corresponding to x is x.n - x.o.
#    This is again a requirement for a sane tzinfo class.
#
# 4. (x+k).s = x.s
#    This follows from #2, and that datimetimetz+timedelta preserves tzinfo.
#
# 5. (x+k).n = x.n + k
#    Again follows from how arithmetic is defined.
#
# Now we can explain tz.fromutc(x).  Let's assume it's an interesting case
# (meaning that the various tzinfo methods exist, and don't blow up or return
# None when called).
#
# The function wants to return a datetime y with timezone tz, equivalent to x.
# x is already in UTC.
#
# By #3, we want
#
#     y.n - y.o = x.n                             [1]
#
# The algorithm starts by attaching tz to x.n, and calling that y.  So
# x.n = y.n at the start.  Then it wants to add a duration k to y, so that [1]
# becomes true; in effect, we want to solve [2] for k:
#
#    (y+k).n - (y+k).o = x.n                      [2]
#
# By #1, this is the same as
#
#    (y+k).n - ((y+k).s + (y+k).d) = x.n          [3]
#
# By #5, (y+k).n = y.n + k, which equals x.n + k because x.n=y.n at the start.
# Substituting that into [3],
#
#    x.n + k - (y+k).s - (y+k).d = x.n; the x.n terms cancel, leaving
#    k - (y+k).s - (y+k).d = 0; rearranging,
#    k = (y+k).s - (y+k).d; by #4, (y+k).s == y.s, so
#    k = y.s - (y+k).d
#
# On the RHS, (y+k).d can't be computed directly, but y.s can be, and we
# approximate k by ignoring the (y+k).d term at first.  Note that k can't be
# very large, since all offset-returning methods return a duration of magnitude
# less than 24 hours.  For that reason, if y is firmly in std time, (y+k).d must
# be 0, so ignoring it has no consequence then.
#
# In any case, the new value is
#
#     z = y + y.s                                 [4]
#
# It's helpful to step back at look at [4] from a higher level:  it's simply
# mapping from UTC to tz's standard time.
#
# At this point, if
#
#     z.n - z.o = x.n                             [5]
#
# we have an equivalent time, and are almost done.  The insecurity here is
# at the start of daylight time.  Picture US Eastern for concreteness.  The wall
# time jumps from 1:59 to 3:00, and wall hours of the form 2:MM don't make good
# sense then.  The docs ask that an Eastern tzinfo class consider such a time to
# be EDT (because it's "after 2"), which is a redundant spelling of 1:MM EST
# on the day DST starts.  We want to return the 1:MM EST spelling because that's
# the only spelling that makes sense on the local wall clock.
#
# In fact, if [5] holds at this point, we do have the standard-time spelling,
# but that takes a bit of proof.  We first prove a stronger result.  What's the
# difference between the LHS and RHS of [5]?  Let
#
#     diff = x.n - (z.n - z.o)                    [6]
#
# Now
#     z.n =                       by [4]
#     (y + y.s).n =               by #5
#     y.n + y.s =                 since y.n = x.n
#     x.n + y.s =                 since z and y are have the same tzinfo member,
#                                     y.s = z.s by #2
#     x.n + z.s
#
# Plugging that back into [6] gives
#
#     diff =
#     x.n - ((x.n + z.s) - z.o) =     expanding
#     x.n - x.n - z.s + z.o =         cancelling
#     - z.s + z.o =                   by #2
#     z.d
#
# So diff = z.d.
#
# If [5] is true now, diff = 0, so z.d = 0 too, and we have the standard-time
# spelling we wanted in the endcase described above.  We're done.  Contrarily,
# if z.d = 0, then we have a UTC equivalent, and are also done.
#
# If [5] is not true now, diff = z.d != 0, and z.d is the offset we need to
# add to z (in effect, z is in tz's standard time, and we need to shift the
# local clock into tz's daylight time).
#
# Let
#
#     z' = z + z.d = z + diff                     [7]
#
# and we can again ask whether
#
#     z'.n - z'.o = x.n                           [8]
#
# If so, we're done.  If not, the tzinfo class is insane, according to the
# assumptions we've made.  This also requires a bit of proof.  As before, let's
# compute the difference between the LHS and RHS of [8] (and skipping some of
# the justifications for the kinds of substitutions we've done several times
# already):
#
#     diff' = x.n - (z'.n - z'.o) =           replacing z'.n via [7]
#             x.n  - (z.n + diff - z'.o) =    replacing diff via [6]
#             x.n - (z.n + x.n - (z.n - z.o) - z'.o) =
#             x.n - z.n - x.n + z.n - z.o + z'.o =    cancel x.n
#             - z.n + z.n - z.o + z'.o =              cancel z.n
#             - z.o + z'.o =                      #1 twice
#             -z.s - z.d + z'.s + z'.d =          z and z' have same tzinfo
#             z'.d - z.d
#
# So z' is UTC-equivalent to x iff z'.d = z.d at this point.  If they are equal,
# we've found the UTC-equivalent so are done.  In fact, we stop with [7] and
# return z', not bothering to compute z'.d.
#
# How could z.d and z'd differ?  z' = z + z.d [7], so merely moving z' by
# a dst() offset, and starting *from* a time already in DST (we know z.d != 0),
# would have to change the result dst() returns:  we start in DST, and moving
# a little further into it takes us out of DST.
#
# There isn't a sane case where this can happen.  The closest it gets is at
# the end of DST, where there's an hour in UTC with no spelling in a hybrid
# tzinfo class.  In US Eastern, that's 5:MM UTC = 0:MM EST = 1:MM EDT.  During
# that hour, on an Eastern clock 1:MM is taken as being in standard time (6:MM
# UTC) because the docs insist on that, but 0:MM is taken as being in daylight
# time (4:MM UTC).  There is no local time mapping to 5:MM UTC.  The local
# clock jumps from 1:59 back to 1:00 again, and repeats the 1:MM hour in
# standard time.  Since that's what the local clock *does*, we want to map both
# UTC hours 5:MM and 6:MM to 1:MM Eastern.  The result is ambiguous
# in local time, but so it goes -- it's the way the local clock works.
#
# When x = 5:MM UTC is the input to this algorithm, x.o=0, y.o=-5 and y.d=0,
# so z=0:MM.  z.d=60 (minutes) then, so [5] doesn't hold and we keep going.
# z' = z + z.d = 1:MM then, and z'.d=0, and z'.d - z.d = -60 != 0 so [8]
# (correctly) concludes that z' is not UTC-equivalent to x.
#
# Because we know z.d said z was in daylight time (else [5] would have held and
# we would have stopped then), and we know z.d != z'.d (else [8] would have held
# and we have stopped then), and there are only 2 possible values dst() can
# return in Eastern, it follows that z'.d must be 0 (which it is in the example,
# but the reasoning doesn't depend on the example -- it depends on there being
# two possible dst() outcomes, one zero and the other non-zero).  Therefore
# z' must be in standard time, and is the spelling we want in this case.
#
# Note again that z' is not UTC-equivalent as far as the hybrid tzinfo class is
# concerned (because it takes z' as being in standard time rather than the
# daylight time we intend here), but returning it gives the real-life "local
# clock repeats an hour" behavior when mapping the "unspellable" UTC hour into
# tz.
#
# When the input is 6:MM, z=1:MM and z.d=0, and we stop at once, again with
# the 1:MM standard time spelling we want.
#
# So how can this break?  One of the assumptions must be violated.  Two
# possibilities:
#
# 1) [2] effectively says that y.s is invariant across all y belong to a given
#    time zone.  This isn't true if, for political reasons or continental drift,
#    a region decides to change its base offset from UTC.
#
# 2) There may be versions of "double daylight" time where the tail end of
#    the analysis gives up a step too early.  I haven't thought about that
#    enough to say.
#
# In any case, it's clear that the default fromutc() is strong enough to handle
# "almost all" time zones:  so long as the standard offset is invariant, it
# doesn't matter if daylight time transition points change from year to year, or
# if daylight time is skipped in some years; it doesn't matter how large or
# small dst() may get within its bounds; and it doesn't even matter if some
# perverse time zone returns a negative dst()).  So a breaking case must be
# pretty bizarre, and a tzinfo subclass can override fromutc() if it is.
2410 2411 2412

try:
    from _datetime import *
2413
except ImportError:
2414 2415 2416
    pass
else:
    # Clean up unused names
2417 2418 2419 2420 2421
    del (_DAYNAMES, _DAYS_BEFORE_MONTH, _DAYS_IN_MONTH, _DI100Y, _DI400Y,
         _DI4Y, _EPOCH, _MAXORDINAL, _MONTHNAMES, _build_struct_time,
         _check_date_fields, _check_int_field, _check_time_fields,
         _check_tzinfo_arg, _check_tzname, _check_utc_offset, _cmp, _cmperror,
         _date_class, _days_before_month, _days_before_year, _days_in_month,
2422 2423 2424 2425
         _format_time, _format_offset, _is_leap, _isoweek1monday, _math,
         _ord2ymd, _time, _time_class, _tzinfo_class, _wrap_strftime, _ymd2ord,
         _divide_and_round, _parse_isoformat_date, _parse_isoformat_time,
         _parse_hh_mm_ss_ff)
2426 2427 2428 2429 2430
    # XXX Since import * above excludes names that start with _,
    # docstring does not get overwritten. In the future, it may be
    # appropriate to maintain a single module level docstring and
    # remove the following line.
    from _datetime import __doc__