Current File : //lib64/python3.6/datetime.py
"""Concrete date/time and related types.

See http://www.iana.org/time-zones/repository/tz-link.html for
time zone and DST data sources.
"""

import time as _time
import math as _math
import sys

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

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

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

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

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

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

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

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

def _days_before_month(year, month):
    "year, month -> number of days in year preceding first day of month."
    assert 1 <= month <= 12, '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))

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)

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

    # 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 = '-'
                                h, m = divmod(offset, timedelta(hours=1))
                                assert not m % timedelta(minutes=1), "whole minute"
                                m //= timedelta(minutes=1)
                                zreplace = '%c%02d%02d' % (sign, h, m)
                    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)

# 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.
# Else offset is checked for being in range, and a whole # of minutes.
# 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 offset.microseconds:
        raise ValueError("tzinfo.%s() must return a whole number "
                         "of seconds, got %s" % (name, offset))
    if not -timedelta(1) < offset < timedelta(1):
        raise ValueError("%s()=%s, must be strictly between "
                         "-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')

def _check_date_fields(year, month, day):
    year = _check_int_field(year)
    month = _check_int_field(month)
    day = _check_int_field(day)
    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)
    return year, month, day

def _check_time_fields(hour, minute, second, microsecond, fold):
    hour = _check_int_field(hour)
    minute = _check_int_field(minute)
    second = _check_int_field(second)
    microsecond = _check_int_field(microsecond)
    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)
    if fold not in (0, 1):
        raise ValueError('fold must be either 0 or 1', fold)
    return hour, minute, second, microsecond, fold

def _check_tzinfo_arg(tz):
    if tz is not None and not isinstance(tz, tzinfo):
        raise TypeError("tzinfo argument must be None or of a tzinfo subclass")

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

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

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

    return q


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

    Supported operators:

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

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

    Representation: (days, seconds, microseconds).  Why?  Because I
    felt like it.
    """
    __slots__ = '_days', '_seconds', '_microseconds', '_hashcode'

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

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

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

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

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

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

    def __repr__(self):
        if self._microseconds:
            return "%s.%s(%d, %d, %d)" % (self.__class__.__module__,
                                          self.__class__.__qualname__,
                                          self._days,
                                          self._seconds,
                                          self._microseconds)
        if self._seconds:
            return "%s.%s(%d, %d)" % (self.__class__.__module__,
                                      self.__class__.__qualname__,
                                      self._days,
                                      self._seconds)
        return "%s.%s(%d)" % (self.__class__.__module__,
                              self.__class__.__qualname__,
                              self._days)

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

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

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

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

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

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

    __radd__ = __add__

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

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

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

    def __pos__(self):
        return self

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

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

    __rmul__ = __mul__

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

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

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

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

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

    # Comparisons of timedelta objects with other.

    def __eq__(self, other):
        if isinstance(other, timedelta):
            return self._cmp(other) == 0
        else:
            return 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):
        if self._hashcode == -1:
            self._hashcode = hash(self._getstate())
        return self._hashcode

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

    # Pickle support.

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

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

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

class date:
    """Concrete date type.

    Constructors:

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

    Operators:

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

    Methods:

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

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

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

        Arguments:

        year, month, day (required, base 1)
        """
        if (month is None and
            isinstance(year, (bytes, str)) and len(year) == 4 and
            1 <= ord(year[2:3]) <= 12):
            # Pickle support
            if isinstance(year, str):
                try:
                    year = year.encode('latin1')
                except UnicodeEncodeError:
                    # More informative error message.
                    raise ValueError(
                        "Failed to encode latin1 string when unpickling "
                        "a date object. "
                        "pickle.load(data, encoding='latin1') is assumed.")
            self = object.__new__(cls)
            self.__setstate(year)
            self._hashcode = -1
            return self
        year, month, day = _check_date_fields(year, month, day)
        self = object.__new__(cls)
        self._year = year
        self._month = month
        self._day = day
        self._hashcode = -1
        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):
        """Construct a date from a proleptic Gregorian ordinal.

        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)

    # 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)'
        """
        return "%s.%s(%d, %d, %d)" % (self.__class__.__module__,
                                      self.__class__.__qualname__,
                                      self._year,
                                      self._month,
                                      self._day)
    # 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):
        if not isinstance(fmt, str):
            raise TypeError("must be str, not %s" % type(fmt).__name__)
        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

    # Standard conversions, __eq__, __le__, __lt__, __ge__, __gt__,
    # __hash__ (and helpers)

    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
        return type(self)(year, month, day)

    # 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."
        if self._hashcode == -1:
            self._hashcode = hash(self._getstate())
        return self._hashcode

    # 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
        (used with permission)
        """
        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.

    def _getstate(self):
        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

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

_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)


class tzinfo:
    """Abstract base class for time zone info classes.

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

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

    def utcoffset(self, dt):
        "datetime -> minutes east of UTC (negative for west of UTC)"
        raise NotImplementedError("tzinfo subclass must override utcoffset()")

    def dst(self, dt):
        """datetime -> DST offset in minutes east of UTC.

        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__
    __eq__, __le__, __lt__, __ge__, __gt__, __hash__

    Methods:

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

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

    def __new__(cls, hour=0, minute=0, second=0, microsecond=0, tzinfo=None, *, fold=0):
        """Constructor.

        Arguments:

        hour, minute (required)
        second, microsecond (default to zero)
        tzinfo (default to None)
        fold (keyword only, default to zero)
        """
        if (isinstance(hour, (bytes, str)) and len(hour) == 6 and
            ord(hour[0:1])&0x7F < 24):
            # Pickle support
            if isinstance(hour, str):
                try:
                    hour = hour.encode('latin1')
                except UnicodeEncodeError:
                    # More informative error message.
                    raise ValueError(
                        "Failed to encode latin1 string when unpickling "
                        "a time object. "
                        "pickle.load(data, encoding='latin1') is assumed.")
            self = object.__new__(cls)
            self.__setstate(hour, minute or None)
            self._hashcode = -1
            return self
        hour, minute, second, microsecond, fold = _check_time_fields(
            hour, minute, second, microsecond, fold)
        _check_tzinfo_arg(tzinfo)
        self = object.__new__(cls)
        self._hour = hour
        self._minute = minute
        self._second = second
        self._microsecond = microsecond
        self._tzinfo = tzinfo
        self._hashcode = -1
        self._fold = fold
        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

    @property
    def fold(self):
        return self._fold

    # Standard conversions, __hash__ (and helpers)

    # Comparisons of time objects with other.

    def __eq__(self, other):
        if isinstance(other, time):
            return self._cmp(other, allow_mixed=True) == 0
        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)

    def _cmp(self, other, allow_mixed=False):
        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),
                        (other._hour, other._minute, other._second,
                         other._microsecond))
        if myoff is None or otoff is None:
            if allow_mixed:
                return 2 # arbitrary non-zero value
            else:
                raise TypeError("cannot compare naive and aware times")
        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."""
        if self._hashcode == -1:
            if self.fold:
                t = self.replace(fold=0)
            else:
                t = self
            tzoff = t.utcoffset()
            if not tzoff:  # zero or None
                self._hashcode = hash(t._getstate()[0])
            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

    # Conversion to string

    def _tzstr(self, sep=":"):
        """Return formatted timezone offset (+xx:xx) or None."""
        off = self.utcoffset()
        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))
            assert 0 <= hh < 24
            off = "%s%02d%s%02d" % (sign, hh, sep, mm)
            if ss:
                off += ':%02d' % ss.seconds
        return off

    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 = ""
        s= "%s.%s(%d, %d%s)" % (self.__class__.__module__,
                                self.__class__.__qualname__,
                                self._hour, self._minute, s)
        if self._tzinfo is not None:
            assert s[-1:] == ")"
            s = s[:-1] + ", tzinfo=%r" % self._tzinfo + ")"
        if self._fold:
            assert s[-1:] == ")"
            s = s[:-1] + ", fold=1)"
        return s

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

        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.
        """
        s = _format_time(self._hour, self._minute, self._second,
                          self._microsecond, timespec)
        tz = self._tzstr()
        if tz:
            s += tz
        return s

    __str__ = isoformat

    def strftime(self, fmt):
        """Format using strftime().  The date part of the timestamp passed
        to underlying strftime should not be used.
        """
        # The year must be >= 1000 else Python's strftime implementation
        # 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):
        if not isinstance(fmt, str):
            raise TypeError("must be str, not %s" % type(fmt).__name__)
        if len(fmt) != 0:
            return self.strftime(fmt)
        return str(self)

    # Timezone functions

    def utcoffset(self):
        """Return the timezone offset in minutes east of UTC (negative west of
        UTC)."""
        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):
        """Return 0 if DST is not in effect, or the DST offset (in minutes
        eastward) if DST is in effect.

        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,
                tzinfo=True, *, fold=None):
        """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
        if fold is None:
            fold = self._fold
        return type(self)(hour, minute, second, microsecond, tzinfo, fold=fold)

    # Pickle support.

    def _getstate(self, protocol=3):
        us2, us3 = divmod(self._microsecond, 256)
        us1, us2 = divmod(us2, 256)
        h = self._hour
        if self._fold and protocol > 3:
            h += 128
        basestate = bytes([h, self._minute, self._second,
                           us1, us2, us3])
        if self._tzinfo is None:
            return (basestate,)
        else:
            return (basestate, self._tzinfo)

    def __setstate(self, string, tzinfo):
        if tzinfo is not None and not isinstance(tzinfo, _tzinfo_class):
            raise TypeError("bad tzinfo state arg")
        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
        self._microsecond = (((us1 << 8) | us2) << 8) | us3
        self._tzinfo = tzinfo

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

    def __reduce__(self):
        return self.__reduce_ex__(2)

_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
    instance of a tzinfo subclass. The remaining arguments may be ints.
    """
    __slots__ = date.__slots__ + time.__slots__

    def __new__(cls, year, month=None, day=None, hour=0, minute=0, second=0,
                microsecond=0, tzinfo=None, *, fold=0):
        if (isinstance(year, (bytes, str)) and len(year) == 10 and
            1 <= ord(year[2:3])&0x7F <= 12):
            # Pickle support
            if isinstance(year, str):
                try:
                    year = bytes(year, 'latin1')
                except UnicodeEncodeError:
                    # More informative error message.
                    raise ValueError(
                        "Failed to encode latin1 string when unpickling "
                        "a datetime object. "
                        "pickle.load(data, encoding='latin1') is assumed.")
            self = object.__new__(cls)
            self.__setstate(year, month)
            self._hashcode = -1
            return self
        year, month, day = _check_date_fields(year, month, day)
        hour, minute, second, microsecond, fold = _check_time_fields(
            hour, minute, second, microsecond, fold)
        _check_tzinfo_arg(tzinfo)
        self = object.__new__(cls)
        self._year = year
        self._month = month
        self._day = day
        self._hour = hour
        self._minute = minute
        self._second = second
        self._microsecond = microsecond
        self._tzinfo = tzinfo
        self._hashcode = -1
        self._fold = fold
        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

    @property
    def fold(self):
        return self._fold

    @classmethod
    def _fromtimestamp(cls, t, utc, tz):
        """Construct a datetime from a POSIX timestamp (like time.time()).

        A timezone info object may be passed in as well.
        """
        frac, t = _math.modf(t)
        us = round(frac * 1e6)
        if us >= 1000000:
            t += 1
            us -= 1000000
        elif us < 0:
            t -= 1
            us += 1000000

        converter = _time.gmtime if utc else _time.localtime
        y, m, d, hh, mm, ss, weekday, jday, dst = converter(t)
        ss = min(ss, 59)    # clamp out leap seconds if the platform has them
        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

            # On Windows localtime_s throws an OSError for negative values,
            # thus we can't perform fold detection for values of time less
            # than the max time fold. See comments in _datetimemodule's
            # version of this method for more details.
            if t < max_fold_seconds and sys.platform.startswith("win"):
                return result

            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

    @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)

        return cls._fromtimestamp(t, tz is not None, tz)

    @classmethod
    def utcfromtimestamp(cls, t):
        """Construct a naive UTC datetime from a POSIX timestamp."""
        return cls._fromtimestamp(t, True, None)

    @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
    def combine(cls, date, time, tzinfo=True):
        "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")
        if tzinfo is True:
            tzinfo = time.tzinfo
        return cls(date.year, date.month, date.day,
                   time.hour, time.minute, time.second, time.microsecond,
                   tzinfo, fold=time.fold)

    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)

    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)


    def timestamp(self):
        "Return POSIX timestamp as float"
        if self._tzinfo is None:
            s = self._mktime()
            return s + self.microsecond / 1e6
        else:
            return (self - _EPOCH).total_seconds()

    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."
        return time(self.hour, self.minute, self.second, self.microsecond, fold=self.fold)

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

    def replace(self, year=None, month=None, day=None, hour=None,
                minute=None, second=None, microsecond=None, tzinfo=True,
                *, fold=None):
        """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
        if fold is None:
            fold = self.fold
        return type(self)(year, month, day, hour, minute, second,
                          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

    def astimezone(self, tz=None):
        if tz is None:
            tz = self._local_timezone()
        elif not isinstance(tz, tzinfo):
            raise TypeError("tz argument must be an instance of tzinfo")

        mytz = self.tzinfo
        if mytz is None:
            mytz = self._local_timezone()
            myoffset = mytz.utcoffset(self)
        else:
            myoffset = mytz.utcoffset(self)
            if myoffset is None:
                mytz = self.replace(tzinfo=None)._local_timezone()
                myoffset = mytz.utcoffset(self)

        if tz is mytz:
            return self

        # Convert self to UTC, and attach the new time zone object.
        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)

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

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

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

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

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

        off = self.utcoffset()
        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:
                assert not ss.microseconds
                s += ":%02d" % ss.seconds
        return s

    def __repr__(self):
        """Convert to formal string, for repr()."""
        L = [self._year, self._month, self._day,  # These are never zero
             self._hour, self._minute, self._second, self._microsecond]
        if L[-1] == 0:
            del L[-1]
        if L[-1] == 0:
            del L[-1]
        s = "%s.%s(%s)" % (self.__class__.__module__,
                           self.__class__.__qualname__,
                           ", ".join(map(str, L)))
        if self._tzinfo is not None:
            assert s[-1:] == ")"
            s = s[:-1] + ", tzinfo=%r" % self._tzinfo + ")"
        if self._fold:
            assert s[-1:] == ")"
            s = s[:-1] + ", fold=1)"
        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):
        """Return the timezone offset in minutes east of UTC (negative west of
        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.
        """
        if self._tzinfo is None:
            return None
        name = self._tzinfo.tzname(self)
        _check_tzname(name)
        return name

    def dst(self):
        """Return 0 if DST is not in effect, or the DST offset (in minutes
        eastward) if DST is in effect.

        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):
            return self._cmp(other, allow_mixed=True) == 0
        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)

    def _cmp(self, other, allow_mixed=False):
        assert isinstance(other, datetime)
        mytz = self._tzinfo
        ottz = other._tzinfo
        myoff = otoff = None

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

        if base_compare:
            return _cmp((self._year, self._month, self._day,
                         self._hour, self._minute, self._second,
                         self._microsecond),
                        (other._year, other._month, other._day,
                         other._hour, other._minute, other._second,
                         other._microsecond))
        if myoff is None or otoff is None:
            if allow_mixed:
                return 2 # arbitrary non-zero value
            else:
                raise TypeError("cannot compare naive and aware datetimes")
        # 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):
        if self._hashcode == -1:
            if self.fold:
                t = self.replace(fold=0)
            else:
                t = self
            tzoff = t.utcoffset()
            if tzoff is None:
                self._hashcode = hash(t._getstate()[0])
            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

    # Pickle support.

    def _getstate(self, protocol=3):
        yhi, ylo = divmod(self._year, 256)
        us2, us3 = divmod(self._microsecond, 256)
        us1, us2 = divmod(us2, 256)
        m = self._month
        if self._fold and protocol > 3:
            m += 128
        basestate = bytes([yhi, ylo, m, self._day,
                           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):
        if tzinfo is not None and not isinstance(tzinfo, _tzinfo_class):
            raise TypeError("bad tzinfo state arg")
        (yhi, ylo, m, self._day, self._hour,
         self._minute, self._second, us1, us2, us3) = string
        if m > 127:
            self._fold = 1
            self._month = m - 128
        else:
            self._fold = 0
            self._month = m
        self._year = yhi * 256 + ylo
        self._microsecond = (((us1 << 8) | us2) << 8) | us3
        self._tzinfo = tzinfo

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

    def __reduce__(self):
        return self.__reduce_ex__(2)


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)
    firstweekday = (firstday + 6) % 7  # See weekday() above
    week1monday = firstday - firstweekday
    if firstweekday > THURSDAY:
        week1monday += 7
    return week1monday

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

    # Sentinel value to disallow None
    _Omitted = object()
    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
            name = None
        elif not isinstance(name, str):
            raise TypeError("name must be a string")
        if not cls._minoffset <= offset <= cls._maxoffset:
            raise ValueError("offset must be a timedelta "
                             "strictly between -timedelta(hours=24) and "
                             "timedelta(hours=24).")
        if (offset.microseconds != 0 or offset.seconds % 60 != 0):
            raise ValueError("offset must be a timedelta "
                             "representing a whole number of minutes")
        return cls._create(offset, name)

    @classmethod
    def _create(cls, offset, name=None):
        self = tzinfo.__new__(cls)
        self._offset = offset
        self._name = name
        return self

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

    def __eq__(self, other):
        if type(other) != timezone:
            return False
        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:
            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)

    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):
        if not delta:
            return 'UTC'
        if delta < timedelta(0):
            sign = '-'
            delta = -delta
        else:
            sign = '+'
        hours, rest = divmod(delta, timedelta(hours=1))
        minutes = rest // timedelta(minutes=1)
        return 'UTC{}{:02d}:{:02d}'.format(sign, hours, minutes)

timezone.utc = timezone._create(timedelta(0))
timezone.min = timezone._create(timezone._minoffset)
timezone.max = timezone._create(timezone._maxoffset)
_EPOCH = datetime(1970, 1, 1, tzinfo=timezone.utc)

# 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.

try:
    from _datetime import *
except ImportError:
    pass
else:
    # Clean up unused names
    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,
         _format_time, _is_leap, _isoweek1monday, _math, _ord2ymd,
         _time, _time_class, _tzinfo_class, _wrap_strftime, _ymd2ord,
         _divide_and_round)
    # 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__
A Beginner's Facts Playing Casino Slots

A Beginner’s Facts Playing Casino Slots

How In Order To Play Slots Find Out The Rules Involving Slot Machines

In most modern devices, the number regarding lines that will pay off for” “a gamer depends on the particular number of credits (money or coin-in) wagered on a new particular spin. Those first machines will be paid out based about the mechanical features of the device. However, modern equipment not merely often employ video reels yet also make full use of random number generators instead of mechanical operation to determine champions.

The strategy of progressive jackpots dates back to be able to 1986 when the particular Megabucks machine seemed to be introduced, allowing earnings to accumulate until the player hit the jackpot. Today, many popular progressive slot machines are connected around multiple casinos, more increasing the jackpot feature potential. Classic slot machines, often referred to be able to as 3-reel slot machine games, provide quick plus satisfying action. These games are great for players who appreciate easy and fast-paced game play. With their standard design and mechanics, classic slots charm to both newbies and seasoned gamers. Typically, these slot machines feature one to three paylines, making them easy in order to understand and enjoy.

Slot Tip 4:  Always Enjoy Within Your Budget And Become Willing To Lower Your Guess Or Stop Playing If You Struck A Limit

Bets can be as minimal as 1c each spin, playing with your local on line casino or online is usually easier than at any time to access your bank roll. Modern slot” “equipment games trace to large and unique machines manufactured by an enthusiastic mechanic (and tinkerer) of typically the late 19th millennium, Charles Fey. The machine that Fey created was very simple but complex in concept, and also this machine was the Liberty Bell. Note that these online slot machine game strategies work finest with games that have the lowest volatility since you will need to adjust the dimensions of the gamble as you proceed. Scatter symbols are usually special icons of which can fork out irregardless of their place on the reels, often triggering reward features mostbet.

  • It’s quick to customize amount of credits you’d like to participate in too.
  • Because of the long odds, seeking to win a huge jackpot is most likely unrealistic.
  • You’ll learn what to be able to expect and exactly how to adjust your current playing style to be able to the features of a particular slot device game.
  • For example, the Blood Suckers slot with the RTP of 98% returns to all players $98 of $100 expended inside; $2 is usually the house edge.
  • Therefore, carry out not rush to immediately place actual bets, but initial, get accustomed to the position controls.

Now, your house edge will vary with respect to the” “video game that players opt to play, and typically the total bet amount which is placed. Developers are continually striving to innovate and even create new ways for players to be able to win in a great attempt to retain player interest. One of those innovations seemed to be respins or cascading down symbols – which in turn are certain emblems which cause reels to respin to produce bigger wins or multipliers with outrageous symbols potentially. With all the success and recognition, there is usually one thing which includes always been some sort of given for position machines. In essence, they have been income generators regarding casinos for several years in spite of featuring large plus relatively frequent affiliate payouts. Once you’ve set your desired bet, press the “Spin” button or draw the lever (if available) to trigger the spin.

Beginners Guide: How To Play Slots Regarding Dummies

Keeping with the straightforward nature of playing slots at on the web casinos, if gamers have trouble, these types of websites offer consumer service. The special offers that online casinos offer purely relate with in-game aspects such as bonus money in addition to free spins for slots. The appeal of slot machines is the possiblity to hit big which has a jackpot payday. Over the years, developers have continued to find ways to boost the jackpots regarding players without stopping too much of the edge for your casino.

The most realistic strategy when betting on slot machines is bankroll management; its essence is usually rather simple. Each player can devote a certain amount on bets, in addition to spending it within one evening is a bad concept; a wise option is to split your bankroll volume into several parts. For example, following making a deposit, you can divide it into components simultaneously and use only one piece per day for making bets mostbet app.

Slot Tournaments

Today almost all progressives are linked electronically to other machines, with all credit played in the particular linked machines adding to a typical jackpot. Woe will be the person who hits three jackpot symbols about a buy-a-pay together with only one gold coin played — typically the player gets practically nothing back. On some sort of multiplier, payoffs are proportionate for each coin played — apart from, usually, for that leading jackpot.

  • Their slots selection includes progressive jackpot feature games, as well as a massive selection of all traditional slots you’d count on to find.
  • This is because slot games can be highly addicting and can prospect a player to chase their losses.
  • Nowadays, known because a philanthropist, Bill Redd (also referred to as Si) was among the Bally group’s designers in the 1971s.
  • With all the achievement and popularity, there will be one thing that has always been a new given for slot machine machines.

The wide collection of slot games, like exclusive titles, guarantees a varied plus exciting gaming knowledge. Here are many of the most effective online casinos for slot machine machines and precisely what causes them to be stand out there. A Night Using Cleo transports gamers to the planet of Ancient Egypt, complete with icons such as scarab beetles and the Eye of Horus. This game holds out for its unique bonus models, which add a great extra layer associated with excitement to the gameplay. Players can easily also make use of the chance feature, that allows all of them to attempt in order to double their winnings after any effective spin.

How To Play Slot Machines On-line: Step By Phase Instructions For Beginners

Among other things, site visitors will discover a day-to-day dose of content articles with the newest poker news, reside reporting from tournaments, exclusive videos, podcasts, reviews and bonus deals and so much more. With these kinds of eligibility factors and even any others you might find, your best choice is always in order to game details or even information before a person commit to enjoying. Sean Chaffin can be a longtime freelance article writer, editor, and former high school writing teacher. If you ever feel it’s learning to be a problem, urgently speak to a helpline in your country for immediate” “assistance. From in-depth testimonials and helpful guidelines to the latest reports, we’re here to be able to help you find a very good platforms and create informed decisions every step of the particular way.

They had been featuring three” “re-writing reels operated by way of a handle and a new single slot to be able to place a coin into. This equipment had only one shell out line, with each and every reel featuring several symbols – many you would acknowledge today – spades, hearts, diamonds, a new horseshoe, and the bell. This method requires players to be able to be more involved with every earn, so having some sort of calculator close by is recommended. Instead of changing the particular size of the particular bet based in won or lost rounds, the method has a set bet determined being a percentage of typically the available balance. Using 5% can become convenient, but all of us prefer staying secure and only wagering 3%. Slot machines top the record with regards to the almost all attractive casino game titles for gamblers, the two online and in land-based casinos.

Top Payment Procedures Available On Stake Casino

This feature means that you can spin a slot machine game game without seeking to connect to the particular game, but you is going to take care to be able to ensure you’re not really spending too much per spin. Wilds usually are special symbols that can replace other symbols on paylines to generate benefits. They are typically the most crucial symbols in the particular game and may also sometimes induce bonus features.

  • Additionally, players could unlock bonus capabilities through scatter signs” “that trigger special features.
  • If a person start thinking, “Well, they’re only credit, ” or even, “They’re already paid out for, ” it’s harder to persuade yourself to guard your bankroll.
  • At the core involving every authentic internet gambling platform is gaming software.
  • Players may also withdraw their funds by hitting “Cash Out and about. ” An individual can will certainly then receive a paper voucher together with the balance amount that can become used in another machine.

The user interface is definitely crafted to mirror the appearance and even ambiance of the conventional gambling establishment, featuring intuitive selections and controls. Volatility measures the frequency as well as the size regarding the wins that will the slots spend. For example, in case you prefer big is the winner less often, then you will want to perform an increased volatility slot; in case you prefer a low volatility slot then an individual will get smaller sized, more frequent is the winner. Commonly, this symbol is very totally different from the other symbols, therefore it is easy to distinguish besides making it simpler to understand the gameplay. Depending how many you obtain, could be dependent about the reward an individual are given; but like always, this may also vary per game.

Are There Different Types Of Slot Machines?

That about wraps upward our How in order to Play Slot Devices for Beginners guidebook. If you’ve appreciated it and are ready to try many free slots with regard to yourself, check out our slot reviews web page now. After a new few spins about those, you’ll grasp all of the particular concepts you’ve figured out about here. Paylines often confuse starter slots players the most, and no Exactly how to Play Slot machine Machines for Beginners guide would be full without explaining all of them further. Each symbol has a different worth and exactly how much you win for making combinations will be identified by the value of the symbols.

  • Don’t forget to be able to carefully experience almost all of the great print, because a few terms & situations can limit claiming, usage or cashing out of bonuses.
  • First, you should note that you can always find out exactly what bonus rounds and even special features the game has by viewing the paytable.
  • The goal with this specific strategy for earning at slots is usually to win back our losses.
  • Slot machines have are available a long approach since being simple machines and actually their role since store vending equipment.
  • Once you’ve established your desired gamble, press the “Spin” button or draw the lever (if available) to initiate the spin.

He’s written several books, generally on the topics of card counting and the different blackjack systems they employed over the particular years. He in addition runs a effective YouTube channel wherever he showcases various blackjack scenarios with beginner tips about how to overcome the dealer. Bets can be since little as 1c compared to typically the common minimum levels of $5 in order to $10 that stand and card games require.” “[newline]Please note that Slotsspot. com doesn’t work any gambling companies.

How To Play Slot Machines Inside A Casino

Bonus rounds can befuddle some new participants, so we believed we’d describe all of them here so that this specific How to Play Slot Machines intended for Beginners piece will be complete. When the cheats inserted particular numbers of coins in a certain order, the device would fork out. In jurisdictions with licensed casinos, the law takes a very dim view of cheating the video poker machines. Cheating licensed casinos is a criminal offence and will carry stiff prison terms. A zero-bonus balances the particular possibility of greater wins than you see in pick’em bonuses.

  • Over in britain, they include a couple of names for all of them, fruit machines in England and puggy in Scotland.
  • They are created to offer the chance-based, easy-to-play video gaming experience where gamers” “can go back home with potentially big wins using a simple rewrite.
  • However, you may stick to certain rules when playing particular titles; by using them, you could decrease risks and boost your winning possibilities.
  • The bonus round is usually activated by way of a minimum of three scatter symbols – but this can easily vary slot in order to slot.
  • Just such as the relaxed nature of how to play slot machines, players from all over have similar carefree love towards online game.

A gamer has numerous game titles available, something intended for every taste plus interest. However, whilst we can’t inform you how in order to play slot devices and win every time, we can show a couple of slot machine techniques that will assist you win more often. This is knowledge we’ve gained above decades, so bring it in and create sure you realize that before choosing which usually game to enjoy. Some slot machines in the 1960s and ‘70s had been vulnerable to ordinary magnets. Cheaters could make use of the magnets in order to make the fishing reels float freely alternatively of stopping about a spin.

How To Play Position Machines: A Step By Step Guide

Usually, classic, fruits, 3D, and progressive jackpot slot equipment are available with all online internet casinos. Old-fashioned slot equipment have only one horizontal payline, along which in turn three winning emblems (usually fruit icons or 7s) have to line upwards for you to be paid out. The vast bulk of today’s position machines, however, are multi-payline, with a few featuring up to 100 paylines or more.

  • So, let’s say that we all start with $100, which usually means our 1st bet is 3%.
  • It works generally the same manner regarding all slot devices, although there may become some variations based on the application developer.
  • These are the added features that assist to boost your payout in the particular game.
  • There is enough diversity and choice available amongst the slot machine game games industry.
  • “Each game comes with a unique combo of features like bonus rounds, thrilling varied animation alternatives, modern machines, multiplier machines, wild icons, and more.

The risk is that a new dry run can lead to a large bet that may be difficult in order to sustain. Some slot machine games feature progressive jackpots, where a small portion of each and every bet contributes to be able to a growing goldmine that can always be won by getting a specific combo or at unique. Find out about slot machines, how that they work and how to play slots for actual money with our own full guide.

How Developers Found Ways To Increase Jackpots

The worst factor you can apply at slot machines is always to chase loss by increasing the bet level. The chances are good that you may lose a lot more cash, and probably crazily run through the bankroll. When selecting an ideal bet level for your slot play, your decision is usually a trade-off among risk and payment.

  • The machine became known as the Liberty Bell and Fey spawned an evergrowing industry.
  • There are video games in penny, 2-cent, nickel, 10-cent, 1 fourth, dollar and also $100 denominations, and several machines allow players in order to choose which denomination they want to be able to use.
  • Nearly everyone is guilty associated with not reading Apple or Google words of service, but you shouldn’t are available to a casino with that same mindset.
  • The slot machine machine landscape has always been dependent upon the improvements and innovations involving software companies.
  • These slots are normally great for players who just want to have many fun create typically the most of their particular play.

It’s important to read the cup or help menus and learn precisely what type of device it is. The three major forms of reel-spinning slot machines are the multiplier, the buy-a-pay along with the progressive. Modern movie slots, of program, don’t have real coins but instead use virtual bridal party. To period pay-out odds, simply cash out your own slot credits straight into a real money balance. If you’re gunning for the big bucks, on the other hand, you would end up being wise to stick to high volatility slots.

Slot Hint 10:  Take Benefit Of Bonuses And Even Promotions

In typically the rest, the recognition of attempting to be able to win at slot machines is surging to the point slot machine game play is rivaling table play. On those machines, the particular big payoffs have been $50 or $100 — not like typically the big numbers slot machine game players expect today. On systems of which electronically link equipment in several casinos, progressive jackpots reach huge amount of money. It’s quick — just drop coins into typically the slot and push the button or even pull the handle. Newcomers will find the particular personal interaction along with dealers or additional players at the particular tables intimidating — slot players prevent that. And besides, the greatest, most lifestyle-changing jackpots in typically the casino are available upon the slots.

The game software giant incorporated a 4-tier progressive goldmine with levels called mega, major, slight, and mini. In order to be eligible for the tiny jackpot – the lowest of the bunch, you must bet at least 1 cent on all twenty-five paylines (a minimal total of $0. 25). When this comes to video slots, these generally include multi-tier accelerating jackpots. Every video clip slot usually provides between 2 plus 12 progressive goldmine levels, and every level provides a established max bet an individual have to help to make in order to be able to be eligible.

What Occurs When You” “Get On A Slot Machine?

Each slot machine features a pay stand that shows just what symbols have to line up for a pay out of varying sums. These are organized with the greatest payouts, known because the jackpot, on top of the tables and subsequent payouts below those. A desk also includes an amount paid relying on the amount of credits a new player puts in the machine. A random number generator, or perhaps RNG, is a computer technology that is definitely used to determine payouts and jackpots. An RNG makes a sequence associated with simulated random amounts to determine exactly where those reels may land, and therefore which payouts” “are distributed to participants. Modern slot equipment have become high-tech machines with advanced online video, sound, graphics, in addition to gameplay.

  • So, you should recognize that playing slot machine machines are extremely basic – which is part of the reason players love these games.
  • Ordinarily, a traditional 3-reel slot will be an ideal opt for for the player who else likes a pared-down game with not any frills and everything perform.
  • For example, if you owned four matching emblems on reels one, two, four, in addition to five, and some sort of wild landed throughout the middle, you’d have a 5 symbol combination.
  • Usually, classic, fruit, 3D, and progressive jackpot slot machines are available from all online casinos.
  • You can typically do this inside the ‘account’ or ‘banking’ section of your own casino.

The scam artists would likely remove the magnetic only when the fishing reels had aligned throughout a winning combo. My top slot machine game machine strategy ideas – you’ll learned about below – consist of 12 do’s and even 6 don’ts that may assist you in answering the top ‘how to succeed at slot machines? Changing the developed payback percentage demands opening the device and replacing a computer chip. Server-based slot machines that will allow casinos in order to change payout proportions remotely, but there are still polices around making these kinds of changes. It’s certainly not unusual to proceed 20 or fifty or more draws without a one payout on a reel-spinning slot, although payouts tend to be more repeated on video video poker machines. Nor would it be unusual for a device to pay again 150 percent or more for many dozen pulls.

What Is Responsible Game Playing And What Makes It Essential?

Given that they are games of chance, playing slots has more to perform with luck as compared to strategy. Even so, there are several strategies you can employ to select some sort of slot machine that may likely pay. As you might have got heard before, a person can’t win large payouts at a intensifying slot if you don’t max the wager. A small section of your bet on a modern slot machine game goes straight into a jackpot or perhaps set of jackpots. The more participants wager on typically the progressive lot the bigger its jackpot gets.

  • Not all machines are made the similar way and programmed with the same RTP or payment percentage.
  • To place a bet on the slot machine, simply insert the coins or currency, select your bet size, and take the lever or perhaps press the rotate button.
  • Alternatively, you can start building up a bankroll by keeping aside small amounts through your savings and after that begin gambling after getting saved enough money for a certain variety of slot machines.
  • Let’s consider a closer look at the sorts of bonus icons you’re more likely to find in a regular online” “slot.

Other accelerating slots are connected within a casino, although some are interconnected across all internet casinos featuring that certain game. For a new genuine casino experience from the coziness of your abode, live dealer games certainly are a must consider. These games, including live blackjack, different roulette games, and baccarat, feature real human retailers who interact along with players via reside video streams. Players can participate in current gameplay, detailed with interpersonal interaction, creating a great immersive and genuine casino atmosphere. They” “come in various themes and give a stimulating blend of gameplay, visuals, plus the possibility for significant winnings. Demo methods are available regarding players to train and even familiarize themselves along with the game with out risking real cash.

Starting In Order To Play Slots

Yes, due to the fact demo versions permit you to test slots, check their particular characteristics, and do not risk your own funds. While wagering, it is essential to control yourself, while emotions often usually tend to get free from control. It is incredibly common when you strike a large reward and lose manage, forgetting about caution as well as the strategy you adhere to. Aside coming from these run-of-the-mill strategies, participate in slot machine tournaments whenever feasible.

  • Understanding design and even mechanics in the sport is essential ahead of spinning the fishing reels.
  • Don’t hesitate in order to ask tough queries; other gamblers are usually willing to out a poor apple.
  • The scam artists would remove the magnet only if the reels had aligned within a winning mixture.
  • Video slots are acknowledged for their advanced graphics and several paylines, which will enhance the chances regarding winning.
  • The paytable also shows the value of every symbol, indicating the amount you win intended for matching different icons on a payline.

When playing video poker machines online, you could decrease or raise your stake by simply clicking on typically the BET/STAKE button. For example, classic on the internet slots based about traditional slot equipment have 3 reels. Three-reel slot games put more importance on their leading jackpots but have got a lesser hit regularity with additional losing spins. If you’re pondering how to win at slots, three-reel position games do offer slot players typically the best possiblity to get big, but additionally the particular best chance in order to lose fast. Every good online gambling establishment will have an array of games to attempt at no cost or true money.

How To Experience Video Poker Machines: The Pokernews Guide

The microprocessors driving today’s machines are set with random-number generation devices that govern winning combinations. Many position players pump money into two or more adjacent devices at a time, although if the casino will be crowded and others are having problems finding places to play, limit yourself to one machine. Select your bets and paylines, and get a theme and bonus feature of which interests you. Online slot software will be governed by the Arbitrary Number Generator, or perhaps RNG. As quickly as you struck the ‘Spin’ key, an algorithm can determine where and if the reels can stop. The process is completely unique, and slot designers have their games examined before they hit the casino industry, along with periodically audited with time.

  • This network impact results in massive jackpots, some of which can become truly life-changing.
  • While learning how in order to play casino slot machine games, there are particular factors that you have to always keep in mind when choosing the proper slot machine game game.
  • Added for the paylines and payout structures, deciphering the bet measurements is likewise crucial, as it can have an effect on both the possible winnings and the particular overall game.
  • You may well also get a feeling whether it’s achievable to win in slot games and even if so how to win in slots.

Now, a new payout and goldmine is determined as quickly as the player hits the switch to spin the particular reels. If you’re purely after massive jackpots, you ought to consider playing the subsequent games. These top rated progressive jackpot slots have paid out many of the greatest online slot jackpots of all time.

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