airflow/utils/dates.py
def round_time(dt, delta, start_date=timezone.make_aware(datetime.min)):
    """
    Returns the datetime of the form start_date + i * delta
    which is closest to dt for any non-negative integer i.
    Note that delta may be a datetime.timedelta or a dateutil.relativedelta
    >>> round_time(datetime(2015, 1, 1, 6), timedelta(days=1))
    datetime.datetime(2015, 1, 1, 0, 0)
    >>> round_time(datetime(2015, 1, 2), relativedelta(months=1))
    datetime.datetime(2015, 1, 1, 0, 0)
    >>> round_time(datetime(2015, 9, 16, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 16, 0, 0)
    >>> round_time(datetime(2015, 9, 15, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 15, 0, 0)
    >>> round_time(datetime(2015, 9, 14, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 14, 0, 0)
    >>> round_time(datetime(2015, 9, 13, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 14, 0, 0)
    """

    if isinstance(delta, six.string_types):
        # It's cron based, so it's easy
        tz = start_date.tzinfo
        start_date = timezone.make_naive(start_date, tz)
        cron = croniter(delta, start_date)
        prev = cron.get_prev(datetime)
        if prev == start_date:
            return timezone.make_aware(start_date, tz)
        else:
            return timezone.make_aware(prev, tz)

    # Ignore the microseconds of dt
    dt -= timedelta(microseconds=dt.microsecond)

    # We are looking for a datetime in the form start_date + i * delta
    # which is as close as possible to dt. Since delta could be a relative
    # delta we don't know its exact length in seconds so we cannot rely on
    # division to find i. Instead we employ a binary search algorithm, first
    # finding an upper and lower limit and then disecting the interval until
    # we have found the closest match.

    # We first search an upper limit for i for which start_date + upper * delta
    # exceeds dt.
    upper = 1
    while start_date + upper * delta < dt:
        # To speed up finding an upper limit we grow this exponentially by a
        # factor of 2
        upper *= 2

    # Since upper is the first value for which start_date + upper * delta
    # exceeds dt, upper // 2 is below dt and therefore forms a lower limited
    # for the i we are looking for
    lower = upper // 2

    # We now continue to intersect the interval between
    # start_date + lower * delta and start_date + upper * delta
    # until we find the closest value
    while True:
        # Invariant: start + lower * delta < dt <= start + upper * delta
        # If start_date + (lower + 1)*delta exceeds dt, then either lower or
        # lower+1 has to be the solution we are searching for
        if start_date + (lower + 1) * delta >= dt:
            # Check if start_date + (lower + 1)*delta or
            # start_date + lower*delta is closer to dt and return the solution
            if (start_date + (lower + 1) * delta) - dt <= dt - (start_date + lower * delta):
                return start_date + (lower + 1) * delta
            else:
                return start_date + lower * delta

        # We intersect the interval and either replace the lower or upper
        # limit with the candidate
        candidate = lower + (upper - lower) // 2
        if start_date + candidate * delta >= dt:
            upper = candidate
        else:
            lower = candidate
def round_time(dt, delta, start_date=timezone.make_aware(datetime.min)):
    """
    Returns the datetime of the form start_date + i * delta
    which is closest to dt for any non-negative integer i.
    Note that delta may be a datetime.timedelta or a dateutil.relativedelta
    >>> round_time(datetime(2015, 1, 1, 6), timedelta(days=1))
    datetime.datetime(2015, 1, 1, 0, 0)
    >>> round_time(datetime(2015, 1, 2), relativedelta(months=1))
    datetime.datetime(2015, 1, 1, 0, 0)
    >>> round_time(datetime(2015, 9, 16, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 16, 0, 0)
    >>> round_time(datetime(2015, 9, 15, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 15, 0, 0)
    >>> round_time(datetime(2015, 9, 14, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 14, 0, 0)
    >>> round_time(datetime(2015, 9, 13, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 14, 0, 0)
    """

    if isinstance(delta, six.string_types):
        # It's cron based, so it's easy
        tz = start_date.tzinfo
        start_date = timezone.make_naive(start_date, tz)
        cron = croniter(delta, start_date)
        prev = cron.get_prev(datetime)
        if prev == start_date:
            return timezone.make_aware(start_date, tz)
        else:
            return timezone.make_aware(prev, tz)

    # Ignore the microseconds of dt
    dt -= timedelta(microseconds=dt.microsecond)

    # We are looking for a datetime in the form start_date + i * delta
    # which is as close as possible to dt. Since delta could be a relative
    # delta we don't know its exact length in seconds so we cannot rely on
    # division to find i. Instead we employ a binary search algorithm, first
    # finding an upper and lower limit and then disecting the interval until
    # we have found the closest match.

    # We first search an upper limit for i for which start_date + upper * delta
    # exceeds dt.
    upper = 1
    while start_date + upper * delta < dt:
        # To speed up finding an upper limit we grow this exponentially by a
        # factor of 2
        upper *= 2

    # Since upper is the first value for which start_date + upper * delta
    # exceeds dt, upper // 2 is below dt and therefore forms a lower limited
    # for the i we are looking for
    lower = upper // 2

    # We now continue to intersect the interval between
    # start_date + lower * delta and start_date + upper * delta
    # until we find the closest value
    while True:
        # Invariant: start + lower * delta < dt <= start + upper * delta
        # If start_date + (lower + 1)*delta exceeds dt, then either lower or
        # lower+1 has to be the solution we are searching for
        if start_date + (lower + 1) * delta >= dt:
            # Check if start_date + (lower + 1)*delta or
            # start_date + lower*delta is closer to dt and return the solution
            if (start_date + (lower + 1) * delta) - dt <= dt - (start_date + lower * delta):
                return start_date + (lower + 1) * delta
            else:
                return start_date + lower * delta

        # We intersect the interval and either replace the lower or upper
        # limit with the candidate
        candidate = lower + (upper - lower) // 2
        if start_date + candidate * delta >= dt:
            upper = candidate
        else:
            lower = candidate
Returns the datetime of the form start_date + i * delta
    which is closest to dt for any non-negative integer i.
    Note that delta may be a datetime.timedelta or a dateutil.relativedelta
    >>> round_time(datetime(2015, 1, 1, 6), timedelta(days=1))
    datetime.datetime(2015, 1, 1, 0, 0)
    >>> round_time(datetime(2015, 1, 2), relativedelta(months=1))
    datetime.datetime(2015, 1, 1, 0, 0)
    >>> round_time(datetime(2015, 9, 16, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 16, 0, 0)
    >>> round_time(datetime(2015, 9, 15, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 15, 0, 0)
    >>> round_time(datetime(2015, 9, 14, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 14, 0, 0)
    >>> round_time(datetime(2015, 9, 13, 0, 0), timedelta(1), datetime(2015, 9, 14, 0, 0))
    datetime.datetime(2015, 9, 14, 0, 0)