def frange(*args):
    """frange([start, ] end [, step [, mode]]) -> generator

    A float range generator. If not specified, the default start is 0.0
    and the default step is 1.0.

    Optional argument mode sets whether frange outputs an open or closed
    interval. mode must be an int. Bit zero of mode controls whether start is
    included (on) or excluded (off); bit one does the same for end. Hence:

        0 -> open interval (start and end both excluded)
        1 -> half-open (start included, end excluded)
        2 -> half open (start excluded, end included)
        3 -> closed (start and end both included)

    By default, mode=1 and only start is included in the output.
    """
    mode = 1  # Default mode is half-open.
    n = len(args)
    if n == 1:
        args = (0.0, args[0], 1.0)
    elif n == 2:
        args = args + (1.0,)
    elif n == 4:
        mode = args[3]
        args = args[0:3]
    elif n != 3:
        raise TypeError('frange expects 1-4 arguments, got %d' % n)
    assert len(args) == 3
    try:
        start, end, step = [a + 0.0 for a in args]
    except TypeError:
        raise TypeError('arguments must be numbers')
    if step == 0.0:
        raise ValueError('step must not be zero')
    if not isinstance(mode, int):
        raise TypeError('mode must be an int')
    if mode & 1:
        i, x = 0, start
    else:
        i, x = 1, start+step
    if step > 0:
        if mode & 2:
            from operator import le as comp
        else:
            from operator import lt as comp
    else:
        if mode & 2:
            from operator import ge as comp
        else:
            from operator import gt as comp
    while comp(x, end):
        yield x
        i += 1
        x = start + i*step