Programming puzzle: Average direction on a circle

circularAverage.py

def enforce0to360range(angle):
    """Converts the given angle (degrees) into the range [0 360).
    >>> enforce0to360range(30)
    30.0
    >>> enforce0to360range(180)
    180.0
    >>> enforce0to360range(360)
    0.0
    >>> enforce0to360range(390.0)
    30.0
    >>> enforce0to360range(9001)
    1.0
    >>> enforce0to360range(-30)
    330.0
    >>> enforce0to360range(-390)
    330.0
    >>> enforce0to360range(-9000.5)
    359.5
    """
    return angle % 360.0  # yay, sensible modulo definition in the language

def enforce180to180range(angle):
    """Converts the given angle (degrees) into the range (-180 180].
    >>> enforce180to180range(30)
    30.0
    >>> enforce180to180range(180.0)
    180.0
    >>> enforce180to180range(-180)
    180.0
    >>> enforce180to180range(360)
    0.0
    >>> enforce180to180range(390.0)
    30.0
    >>> enforce180to180range(9001)
    1.0
    >>> enforce180to180range(-30)
    -30.0
    >>> enforce180to180range(-390)
    -30.0
    >>> enforce180to180range(-9000.5)
    -0.5
    """
    return -enforce0to360range(180.0-angle) + 180.0


def circularAverage(angles):
    """ Returns the angle that is in the central position around a circle.
        Angles are specified in degrees.
    >>> enforce0to360range(circularAverage([0, 0, 90]))
    30.0
    >>> enforce0to360range(circularAverage([60, 60, 330]))
    30.0
    >>> enforce0to360range(circularAverage([90, 180, 270]))
    180.0
    >>> abs(enforce180to180range(circularAverage([0, 0, 180])))  # 2/3 towards 0
    60.0
    >>> abs(enforce180to180range(circularAverage([90, 270]) + 90))
    90.0
    """

    return 30   # left as an exercise to the reader

if __name__ == '__main__':
    import doctest
    doctest.testmod()