Complete Data Model

from array import array
import math
class Vector2d:
    __match_args__ = ('x', 'y')
    typecode = 'd'
    def __init__(self, x, y):
        self.__x = float(x)
        self.__y = float(y)
    @property
    def x(self):
        return self.__x
    @property
    def y(self):
        return self.__y
    def __iter__(self):
        return (i for i in (self.x, self.y))
    def __repr__(self):
        class_name = type(self).__name__
        return '{}({!r}, {!r})'.format(class_name, *self)
    def __str__(self):
        return str(tuple(self))
    def __bytes__(self):
        return (bytes([ord(self.typecode)]) +
                bytes(array(self.typecode, self)))
    def __eq__(self, other):
        return tuple(self) == tuple(other)
    def __hash__(self):
        return hash((self.x, self.y))
    def __abs__(self):
		return math.hypot(self.x, self.y)
    def __bool__(self):
        return bool(abs(self))
    def angle(self):
        return math.atan2(self.y, self.x)
    def __format__(self, fmt_spec=''):
        if fmt_spec.endswith('p'):
            fmt_spec = fmt_spec[:-1]
            coords = (abs(self), self.angle())
            outer_fmt = '<{}, {}>'
        else:
            coords = self
            outer_fmt = '({}, {})'
        components = (format(c, fmt_spec) for c in coords)
        return outer_fmt.format(*components)
    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(*memv)

>>> v1 = Vector2d(3, 4)
>>> print(v1.x, v1.y)
3.0 4.0
>>> x, y = v1
>>> x, y
(3.0, 4.0)
>>> v1
Vector2d(3.0, 4.0)
>>> v1_clone = eval(repr(v1))
>>> v1 == v1_clone
True
>>> print(v1)
(3.0, 4.0)
>>> octets = bytes(v1)
>>> octets
b'd\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
>>> abs(v1)
5.0
>>> bool(v1), bool(Vector2d(0, 0))
(True, False)
#Test of ``.frombytes()`` class method:
>>> v1_clone = Vector2d.frombytes(bytes(v1))
>>> v1_clone
Vector2d(3.0, 4.0)
>>> v1 == v1_clone
True
#Tests of ``format()`` with Cartesian coordinates:
>>> format(v1)
'(3.0, 4.0)'
>>> format(v1, '.2f')
'(3.00, 4.00)'
>>> format(v1, '.3e')
'(3.000e+00, 4.000e+00)'
#Tests of the ``angle`` method::
>>> Vector2d(0, 0).angle()
0.0
>>> Vector2d(1, 0).angle()
0.0
>>> epsilon = 10**-8
>>> abs(Vector2d(0, 1).angle() - math.pi/2) < epsilon
True
>>> abs(Vector2d(1, 1).angle() - math.pi/4) < epsilon
True
#Tests of ``format()`` with polar coordinates:
>>> format(Vector2d(1, 1), 'p')  # doctest:+ELLIPSIS
'<1.414213..., 0.785398...>'
>>> format(Vector2d(1, 1), '.3ep')
'<1.414e+00, 7.854e-01>'
>>> format(Vector2d(1, 1), '0.5fp')
'<1.41421, 0.78540>'
#Tests of `x` and `y` read-only properties:
>>> v1.x, v1.y
(3.0, 4.0)
>>> v1.x = 123
Traceback (most recent call last):
	...
AttributeError: can't set attribute 'x'
# Tests of hashing:
>>> v1 = Vector2d(3, 4)
>>> v2 = Vector2d(3.1, 4.2)
>>> len({v1, v2})
2