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A 2-dimensional vector class
    >>> v1 = Vector2d(3, 4)
    >>> print(v1.x, v1.y)
    >>> x, y = v1
    >>> x, y
    (3.0, 4.0)
    Vector2d(3.0, 4.0)
    >>> v1_clone = eval(repr(v1))
    >>> v1 == v1_clone
    >>> 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)
    >>> 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
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()
    >>> Vector2d(1, 0).angle()
    >>> epsilon = 10**-8
    >>> abs(Vector2d(0, 1).angle() - math.pi/2) < epsilon
    >>> abs(Vector2d(1, 1).angle() - math.pi/4) < epsilon
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>'
# tag::VECTOR2D_V3_DEMO[]
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
# end::VECTOR2D_V3_HASH_DEMO[]
Tests of hashing:
# tag::VECTOR2D_V3_HASH_DEMO[]
    >>> v1 = Vector2d(3, 4)
    >>> v2 = Vector2d(3.1, 4.2)
    >>> hash(v1), hash(v2)
    >>> len({v1, v2})
# end::VECTOR2D_V3_DEMO[]
from array import array
import math
# tag::VECTOR2D_V3_PROP[]
class Vector2d:
    typecode = 'd'
    def __init__(self, x, y):
        self.__x = float(x)  # <1>
        self.__y = float(y)
    @property  # <2>
    def x(self):  # <3>
        return self.__x  # <4>
    @property  # <5>
    def y(self):
        return self.__y
    def __iter__(self):
        return (i for i in (self.x, self.y))  # <6>
    # remaining methods follow (omitted in book listing)
# end::VECTOR2D_V3_PROP[]
    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)
# tag::VECTOR_V3_HASH[]
    def __hash__(self):
        return hash(self.x) ^ hash(self.y)
# end::VECTOR_V3_HASH[]
    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)

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