Float number powered by an integer

my_pow.py

import math

def my_pow(a, b):
    """
    Returns the value of the `a` raised to the power of `b`.
    Assume that `a` is a float number and `b` is an integer.
    Special cases:
    * if `b` is zero, then result is 1.0
    * if `a` is NaN and `b` is non-zero, then the result is NaN.
    * if `a` is 0 and `b` < 0, or `a` is +Inf and `b` > 0, then the
      result is +Inf.
    * if `a` is -0.0 and `b` > 0 and `b` is not a finite odd
      integer, or if `a` is -Inf and `b` < 0 and `b` is not a finite
      odd integer, then the result is +0.0
    * if `a` is -0.0 and `b` > 0 and `b` is a positive finite odd
      integer, or `a` is -Inf and `b` < 0 and `b` is a finite odd
      integer, then the result is -0.0
    * if `a` is -0.0 and `b` < 0 and not a finite odd integer, or
      `a` is -Inf and `b` > 0 but not a finite odd integer, then
      the result is +Inf.
    * if `a` is -0.0 and `b` < 0 and is a finite odd integer, or `a`
      is -Inf and `b` is a positive finite odd integer, then the
      result is -Inf.

    >>> my_pow(42, 0)
    1.0
    >>> my_pow(float('nan'), 42)
    nan

    >>> my_pow(0.0, -1)
    inf
    >>> my_pow(float('inf'), 42)
    inf

    >>> my_pow(-0.0, 2)
    0.0
    >>> my_pow(float('-inf'), -2)
    0.0

    >>> my_pow(-0.0, 3)
    -0.0
    >>> my_pow(float('-inf'), -3)
    -0.0

    >>> my_pow(-0.0, -42)
    inf
    >>> my_pow(float('-inf'), 42)
    inf

    >>> my_pow(-0.0, -3)
    -inf
    >>> my_pow(float('-inf'), 3)
    -inf

    >>> my_pow(2, 42)
    4398046511104.0

    """

    a = float(a)
    b = int(b)

    if b == 0:
        return 1.0
    if math.isnan(a):
        return a
    # reciprocal
    if b < 0:
        b = -b
        a_sign = math.copysign(1.0, a)
        if a == 0:
            a = a_sign * float('inf')
        else:
            a = 1 / a
    # do the math
    ret = 1.0
    while b > 0:
        if b & 1:
            ret *= a
        b >>= 1
        a *= a
    return ret

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