प्रोग्राम की सुविधाएँ · तेज दुगुनेपन से फिबोनाची

def fibonacci(index):
    if type(index) is not int or not 0 <= index <= 10000:
        raise ValueError("index.range")
    a, b = 0, 1
    for bit in bin(index)[2:]:
        c = a * (2 * b - a)
        d = a * a + b * b
        a, b = (c, d) if bit == "0" else (d, c + d)
    return a