main.py

# Todo: change * to +.
# Todo: implement stern-brocot approximations

class Turn:
    def __init__(self, c, n):
        assert c != 0
        self.c = c
        self.n = n

    def __mul__(x, y):
        return Turn(x.c*y.c, x.n+y.n+oflow(x.c, y.c))

    def __repr__(self):
        return '{}.{}'.format(self.c, self.n)

    def __pow__(self, n):
        if n < 0:
            return Turn(1/self.c, -self.n-1+(self.c==1))**-n
        y = Turn.zero
        for _ in range(n):
            y *= self
        return y

    def __le__(x, y):
        z = x**-1 * y
        return z.n >= 0

Turn.zero = Turn(1, 0)

def idiv(a):
    if a.real > 0 and a.imag >= 0:
        return a, 0
    if a.real <= 0 and a.imag > 0:
        return -a*1j, 1
    if a.real < 0 and a.imag <= 0:
        return -a, 2
    if a.real >= 0 and a.imag < 0:
        return a*1j, 3

def oflow(a, b):
    ar, aq = idiv(a)
    br, bq = idiv(b)
    if aq+bq <= 2:
        return False
    if aq+bq >= 4:
        return True
    return (ar*br).real <= 0

a = Turn(1+4j, 0)