Example Implementation of arctan(x)

arctan.py

def arctan(n, x):
    if x > 1.0:
        return math.pi/2.0 - my_preferred_arctan_implementation(n, 1/x)
    else:
        return my_preferred_arctan_implementation(n, x)

continued_fraction_arctan.py

def continued_faction_arctan(n, x):
    x2 = x*x
    d = n * 2 + 1
    for k in range(n, 0, -1):
        f = k * 2 - 1
        d = f + k*k*x2/d
    return x / d

taylor_arctan.py

def taylor_arctan(n, x):
  approx = 0
  for k in xrange(n):
    j = 2 * k + 1
    approx += ( (-1)**k * x**j ) / j
  return approx