Trigonometric functions using CORDIC algorithm (Python)

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See CORDIC article on Wikipedia for an explanation of the algorithm. 

<<cordic.py>>=
#!/usr/bin/python
from __future__ import division
from math import atan,pi,sqrt
import sys
# Calculate the arc Tan table once
ArcTanTable = []
for i in range(2048):
  ArcTanTable.append(    atan( 2.0**(-1 * i) )    )
# Calculate the scaling factor K once
KN = []
value = 1.0
for i in range(2048):
  value = value * sqrt(  1.0 + 2.0**(-2 * i)  )  
  KN.append(1.0 / value)
def CORDIC_function(degrees,iterations = 8):
  # convert from degrees into radians
  beta = degrees * pi / 180.0
  # ensure that iterations is not greater than 2048
  if iterations > 2048:
    iterations = 2048
  # Calculate the sine and cosine values using CORDIC algorithm
  Vx,Vy = 1.0 , 0.0
  for i in range(iterations):
    if beta < 0:
      Vx,Vy = Vx + Vy * 2.0**(-1 * i)  ,  Vy - Vx * 2.0**(-1 * i)
      beta = beta + ArcTanTable[i]
    else:
      Vx,Vy = Vx - Vy * 2.0**(-1 * i)  ,  Vy + Vx * 2.0**(-1 * i)
      beta = beta - ArcTanTable[i]
  # Multiply by the scaling factor K
  Vx,Vy = Vx * KN[iterations - 1] , Vy * KN[iterations - 1]
  return (Vx,Vy,KN[iterations - 1])
if __name__ == '__main__':
  if len(sys.argv) == 2:
    deg  = float(sys.argv[1])
    iter = 8
  elif len(sys.argv) == 3:
    deg  = float(sys.argv[1])
    iter = int(sys.argv[2])
  else:
    print "using default values of 17 degrees and 8 iterations"
    deg  = 17.0
    iter = 8
  (sine,cosine,K)=CORDIC_function(deg,iter)
  print "K = %14.12f" % (K)
  print "Sin(%4.1f) = %14.12f  and  Cos(%4.1f) = %14.12f" % (deg,sine,deg,cosine)
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