CORDIC with Scipy

It is that trigonometric functions can be calculated only by addition, subtraction, and shift operations. For details, this page was very easy to understand. The code I actually wrote is calculated with floating point numbers, so multiplication is used instead of shift operation. Even so, I often come up with such an algorithm.

Below is the code and execution results.

cordic.py

#!/usr/bin/env python
from __future__ import division
import scipy as sp
import numpy as np
import matplotlib.pyplot as plt
import math

term_num = 17
thetas =  map( lambda x : math.atan( 1.0 / math.pow( 2.0,x ) ) , range( term_num  + 1) )
hypot_length =  1.0 / reduce( lambda x,y:  x * ( 1.0 / math.cos(y) ) ,thetas,1.0 )

def cos_cordic( angle ):
        x,y = (1.0,1.0)
        acc_theta = thetas[0]
        scale_ratio = 1.0
        for i,theta in enumerate( thetas[1:] ):
                x1,y1 = x,y
                scale_ratio *= 0.5
                if acc_theta < angle :
                        acc_theta += theta
                        x -= scale_ratio * y1
                        y += scale_ratio * x1
                else:
                        acc_theta -= theta
                        x += scale_ratio * y1
                        y -= scale_ratio * x1
        return ( x * hypot_length )


if __name__ == '__main__':
        t = [ x * ( math.pi / 200.0 ) for x in range( 100 ) ]
        result = map( cos_cordic,t )

        plt.plot( result )
        plt.show()