Demo of the 8087's CORDIC tangent algorithm

tan.py

import math

# 8087 tangent algorithm, from Implementing Transcendental Functions, R. Nave

atan_table = [math.atan(2 ** -i) for i in range(0, 17)]

def cordic_tan(z):
  # Compute tan of angle z, using CORDIC
  q = []
  # Break down z into sum of angles, where each angle is 0 or atan(2**-i)
  # q holds corresponding 0 or 1 bits
  for i in range(1, 17):
    if z >= atan_table[i]:
      z -=atan_table[i]
      q.append(1)
    else:
      q.append(0)

  # Approximate tan of remaining z (very small)
  tg = (3 * z) / (3 - z * z)

  # Create a (non-unit) vector with angle of the remaining z
  # tan(remaining z) = y/x
  y = tg
  x = 1

  # Rotate the vector for each angle in the original sum of angles
  # This will bring the vector back to the original angle z
  # (Vector is also scaled, but that doesn't affect the tangent.)
  for i in range(16, 0, -1):
    if q[i - 1]:
      y_tmp = y + x * 2**-i
      x = x - y * 2**-i
      y = y_tmp

  # Angle of vector is now the original z
  # So tan(z) = y/x
  return y / x

# demo the function
z = 0
while z < math.pi / 4:
  print(z, cordic_tan(z), math.tan(z))
  z += 0.1