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Demo of the 8087's CORDIC tangent algorithm
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
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