function v = cordic(beta,n)
% This function computes v = [cos(beta), sin(beta)] (beta in radians)
% using n iterations. Increasing n will increase the precision.
if beta < -pi/2 || beta > pi/2
if beta < 0
v = cordic(beta + pi, n);
else
v = cordic(beta - pi, n);
end
v = -v; % flip the sign for second or third quadrant
return
end
% Initialization of tables of constants used by CORDIC
% need a table of arctangents of negative powers of two, in radians:
% angles = atan(2.^-(0:27));
angles = [ ...
0.78539816339745 0.46364760900081 0.24497866312686 0.12435499454676 ...
0.06241880999596 0.03123983343027 0.01562372862048 0.00781234106010 ...
0.00390623013197 0.00195312251648 0.00097656218956 0.00048828121119 ...
0.00024414062015 0.00012207031189 0.00006103515617 0.00003051757812 ...
0.00001525878906 0.00000762939453 0.00000381469727 0.00000190734863 ...
0.00000095367432 0.00000047683716 0.00000023841858 0.00000011920929 ...
0.00000005960464 0.00000002980232 0.00000001490116 0.00000000745058 ];
% and a table of products of reciprocal lengths of vectors [1, 2^-j]:
Kvalues = [ ...
0.70710678118655 0.63245553203368 0.61357199107790 0.60883391251775 ...
0.60764825625617 0.60735177014130 0.60727764409353 0.60725911229889 ...
0.60725447933256 0.60725332108988 0.60725303152913 0.60725295913894 ...
0.60725294104140 0.60725293651701 0.60725293538591 0.60725293510314 ...
0.60725293503245 0.60725293501477 0.60725293501035 0.60725293500925 ...
0.60725293500897 0.60725293500890 0.60725293500889 0.60725293500888 ];
Kn = Kvalues(min(n, length(Kvalues)));
% Initialize loop variables:
v = [1;0]; % start with 2-vector cosine and sine of zero
poweroftwo = 1;
angle = angles(1);
% Iterations
for j = 0:n-1;
if beta < 0
sigma = -1;
else
sigma = 1;
end
factor = sigma * poweroftwo;
R = [1, -factor; factor, 1];
v = R * v; % 2-by-2 matrix multiply
beta = beta - sigma * angle; % update the remaining angle
poweroftwo = poweroftwo / 2;
% update the angle from table, or eventually by just dividing by two
if j+2 > length(angles)
angle = angle / 2;
else
angle = angles(j+2);
end
end
% Adjust length of output vector to be [cos(beta), sin(beta)]:
v = v * Kn;
return
cordic.zip_Cordic Rotation_coordinate _cordic_cordic MATLAB
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