CORDIC - Software Implementation

Software Implementation

The following is a MATLAB/GNU Octave implementation of CORDIC that does not rely on any transcendental functions except in the precomputation of tables. If the number of iterations n is predetermined, then the second table can be replaced by a single constant. The two-by-two matrix multiplication represents a pair of simple shifts and adds. With MATLAB's standard double-precision arithmetic and "format long" printout, the results increase in accuracy for n up to about 48.

function v = cordic(beta,n) % This function computes v = (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 : 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 = ; % 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 = ; 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 : v = v * Kn; return