CORDIC: Difference between revisions
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Also: [[j:Vocabulary/SpecialCombinations#Preexecuting_verbs_with_.28.28_.29.29|double parenthesis around a noun phrase]] tells the interpreter that that expression is a constant which should be evaluated once, ahead of time. |
Also: [[j:Vocabulary/SpecialCombinations#Preexecuting_verbs_with_.28.28_.29.29|double parenthesis around a noun phrase]] tells the interpreter that that expression is a constant which should be evaluated once, ahead of time. |
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=={{header|Java}}== |
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{{trans|C}} |
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<syntaxhighlight lang="Java"> |
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public class CordicCalculator { |
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// Constants |
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private static final double[] angles = { |
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0.78539816339745, 0.46364760900081, 0.24497866312686, 0.12435499454676, |
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0.06241880999596, 0.03123983343027, 0.01562372862048, 0.00781234106010, |
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0.00390623013197, 0.00195312251648, 0.00097656218956, 0.00048828121119, |
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0.00024414062015, 0.00012207031189, 0.00006103515617, 0.00003051757812, |
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0.00001525878906, 0.00000762939453, 0.00000381469727, 0.00000190734863, |
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0.00000095367432, 0.00000047683716, 0.00000023841858, 0.00000011920929, |
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0.00000005960464, 0.00000002980232, 0.00000001490116, 0.00000000745058 |
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}; |
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private static final double[] kvalues = { |
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0.70710678118655, 0.63245553203368, 0.61357199107790, 0.60883391251775, |
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0.60764825625617, 0.60735177014130, 0.60727764409353, 0.60725911229889, |
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0.60725447933256, 0.60725332108988, 0.60725303152913, 0.60725295913894, |
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0.60725294104140, 0.60725293651701, 0.60725293538591, 0.60725293510314, |
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0.60725293503245, 0.60725293501477, 0.60725293501035, 0.60725293500925, |
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0.60725293500897, 0.60725293500890, 0.60725293500889, 0.60725293500888 |
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}; |
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// Convert degrees to radians |
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private static double radians(double degrees) { |
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return degrees * Math.PI / 180.0; |
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} |
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// Cordic algorithm implementation |
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private static void cordic(double alpha, int n, double[] result) { |
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int i, ix, sigma; |
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double kn, x, y, atn, t, theta = 0.0, pow2 = 1.0; |
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int newsgn = (int)Math.floor(alpha / (2.0 * Math.PI)) % 2 == 1 ? 1 : -1; |
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if (alpha < -Math.PI/2.0 || alpha > Math.PI/2.0) { |
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if (alpha < 0) { |
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cordic(alpha + Math.PI, n, result); |
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} else { |
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cordic(alpha - Math.PI, n, result); |
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} |
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result[0] = result[0] * newsgn; |
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result[1] = result[1] * newsgn; |
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return; |
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} |
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ix = n - 1; |
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if (ix > 23) ix = 23; |
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kn = kvalues[ix]; |
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x = 1; |
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y = 0; |
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for (i = 0; i < n; ++i) { |
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atn = angles[i]; |
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sigma = (theta < alpha) ? 1 : -1; |
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theta += sigma * atn; |
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t = x; |
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x -= sigma * y * pow2; |
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y += sigma * t * pow2; |
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pow2 /= 2.0; |
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} |
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result[0] = x * kn; |
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result[1] = y * kn; |
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} |
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// Main method |
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public static void main(String[] args) { |
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double c_cos, c_sin; |
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double[] result = new double[2]; |
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double[] angles = {-9.0, 0.0, 1.5, 6.0}; |
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String format; |
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System.out.println(" x sin(x) diff. sine cos(x) diff. cosine"); |
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format = "%+03d.0° %+.8f (%+.8f) %+.8f (%+.8f)\n"; |
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for (int th = -90; th <= +90; th += 15) { |
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double thr = radians(th); |
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cordic(thr, 24, result); |
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c_cos = result[0]; |
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c_sin = result[1]; |
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System.out.printf(format, th, c_sin, c_sin - Math.sin(thr), c_cos, c_cos - Math.cos(thr)); |
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} |
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System.out.println("\nx(rads) sin(x) diff. sine cos(x) diff. cosine"); |
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format = "%+4.1f %+.8f (%+.8f) %+.8f (%+.8f)\n"; |
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for (int i = 0; i < angles.length; ++i) { |
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double thr = angles[i]; |
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cordic(thr, 24, result); |
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c_cos = result[0]; |
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c_sin = result[1]; |
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System.out.printf(format, thr, c_sin, c_sin - Math.sin(thr), c_cos, c_cos - Math.cos(thr)); |
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} |
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} |
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} |
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</syntaxhighlight> |
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{{out}} |
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<pre> |
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x sin(x) diff. sine cos(x) diff. cosine |
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-90.0° -1.00000000 (+0.00000000) -0.00000007 (-0.00000007) |
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-75.0° -0.96592585 (-0.00000003) +0.25881895 (-0.00000009) |
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-60.0° -0.86602545 (-0.00000005) +0.49999992 (-0.00000008) |
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-45.0° -0.70710684 (-0.00000006) +0.70710672 (-0.00000006) |
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-30.0° -0.49999992 (+0.00000008) +0.86602545 (+0.00000005) |
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-15.0° -0.25881895 (+0.00000009) +0.96592585 (+0.00000003) |
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+00.0° +0.00000007 (+0.00000007) +1.00000000 (-0.00000000) |
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+15.0° +0.25881895 (-0.00000009) +0.96592585 (+0.00000003) |
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+30.0° +0.49999992 (-0.00000008) +0.86602545 (+0.00000005) |
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+45.0° +0.70710684 (+0.00000006) +0.70710672 (-0.00000006) |
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+60.0° +0.86602545 (+0.00000005) +0.49999992 (-0.00000008) |
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+75.0° +0.96592585 (+0.00000003) +0.25881895 (-0.00000009) |
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+90.0° +1.00000000 (-0.00000000) -0.00000007 (-0.00000007) |
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x(rads) sin(x) diff. sine cos(x) diff. cosine |
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-9.0 -0.41211842 (+0.00000006) -0.91113029 (-0.00000003) |
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+0.0 +0.00000007 (+0.00000007) +1.00000000 (-0.00000000) |
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+1.5 +0.99749499 (+0.00000000) +0.07073719 (-0.00000002) |
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+6.0 -0.27941552 (-0.00000002) +0.96017028 (-0.00000001) |
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</pre> |
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=={{header|Julia}}== |
=={{header|Julia}}== |
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