我的CORDIC算法有什麼問題？

Question

改編到Java從Wikipedia page on CORDIC：

class MathFunctions { 
final static double[] 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}; 
final static double[] Kvalues = { 
    0.70710678118655, 0.63245553203368, 0.61357199107790, 0.60883391251775, 
    0.60764825625617, 0.60735177014130, 0.60727764409353, 0.60725911229889, 
    0.60725447933256, 0.8988, 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}; 
public static double[] cordic(double theta, int n) { 
    double[] v = new double[2]; 
    if (theta < -Math.PI/2 || theta > Math.PI/2) { 
     v = (theta < 0)? cordic(theta + Math.PI, n):cordic(theta - Math.PI, n); 
     return new double[]{-v[0],-v[1]}; 
    } 
    double angle=angles[0], Kn=Kvalues[Math.min(n, Kvalues.length-1)]; 
    double sigma, factor, poweroftwo=1; 
    for (int i=0; i<n-1; i++) { 
     sigma = (theta < 0)? -1 : 1; 
     factor = sigma*poweroftwo; 
     v = new double[]{v[0] - v[1]*factor, v[0]*factor + v[1]}; 
     theta -= sigma*angle; 
     poweroftwo /= 2; 
     angle = (i+2 > angles.length)? angle/2 : angles[i+2]; 
    } 
    return new double[]{v[0]*Kn, v[1]*Kn}; 
}} 

我只是測試的代碼與cos PI這樣的：

double cosPI = MathFunctions.cordic(Math.PI, 8)[0]; 
System.out.printf("cos(PI) = %f%n",cosPI); 

出於某種原因，它給了我-0.0而不是-1。

Answer 1

簡短的回答是，你沒有正確初始化v向量。更新後的代碼如下。請注意，在Java這仍然不是很準確。

class MathFunctions { 
    final static double[] angles = { 
    0.78539816339745d, 0.46364760900081d, 0.24497866312686d, 0.12435499454676d, 
    0.06241880999596d, 0.03123983343027d, 0.01562372862048d, 0.00781234106010d, 
    0.00390623013197d, 0.00195312251648d, 0.00097656218956d, 0.00048828121119d, 
    0.00024414062015d, 0.00012207031189d, 0.00006103515617d, 0.00003051757812d, 
    0.00001525878906d, 0.00000762939453d, 0.00000381469727d, 0.00000190734863d, 
    0.00000095367432d, 0.00000047683716d, 0.00000023841858d, 0.00000011920929d, 
    0.00000005960464d, 0.00000002980232d, 0.00000001490116d, 0.00000000745058d}; 
    final static double[] Kvalues = { 
    0.70710678118655d, 0.63245553203368d, 0.61357199107790d, 0.60883391251775d, 
    0.60764825625617d, 0.60735177014130d, 0.60727764409353d, 0.60725911229889d, 
    0.60725447933256d, 0.8988d, 0.60725303152913d, 0.60725295913894d, 
    0.60725294104140d, 0.60725293651701d, 0.60725293538591d, 0.60725293510314d, 
    0.60725293503245d, 0.60725293501477d, 0.60725293501035d, 0.60725293500925d, 
    0.60725293500897d, 0.60725293500890d, 0.60725293500889d, 0.60725293500888d}; 

    public static double[] cordic(double theta, int n) { 
    double[] v; 
    if (theta < -Math.PI/2 || theta > Math.PI/2) { 
     v = (theta < 0)? cordic(theta + Math.PI, n):cordic(theta - Math.PI, n); 
     return new double[]{-v[0],-v[1]}; 
    } 
    // You didn't initialise v properly 
    v = new double[] {1.0d, 0, }; 
    double angle=angles[0], Kn=Kvalues[Math.min(n, Kvalues.length-1)]; 
    double sigma, factor, poweroftwo=1; 
    for (int i=0; i<n; i++) { 
     sigma = (theta < 0)? -1 : 1; 
     factor = sigma*poweroftwo; 
     v = new double[]{v[0] - v[1]*factor, v[0]*factor + v[1]}; 
     theta -= sigma*angle; 
     poweroftwo /= 2; 
     angle = (i+2 > angles.length)? angle/2 : angles[i+2]; 
    } 
    return new double[]{v[0]*Kn, v[1]*Kn}; 
    } 

    public static void main(String[] args) 
    { 
    double[] values; 
    values = MathFunctions.cordic(Math.PI, 8); 
    System.out.printf("cos(PI) = %f, sin(PI) = %f%n",values[0], values[1]); 
    values = MathFunctions.cordic(Math.PI/2, 8); 
    System.out.printf("cos(PI/2) = %f, sin(PI/2) = %f%n",values[0], values[1]); 
    values = MathFunctions.cordic(0, 15); 
    System.out.printf("cos(0) = %f, sin(0) = %f%n",values[0], values[1]); 
    } 
} 

Answer 2

該代碼仍然有一個主要的錯誤。代碼

angle = (i+2 > angles.length)? angle/2 : angles[i+2]; 

應該是

angle = (i+2 > angles.length)? angle/2 : angles[i+1];