code: import static java.lang.Math.*;
  
  public class Test {
      final static int N = 32;
      final static int N2 = (N * (N - 1) / 2);
      final static double STEP = 0.05;
  
      static double[] xval = new double[N];
      static double[] t_sin = new double[N];
      static double[] t_cos = new double[N];
      static double[] t_tan = new double[N];
  
      static double[] r_sin = new double[N2];
      static double[] r_cos = new double[N2];
      static double[] r_tan = new double[N2];
  
      static double rho(double[] x, double[] y, double[] r, int i, int n) {
          if (n < 0)
              return 0;
  
          if (n == 0)
              return y[i];
  
          int idx = (N - 1 - n) * (N - n) / 2 + i;
          if (r[idx] != r[idx])
              r[idx] = (x[i] - x[i + n])
                      / (rho(x, y, r, i, n - 1) - rho(x, y, r, i + 1, n - 1))
                      + rho(x, y, r, i + 1, n - 2);
  
          return r[idx];
      }
  
      static double thiele(double[] x, double[] y, double[] r, double xin, int n) {
          if (n > N - 1)
              return 1;
          return rho(x, y, r, 0, n) - rho(x, y, r, 0, n - 2)
                  + (xin - x[n]) / thiele(x, y, r, xin, n + 1);
      }
  
      public static void main(String[] args) {
          for (int i = 0; i < N; i++) {
              xval[i] = i * STEP;
              t_sin[i] = sin(xval[i]);
              t_cos[i] = cos(xval[i]);
              t_tan[i] = t_sin[i] / t_cos[i];
          }
  
          for (int i = 0; i < N2; i++)
              r_sin[i] = r_cos[i] = r_tan[i] = Double.NaN;
  
          System.out.printf("%16.14f%n", 6 * thiele(t_sin, xval, r_sin, 0.5, 0));
          System.out.printf("%16.14f%n", 3 * thiele(t_cos, xval, r_cos, 0.5, 0));
          System.out.printf("%16.14f%n", 4 * thiele(t_tan, xval, r_tan, 1.0, 0));
      }
  }
  