// TestComplexSeries.java  series approximations vs ComplexFunctions

public class TestComplexSeries
{
  public TestComplexSeries()
  {
    double err, sumerrsin=0.0, numerr=0.0, maxx=0.0;
    double sumerrhsin=0.0, sumerrhcos=0.0, sumerrhatan=0.0;
    double sumerrasin=0.0, sumerracos=0.0;
    double maxerrasin=0.0, maxerracos=0.0;
    Complex a;
    
    System.out.println("TestComplexSeries running");
    for(double x=1.0e-3; x<=0.6; x=x*2.0)
    {
      for(double y=1.0e-3; y<=0.6; y=y*2.0)
      {
        a = new Complex(x,y);
        err=(a.sin().subtract(sinser(a))).abs();
        sumerrsin = sumerrsin+err;
        err=(a.sin().subtract(sinhor(a))).abs();
        sumerrhsin = sumerrhsin+err;
        err=(a.cos().subtract(coshor(a))).abs();
        sumerrhcos = sumerrhcos+err;
        err=(a.atan().subtract(atanhor(a))).abs();
        sumerrhatan = sumerrhatan+err;
        err=(a.asin().subtract(asinser(a))).abs();
        sumerrasin = sumerrasin+err;
        maxerrasin = Math.max(maxerrasin, err);
        err=(a.acos().subtract(acosser(a))).abs();
        sumerracos = sumerracos+err;
        maxerracos = Math.max(maxerracos, err);
        numerr = numerr+1.0;
      }
      maxx = Math.max(maxx, x);
    }
    System.out.println("sin  vs series count="+numerr+", avg err="+sumerrsin/numerr);
    System.out.println("sin  vs horner count="+numerr+", avg err="+sumerrhsin/numerr);
    System.out.println("cos  vs horner count="+numerr+", avg err="+sumerrhcos/numerr);
    System.out.println("atan vs horner count="+numerr+", avg err="+sumerrhatan/numerr);
    System.out.println("asin vs series count="+numerr+", avg err="+sumerrasin/numerr);
    System.out.println("asin vs series count="+numerr+", max err="+maxerrasin);
    System.out.println("acos vs series count="+numerr+", avg err="+sumerracos/numerr);
    System.out.println("acos vs series count="+numerr+", max err="+maxerracos);
    System.out.println("max x and y ="+maxx);
  }
  
  static Complex sinser(Complex z)
  {
    Complex z2 =  z.multiply(z);
    Complex z3 =  z.multiply(z2).divide(-6.0);
    Complex z5 = z3.multiply(z2).divide(120.0);
    Complex z7 = z5.multiply(z2).divide(-5040.0);
    Complex z9 = z7.multiply(z2).divide(362880.0);
    return z.add(z3.add(z5.add(z7.add(z9))));
  }
  
  static Complex sinhor(Complex z)
  {
    double d[] = {362880.0, -5040.0, 120.0, -6.0, 1.0};
    Complex z2 = z.multiply(z);
    Complex result = new Complex(0.0);
    for(int i=0; i<d.length; i++) result = z.divide(d[i]).add(result.multiply(z2));
    return result;
  }
  
  static Complex coshor(Complex z)
  {
    double d[] = {40320.0, -720.0, 24.0, -2.0};
    Complex z2 = z.multiply(z);
    Complex result = new Complex(0.0);
    for(int i=0; i<d.length; i++) result = z2.divide(d[i]).add(result.multiply(z2));
    return result.add(1.0);
  }
  
  static Complex asinser(Complex z)
  {
    Complex z2 =  z.multiply(z);
    Complex z3 =  z.multiply(z2).divide(6.0);
    Complex z5 = z3.multiply(z2).divide(40.0).multiply(3.0);
    Complex z7 = z5.multiply(z2).divide(112.0).multiply(5.0);
    Complex z9 = z7.multiply(z2).divide(1152.0).multiply(35.0);
    return z.add(z3.add(z5.add(z7.add(z9))));
  }

  static Complex acosser(Complex z)
  {
    double halfPi = 3.14159265358979323846/2.0;
    return (z.asin().negate()).add(halfPi);
  }  
  static Complex atanhor(Complex z)
  {
    double d[] = {-11.0, 9.0, -7.0, 5.0, -3.0, 1.0};
    Complex z2 = z.multiply(z);
    Complex result = new Complex(0.0);
    for(int i=0; i<d.length; i++) result = z.divide(d[i]).add(result.multiply(z2));
    return result;
  }
 
  public static void main(String args[]) // "main" required
  {
    new TestComplexSeries(); // construct and execute
  }
}