public class Test {
  /*
  The idea is to write a version of Math.pow(x,y), to find x^y, without
  using any library functions.
  If y is a positive integer, we just do a loop x X x X x.. y times.
  But if y is not an integer?
  We do exp( y log x )
  So we need to write a log function and an exponential

  */

  static double abs(double x)
  { // version of Maths.abs
    return x<0?-x:x;
  }

  static double log(double xx) {
    final double E = 2.7182818284590452353602874713527; // Euler's constant, e
    if (xx < 0) { // no log negative number
      throw new IllegalArgumentException();
    }
    double nn=0; // see later
    if (xx > 1) { // use Maclaurin series for log(1+x)
      while (xx>E) // remove powers of e
      {
        xx/=E;
        nn++; // counting them - we add in nn at the end
      } // now xx is from 0 to 2.71...
      if (xx>2) // power series really bad for 2 to 2.71 so
      {
        nn+=0.69314718; // this is log 2
        xx/=2; // now xx is max 1.359
      }
      double x = xx - 1; // set up for power series
      double result = 0;
      int n = 1;
      double pow = -1;
      double term;
      do {
        pow *= -x;
        term = pow / n;
        n++;
        result += term;

      } while (abs(term)>1e-6);
      return result+nn;
    }
    if (xx == 1) {
      return 0;
    }
    // use Maclaurin series log(1-x)
    double x = 1 - xx;
    double result = 0;
    int n = 1;
    double pow = 1;
    double term;
    do {
      pow *= x;
      term = pow / n;
      n++;
      result -= term;

    } while (n < 500);
    return result;
  }

  static double exp(double x)
  { // standard power series for e^x
    double pow=1;
    double n=1;
    double result=1;
    double div=1;
    do
    {
      pow*=x;
      div*=n;
      result+=pow/div;
      n++;

    } while (n<50);
    return result;
  }

  static double pow(double x, double y)
  {
    return exp(y*log(x));
  }

  public static void main(String[] d) {

    // test log
    // System.out.println(log(-2)); //exception
    System.out.println(log(2.1)); //0.7419373466666667
    System.out.println(log(3)); //1.0986122718454672
    System.out.println(log(1)); //0.0
    System.out.println(log(0.5)); //-0.6931471805599451
    System.out.println(log(0.1)); //-2.302585092994046
    // test exp
    System.out.println(exp(2)); //7.389056098930649
    System.out.println(exp(5)); //148.41315910257657
    System.out.println(exp(1)); //2.7182818284590455
    System.out.println(exp(0.5)); //1.6487212707001278
    System.out.println(exp(0)); // 1.0
    System.out.println(exp(-1)); //0.36787944117144245
    // test pow

    System.out.println(pow(2,2)); //3.9999960000044585
    System.out.println(pow(2,3)); //7.999988000016374
    System.out.println(pow(4,-1)); //0.24999993536993692
    System.out.println(pow(3,2.1)); //10.04510821143608

  }
}