main.java

/* Aurora Pariseau
  Floating point arithmetic
*/

import java.util.*;

class main
{
  public static void main (String args[])
  {
      float sum = 0.0f;
      float sum2 = 0.0f;
      for(float n = 1.0f; n <= 150000.0f; n++)
      {
        if(n == 3)
        {
          System.out.println("sum: " + sum);
          System.out.println("sum after: " + (sum + 1.0f/n));
          System.out.println("difference: " + ((sum + 1.0f/n) - sum));
        }
        if(150001-n == 3)
        {
          System.out.println("sum2: " + sum2);
          System.out.println("sum2 after: " + (sum2 + 1.0f/(150001-n)));
          System.out.println("difference: " + (
            (sum2 + 1.0f/(150001-n) - sum2))
          );
        }
        float value = 1.0f/n;
        float value2 = 1.0f/(150001-n);

        sum += value;
        sum2 += value2;

      }
      System.out.println(sum + " " + sum2);
  }
}

/*
  As seen above, there is a rounding error in the arithmetic based on the
  precision of the leading number. This accounts for the difference between
  sum and sum2
*/