A Loop with an Integer Variable

Often a program uses an integer loop control variable which is used to compute a floating point x for every iteration of the loop:

class LogTable
{
  public static void main ( String[] args )
  {
    System.out.println( "x" + "\t ln(x)" );

    for ( int j = 1; j <= 20; j++ )
    {
      double x = j/10.0 ;
      System.out.println( x + "\t" + Math.log( x ) );
    }
  } 
}

This is not without problems, but at least the errors in x are not accumulating. Here is the output:

x        ln(x)
0.1     -2.3025850929940455
0.2     -1.6094379124341003
0.3     -1.2039728043259361
0.4     -0.916290731874155
0.5     -0.6931471805599453
0.6     -0.5108256237659907
0.7     -0.35667494393873245
0.8     -0.2231435513142097
0.9     -0.10536051565782628
1.0     0.0
1.1     0.09531017980432493
1.2     0.1823215567939546
1.3     0.26236426446749106
1.4     0.33647223662121284
1.5     0.4054651081081644
1.6     0.4700036292457356
1.7     0.5306282510621704
1.8     0.5877866649021191
1.9     0.6418538861723947
2.0     0.6931471805599453

The result of dividing  j by 10.0 is not completely accuracy. However, dividing an integer by a power of two, is accurate (as long as the result is not too small).