8. Nicer Table



Answer:
Yes: 2*2*2 == 8










Nicer Table
Here is the program again, this time with better
accuracy because the divisor is 8, a power of two.




    
        

        

        

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

    for ( double x = 1.0/8.0; x <= 2.0; x = x + 1.0/8.0  )
    {
      System.out.println( x + "\t" + Math.log( x ) );
    }
  } 
}      

            		
        

    


Here is its output:




    
        

        

        

            
                
               
x        ln(x)
0.125   -2.0794415416798357
0.25    -1.3862943611198906
0.375   -0.9808292530117262
0.5     -0.6931471805599453
0.625   -0.4700036292457356
0.75    -0.2876820724517809
0.875   -0.13353139262452263
1.0     0.0
1.125   0.11778303565638346
1.25    0.22314355131420976
1.375   0.3184537311185346
1.5     0.4054651081081644
1.625   0.4855078157817008
1.75    0.5596157879354227
1.875   0.6286086594223741
2.0     0.6931471805599453

            		
        

    






This is our best table yet! Unfortunately, because of the awkward increment value (of 1/8) the table is inconvenient for human consumption. But computing a table of numbers for display purposes is rare. Usually the numbers computed in a loop are
    used by the program itself for some larger task, such as drawing a picture, or for an engineering computation, and there is no particular reason to use a step size of one tenth. No human will actually look at the numbers.






Question 8:
(Thought question: ) Binary-based floating point numbers have accuracy problems. So why not build 
 computers that use decimal-based floating point numbers?
Hint: chocolate-chip cookies are three for a dollar. How much is one cookie?