Is 8 a power of two?

A good answer might be:

Yes: 2*2*2 == 8

Here is the program again, this time with better accuracy because the amount of the increment is one over a power of two.

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

Unfortunately, because of the awkward increment value ( of 1/8 ) the table is inconvenient for human consumption. But computing a table of numbers like this is a relatively rare demand for a computer. Usually the numbers computed in a loop are used by the program itself for some larger task such as drawing a picture.

QUESTION 8:

(Thought question: ) If using binary-based floating point numbers has these accuracy problems, why not use decimal-based floating point numbers?