Can someone explain this phenomenon?

[Maximilian]

public class Test {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        
        for(double aDouble = -1.0; aDouble <= 1.0; aDouble = aDouble + 0.1)
        {
            System.out.println(aDouble);
        }
        
    }
    
}

Output:

-1.0
-0.9
-0.8
-0.7000000000000001
-0.6000000000000001
-0.5000000000000001
-0.40000000000000013
-0.30000000000000016
-0.20000000000000015
-0.10000000000000014
-1.3877787807814457E-16
0.09999999999999987
0.19999999999999987
0.2999999999999999
0.3999999999999999
0.4999999999999999
0.5999999999999999
0.6999999999999998
0.7999999999999998
0.8999999999999998
0.9999999999999998

float does it as well.

 

[Chaotic42]

Floating point rounding error. http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

 

[mv2devnull]

Floating point values have limited precision.
http://en.wikipedia.org/wiki/Floating_point

Limited precision means that you can only have discrete values. Apparently, -0.7 is not one of them, so the result of -0.8+0.1 has the nearest possible value.

If you limit the number of digits that the println does show, then println will round and you will not know that the "-0.7" you will see is not what aDouble actually holds.

 

[Cogman]

It comes down to how floating points are represented and the fact that it is base 2.

Imagine you want to represent 0.125. In base ten we could say that is 1/10 + 2/100 + 5/1000

The same concept is applied with floats, only the denominator is base 2 so we would have the problem of

0.125 = x/2 + y/4 + z/8 + i/16 + j/32

or

0.125 = 0/2 + 0/4 + 1/8 + 0/16 + 0/32

Because of this. Certain numbers can't be represented 0.1 is one of them. It is a repeating number (like 1/3).

So in the end, the compiler and the language does its best bet. It is the same problem

1/3 + 1/3 + 1/3 = 1, right?

Yet if we truncate it we would end up with something like

0.33333333333 + 0.33333333333 + 0.33333333333 = 0.99999999999


see This wiki article for more examples

 

[Childs]

Isn't -1.3877787807814457E-16 what he is asking about? Shouldn't it be something like -0.000000000000000nn?

 

[Chaotic42]

Isn't -1.3877787807814457E-16 what he is asking about? Shouldn't it be something like -0.100000000000000nn?

Nope. It's a negative number which is very, very close to zero. ~-1.39*10^(-16)

 

[Childs]

Nope. It's a negative number which is very, very close to zero. ~-1.39*10^(-16)

doh, E-16.