Why is 0.5==0.5f is true but 0.1==0.1f is false? [duplicate]

Question

Please look at following two code:

public static void main(String... args)
{
   System.out.println(0.5==0.5f);
}

Output : true

 public static void main(String... args)
 {
   System.out.println(0.1==0.1f);
 }

Output: false

Why is it happening so?

Answer 1

You are comparing two types of values: double and float. Think about the limitations of size with inexact numbers.

An example:

Exact values (decimal)

value1 -> 1/2 with 5 decimals is 0.50000
value2 -> 1/2 with 10 decimals is 0.5000000000

then

value1 == value2 -> returns true

Inexact values (decimal)

value3 -> 1/3 with 5 decimals is 0.33333
value4 -> 1/3 with 10 decimals is 0.3333333333

then

value3 == value4 -> returns false because they aren't the same.

0.1 cannot be represent exactly in binary (like 1/3 in decimal) but 0.5 can be.

The binary representation of 0.1d -> 0.000(1100)1100110011...
The binary representation of 0.5d -> 0.1

Answer 2

This has to do with the fact that floating point numbers are represented in the form c*2^q. 0.5 can be represented as 1*2^-1 while 0.1 is impossible to represent accurately independent of how large you make c and q.

When comparing a float to a double, the float is cast to a double. If the number that is represented is already correctly representable as a float, it will have the same value when cast as a double, but if not, the double will have some extra significant digits and hence will compare non equal.