c++ - Error subtracting floating point numbers when passing through 0.0

Question

The following program:

#include <stdio.h>

int main()
{
    double val = 1.0;
    int i;

    for (i = 0; i < 10; i++)
    {
        val -= 0.2;
        printf("%g %s
", val, (val == 0.0 ? "zero" : "non-zero"));
    }

    return 0;
}

Produces this output:

0.8 non-zero
0.6 non-zero
0.4 non-zero
0.2 non-zero
5.55112e-17 non-zero
-0.2 non-zero
-0.4 non-zero
-0.6 non-zero
-0.8 non-zero
-1 non-zero

Can anyone tell me what is causing the error when subtracting 0.2 from 0.2? Is this a rounding error or something else? Most importantly, how do I avoid this error?

EDIT: It looks like the conclusion is to not worry about it, given 5.55112e-17 is extremely close to zero (thanks to @therefromhere for that information).

Answer 1

Its because floating points numbers can not be stored in memory in exact value. So it is never safe to use == in floating point values. Using double will increase the precision, but again that will not be exact. The correct way to compare a floating point value is to do something like this:

val == target;   // not safe

// instead do this
// where EPS is some suitable low value like 1e-7
fabs(val - target) &lt EPS; 

EDIT: As pointed in the comments, the main reason of the problem is that 0.2 can't be stored exactly. So when you are subtracting it from some value, every time causing some error. If you do this kind of floating point calculation repeatedly then at certain point the error will be noticeable. What I am trying to say is that all floating points values can't be stored, as there are infinites of them. A slight wrong value is not generally noticeable but using that is successive computation will lead to higher cumulative error.