C- Floating point precision

Question

I have a program:

int main() 
{   
        float f = 0.0f;  
        int i;  

        for (i = 0 ; i < 10 ; i++) 
                f = f + 0.1f; 

        if (f == 1.0f) 
                printf("f is 1.0 \n"); 
        else 
                printf("f is NOT 1.0\n"); 

        return 0; 
} 

It always prints f is NOT 1.0 . I understand this is related to floating point precision in C. But I am not sure exactly where it is getting messed up. Can someone please explain me why it is not printing the other line?

Answer 1

Binary floating point cannot represent the value 0.1 exactly, because its binary expansion does not have a finite number of digits (in exactly the same way that the decimal expansion of 1/7 does not).

The binary expansion of 0.1 is

0.000110011001100110011001100...

When truncated to IEEE-754 single precision, this is approximately 0.100000001490116119 in decimal. This means that each time you add the "nearly 0.1" value to your variable, you accumulate a small error - so the final value is slightly higher than 1.0 .

Answer 2

This is equivelent to adding 0.33 together 3 times (0.99) and wondering why it is not equal to 1.0.

You may wish to read What Every Programmer Should Know About Floating Point Arithmetic

Answer 3

You cannot compare floats like this. You need to define a threshold and compare based on that. This blog post explains

Answer 4

For floating point numbers you should always use an epsilon value when comparing them:

#define EPSILON 0.00001f

inline int floatsEqual(float f1, float f2)
{
    return fabs(f1 - f2) < EPSILON; // or fabsf
}