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?

You've answered the question yourself. It's related to precision. Google will give you 1000.001 explanations. — John3136, Mar 06 '12 at 02:42

caf · Answer 1 · 2023-04-12T23:37:00.130

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.

score 3 · Answer 2 · answered Mar 06 '12 at 02:41

3

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

answered Mar 06 '12 at 02:41

ACC

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Thanks a lot for the answer. I went through the link and found this other link which explained to me what i was missing. http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm – Pkp Mar 06 '12 at 02:52

score 3 · Answer 3 · answered Mar 06 '12 at 02:47

3

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

answered Mar 06 '12 at 02:47

dawg

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score 2 · Answer 4 · edited Mar 06 '12 at 02:49

2

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
}

edited Mar 06 '12 at 02:49

paxdiablo

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answered Mar 06 '12 at 02:42

Richard J. Ross III

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Richard, +1 since I prefer self-contained answers but the function you're looking for is `fabs` rather than `abs` - I fixed that for you :-) – paxdiablo Mar 06 '12 at 02:50
Thank you. This helps and explains a lot. – Pkp Mar 06 '12 at 02:54
Downvoted for misleading *"should always use"*. Using epsilon comparison gives inconsistent results on float value range. On extreme values comparison is only an inefficient `==`. Epsilon comparison can be useful sometimes, but only sometimes. – user694733 Feb 27 '18 at 11:31

C- Floating point precision

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