Calculating greatest common divisor

Question

I have written the following function to calculate GCD of floating point numbers, but when I run this for the input (111.6, 46.5), the calculation of fmod(a,b) in the funciton starts giving the wrong result after 2 recursive calls. I am unable to find the error here. Can anyone find what is going wrong here?

float gcd(float a, float b){
if (a>b) {
    if(b==0){
        return a;
    }
    else {
        return gcd(b, fmod(a,b));
    }
}
else {
    if (a==0) {
        return b;
    }
    else {
        return gcd(fmod(b,a), a);
    }
}

}

Answer 1

Because of the way that floating-point values are represented, the source text “111.6” is converted to 111.599999999999994315658113919198513031005859375, and the source text “46.5” is converted to 46.5. Then your gcd function returns 7.62939453125e-06. That is the correct GCD of the two input values.

Note that the first value is 14627635/131072. All floating-point numbers are some integer (within a certain range) multiplied or divided by a power of two. It is impossible to represent 111.6 exactly with binary floating-point. Since you cannot represent 111.6 exactly, you cannot do exact arithmetic with it. Floating-point is largely designed for approximate arithmetic. Doing exact arithmetic requires a great deal of care.

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What does it mean to talk about the GCD of real numbers (as opposed to integers)?

The GCD of a and b is the largest number c such that a/c and b/c are integers.