Gcd for real numbers

Question

Hello! I have the following task: to write in C ++ a method that calculates the GCD for 2 int numbers OR double (template class).

I took the Euclidean algorithm with a few changes:

template <typename T> T rational<T>::nod(T a, T b) { if (a == b) { return a; } if (a > b) { T tmp = a; a = b; b = tmp; } return nod(a, b - a); }

Works with:

 rational<double> rat(5, 10);//рациональная дробь 5/10 rat.nod(5, 10);//вычисление НОД 5 и 10

And does not work when:

 rational<double> rat(5.1, 10);//рациональная дробь 5/10 rat.nod(5.1, 10);//вычисление НОД 5.1 и 10

Question: why is this happening, and how to fix it in order to work in both variants? Thanks in advance for the answers!

And “does not work”, apparently, because 0.1 does not appear to be exactly in the double data type.
In particular, checking for equality of double meaningless.
Apparently, you need rational numbers over the ring of integers, that is, rational<int> .
For double there is no such thing, therefore it is impossible to calculate what is not ... Therefore, when using double arguments, the first thing to do is to convert their type to an integer (if necessary, with rounding), to get an integer GCD and convert it back to double .

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