如何使用模板在编译时查找2个数字的HCF？

Question

I want to calculate HCF of 2 numbers using value of enum with template recursion:

#include <stdio.h>
template<int x,int y,int r>
struct s{
    enum{e=x%r==0 && y%r==0?r:s<x,y,r-1>::e};
};

int main(){
    printf("%d\n",s<3,5,MIN(3,5)>::e);
    return 0;
};

which x and y are the 2 numbers,r is the value to test, the principle is that find a number to divide x and y, start from min of x and y, then decrease by 1 until a value of r can divide both x and y. But this code cannot compile because of following errors:

xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -252>'     requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -251>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -250>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -249>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -248>' requested here
xxx.cpp:4:31: note: (skipping 246 contexts in backtrace; use -ftemplate-backtrace-limit=0 to see all)
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -1>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, 0>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, 1>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, 2>' requested here
xxx.cpp:8:19: note: in instantiation of template class 's<3, 5, 3>' requested here
printf("%d\n",s<3,5,3>::e);
              ^
xxx.cpp:4:31: note: use -ftemplate-depth=N to increase recursive template instantiation depth
enum{e=x%r==0 && y%r==0?r:s<x,y,r-1>::e};
                          ^
1 error generated.

What is the problem?

Answer 1

@moonshadow's comment is the core answer, but let me expand it into a full answer.

The compiler output luckily shows the relevant instantiations:

xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, -1>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, 0>' requested here
xxx.cpp:4:31: note: in instantiation of template class 's<3, 5, 1>' requested here

Let's look at the actual instantiation

template<int x = 3, int y = 5, int r = 0>
struct s{
    enum{e = 3%0==0 && 5%0==0 ? 0 : s<5,3,-1>::e};
};

Obviously, two things are wrong:

1. 3 % 0 is a division by zero
2. The instantiation of s<5,3,-1> is unnecessary.

This is easily fixed with constexpr , but let's stick with a templated solution. Recursion needs an special case for the end, and HCF(x,y)=1 is that special case for co-primes.

template <int x, int y> 
struct s<x,y,1> { enum e = 1 };

That said, you really should use Euclid's algorithm as this brute-force search won't work for something as easy as s<300,300,300> .