This will embarrass me later, when I think of a better solution. But, sometimes, you need a fast and dirty answer.

I want a modulus operator Mod(a,b,m) such that:

• Mod(2,6,7)=-3
• Mod(6,2,7)=3

That is, the operator avoids the 4-hop path between 2 and 6 and, instead, circles around via a path of length 3. The answer preserves the path direction if you leave from a and go to b.

The following code calculates this. There's got to be a better way.

#include <iostream>
#include <cmath>

double absmin(double a, double b){
  if(std::abs(a)<std::abs(b))
    return a;
  else
    return b;
}

double ModDist(double src, double dest, double m){
  if(dest<src)
    return absmin(dest+m-src, dest-src);
  else
    return absmin(dest-src, dest-m-src);
}

int main(){
  std::cout<<ModDist(2,6,7)<<std::endl;
  std::cout<<ModDist(6,2,7)<<std::endl;
}