# Sign preserving modular distance

In Math.

tags: c++ programming math

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;
}
```