Mod of negative number is melting my brain

I always use my own mod function, defined as

int mod(int x, int m) {
    return (x%m + m)%m;
}

Of course, if you're bothered about having two calls to the modulus operation, you could write it as

int mod(int x, int m) {
    int r = x%m;
    return r<0 ? r+m : r;
}

or variants thereof.

The reason it works is that "x%m" is always in the range [-m+1, m-1]. So if at all it is negative, adding m to it will put it in the positive range without changing its value modulo m.

Please note that C# and C++'s % operator is actually NOT a modulo, it's remainder. The formula for modulo that you want, in your case, is:

float nfmod(float a,float b)
{
    return a - b * floor(a / b);
}

You have to recode this in C# (or C++) but this is the way you get modulo and not a remainder.

Single-line implementation using % only once:

int mod(int k, int n) {  return ((k %= n) < 0) ? k+n : k;  }