The four special functions

The modulus, the signum, the greatest integer and the fractional part are all short rules. You will write three of them without the math module, and test them on tricky inputs.

The idea. int(x) cuts off the decimals, which is $[x]$ only for $x \geq 0$. For a negative $x$ that is not whole, $[x]$ is one less than int(x).

Your tasks.

1. In sgn, return $1$, $-1$ or $0$.
2. In greatest, return $[x]$.
3. In frac, return $\{x\} = x - [x]$.