Near misses for the root of 2

No fraction has a square of exactly $2$. But some come very close. For each bottom $q$, take the top $p$ nearest to $q\sqrt{2}$, and measure the miss $p^2 - 2q^2$. You will find the bottoms up to $1000$ where the miss is only $1$ or $-1$.

The idea. If the miss were ever $0$, then $\left(\dfrac{p}{q}\right)^2 = 2$ exactly, and $\sqrt{2}$ would be rational.

Your tasks.

1. In best_top, return the whole number nearest to q * sqrt(2).
2. In miss, return p * p - 2 * q * q, where p = best_top(q).
3. Fill close with the bottoms q from $1$ to $1000$ whose miss is $1$ or $-1$, in order.