Distances among Point Sets in R^2 and R^3

For a finite set $P\subset\mathbb{R}^d$, let $f_d(P)$ be its number of pairs at unit distance and let $g_d(P)$ be its number of distinct pairwise distances. For $d\in\{2,3\}$, determine tight asymptotic bounds for $f_d(n)=\max_{|P|=n}f_d(P)$ and $g_d(n)=\min_{|P|=n}g_d(P)$.