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

For a point set $P$ in $\mathbb{R}^d$, let $f_d(P)$ be the number of unit-distance point pairs:

$$f_d(P) = \left| \{ (u,v) \mid u, v \in P , \, \|u-v\| = 1 \} \right| \; ;$$

and let $f_d(n)$ be the maximum over all sets of $n$ points:

$$f_d(n) = \max_{|P| = n} f_d(P) \; .$$

Further, let $g_d(P)$ denote the number of distinct distances induced by a set of points $P$:

$$g_d(P) = \left| \{ \|u-v\| \mid u, v \in P \} \right| \; ;$$

and let $g_d(n)$ be the minimum over all sets of $n$ points:

$$g_d(n) = \min_{|P|=n} g_d(P) \; .$$

Give upper and lower bounds on $f_d(n)$ and $g_d(n)$, particularly for $d=2$ and $d=3$.