Return $D_{KL}(P \parallel Q)$ in bits.

$$D_{KL}(P \parallel Q) = \sum_i p_i \log_2 \frac{p_i}{q_i}$$

Skip terms where $p_i = 0$. It is not symmetric, and it is not a distance: $D_{KL}(P \parallel Q)$ generally differs from $D_{KL}(Q \parallel P)$, which is exactly why the direction matters when it appears in a loss.

Input

p = [0.5, 0.5]
q = [0.5, 0.5]

Output

0.0