The function is introduced in [Regis 2014] and extended here by a parameter \(p_{shift}\).
It is used to squash functions with a large range into a smalller range.
Let \(y' = (y-p_{shift})\):
$$ plog(y) = \ln(1+ y'), \quad\mbox{if}\quad y' \ge 0 $$
$$ plog(y) = -\ln(1- y'), \quad\mbox{if}\quad y' < 0 $$