Avoid overflow with softplus function in python

Question

I am trying to implement the following softplus function:

log(1 + exp(x))

I\'ve tried it with math/numpy and float64 as data type, but whenever

Answer 1

What I'm currently using (slightly inefficient but clean and vectorized):

def safe_softplus(x, limit=30):
    return np.where(x>limit, x, np.log1p(np.exp(x)))