Just write your function like this
function LOGISTIC(T)
log(one(T)/eps(T) - one(T))
end
function logistic(x::T) where {T}
LOGISTIC_T = LOGISTIC(T)
x > LOGISTIC_T && return one(x)
x < -LOGISTIC_T && return zero(x)
return one(x) / (one(x) + exp(-x)) end
This way, your function will work for any type supporting eps, one, and exp. Note that due to specialization, this should be just as fast as your implementation.