A certain class of stochastic summability methods of mantissa type is introduced and its connection to almost sure limit theorems
is discussed. The summability methods serve as suitable weights in almost sure limit theory, covering all relevant known examples
for, e.g., normalized sums or maxima of i.i.d. random variables. In the context of semistable domains of attraction the methods
lead to previously unknown versions of semistable almost sure limit theorems.