Softmax on the go

Softmax (“Scores into chances”) divides each exp(score) by the total of them all. Scores now arrive one at a time and can’t be kept, so keep a small state instead: [biggest, total], the biggest score so far and total = Σ exp(score − biggest) over the scores so far, measured from that biggest one so nothing overflows. Before the first score the state is None. Write update(state, score): the new state after one more score arrives.