[LegionMammal978]

You also need some extra bits at the top so that it doesn't overflow (e.g., on an adversarial input filled with copies of the max finite value, followed by just as many copies of its negation, so that it sums to 0). The exact number will depend on the maximum input length, but for arrays stored in addressible memory it will add up to no more than 64 or so.

[tialaramex]

Thanks, you're right there for accumulating excess, I don't think you can actually get to 64 extra bits but sure, lets say 64 extra bits if you want a general purpose in memory algorithm, it's not cheap but we shouldn't be surprised it can be done.