[tgflynn]

I would think that in most cases you should be able to prove an upper bound on the sum and make sure the accumulator is large enough to accommodate it. My guess is that 512 bits should be enough to span all physically/computationally relevant scales.

[pascal_cuoq]

This article lists some real examples that require more than 512 bits: https://res.mdpi.com/d_attachment/mathematics/mathematics-03...

Note that digits of precision are expressed in decimal unless explicitly given as “bits”, so that the phrase “10,000-digit arithmetic” really means around 33,000 bits.

[tgflynn]

Certainly if you have errors that grow exponentially all bets are off. I wouldn't think that would apply to simply summing a set of numbers though.