All shards compute their own, and send the result in a non deterministic order. My explanation is that the merge part of HLL depends on the order.

Line 95 of this method [1] from this implementation [2] shows a max(mask(x), mask(y)), which is not associative but is a close proxy to max()(which is associative).

[1] https://github.com/addthis/stream-lib/blob/af045cb4199959c07...

[2] https://github.com/addthis/stream-lib/blob/master/src/main/j...