Shift-Right in Gear rollsum messes with resynchronisation after changes. about deduplication HOT 1 CLOSED

After thinking about this a bit more, older values will expire from the hash in a probabilistic way when using a right-shift. This means the effective window size is variable, but the probabilities of it getting large are actually small. There could still be degenerate cases that make it very large, but on average, assuming random behavior, it should be OK.

Using a right-shift, the hash becomes the most significant 32 bits of a very large sum of values, where the oldest byte is adding a 32 bit number to the sum. Assuming random numbers, there is a 50% chance that this propagates a bit change to to the 33rd bit, 25% change to the 34th bit, etc. So the chance that it propagates a bit change into the most significant 32 bits used for the hash is 1/2^(len-32), where len is the number of bytes included in the sum. So there is a less than 0.4% chance of the effective sliding window being larger than 40 bytes.

So I think using a right-shift is probably OK, and the effective increase in the sliding window size probably helps more by strengthening the hash more than the problems caused by the low chance of it getting too big. It's probably worth testing.

from deduplication.