Summary:
Consider BlockReadAmpBitmap with bytes_per_bit = 32. Suppose bytes [a, b) were used, while bytes [a-32, a)
and [b+1, b+33) weren't used; more formally, the union of ranges passed to BlockReadAmpBitmap::Mark() contains [a, b) and doesn't intersect with [a-32, a) and [b+1, b+33). Then bits [floor(a/32), ceil(b/32)] will be set, and so the number of useful bytes will be estimated as (ceil(b/32) - floor(a/32)) * 32, which is on average equal to b-a+31.
An extreme example: if we use 1 byte from each block, it'll be counted as 32 bytes from each block.
It's easy to remove this bias by slightly changing the semantics of the bitmap. Currently each bit represents a byte range [i*32, (i+1)*32).
This diff makes each bit represent a single byte: i*32 + X, where X is a random number in [0, 31] generated when bitmap is created. So, e.g., if you read a single byte at random, with probability 31/32 it won't be counted at all, and with probability 1/32 it will be counted as 32 bytes; so, on average it's counted as 1 byte.
*But there is one exception: the last bit will always set with the old way.*
(*) - assuming read_amp_bytes_per_bit = 32.
Closes https://github.com/facebook/rocksdb/pull/2259
Differential Revision: D5035652
Pulled By: lightmark
fbshipit-source-id: bd98b1b9b49fbe61f9e3781d07f624e3cbd92356
Aaron Gao