Hi GHC devs, As some of you may know, I am working on fixing several longstanding issues with GHC's big numbers implementation (Integer, Natural). You can read more about it here: https://gitlab.haskell.org/hsyl20/ghc/raw/hsyl20-integer/libraries/ghc-bignu... To summarize, we would have a single `ghc-bignum` package with different backends (GMP, pure Haskell, etc.). The backend is chosen with a Cabal flag and new backends are way easier to add. All the backends use the same representation which allows Integer and Natural types and datacons to be wired-in which has a lot of nice consequences (remove some dependency hacks in base package, make GHC agnostic of the backend used, etc.). A major roadblock in previous attempts was that integer-simple doesn't use the same representations for numbers as integer-gmp. But I have written a new pure Haskell implementation which happens to be faster than integer-simple (see perf results in the document linked above) and that uses the common representation (similar to what was used in integer-gmp). I am very close to submit a merge request but there is a remaining question about the Bits instance for negative Integer numbers: We don't store big negative Integer using two's complement encoding, instead we use signed magnitude representation (i.e. we use constructors to distinguish between (big) positive or negative numbers). It's already true today in integer-simple and integer-gmp. However integer-gmp and integer-simple fake two's complement encoding for Bits operations. As a consequence, every Bits operation on negative Integers does *a lot* of stuff. E.g. testing a single bit with `testBit` is linear in the size of the number, a logical `and` between two numbers involves additions and subtractions, etc. Question is: do we need/want to keep this behavior? There is nothing in the report that says that Integer's Bits instance has to mimic two's complement encoding. What's the point of slowly accessing a fake representation instead of the actual one? Could we deprecate this? The instance isn't even coherent: popCount returns the negated numbers of 1s in the absolute value as it can't return an infinite value. Thanks, Sylvain