> Question is: do we need/want to keep this behavior?

I think we really do want to keep this behavior.

And not just because I for one have a decent cross-section of code that would just become horribly broken (and would have to find some way to jerry-rig the existing behavior anyways) if we randomly changed it.

The current underlying representation if more directly exposed would be quite surprising to users and doesn't at all fit the mental model of what an Int-like thing is.

Other examples: Conor McBride's work on co-deBruijn syntax exploits the current Bits instance heavily (and can be greatly streamlined by making more use of it that he doesn't, quite yet.)

-Edward

On Fri, Nov 15, 2019 at 9:34 PM Sylvain Henry <sylvain@haskus.fr> wrote:

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-bignum/docs/ghc-bignum.rst

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
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