I know that Sergei Lebedev did quite a bit of work (for the bitset package) optimizing certain Integer bit operations. That code doesn't work with the new Integer, but it can probably be adapted.

On Sat, 18 Jun 2016, Carter Schonwald wrote:

> Henning: I suggest you read the gmp source and tell us :)

I hoped you have already done so. :-)

Does GHC call GMP for bit operations on Integer?
Aha, yes, it calls integer_gmp_mpn_and_n for (.&.) :
   https://hackage.haskell.org/package/integer-gmp-1.0.0.1/docs/src/GHC.Integer.Type.html#c_mpn_and_n
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