The 2-by-1 and 3-by-2 division functions described in the paper result in a very measurable speedup in my code. I think you're confusing those with the reciprocal calculation itself (which can be computed with a lookup table). I agree that part doesn't really lend itself to any significant performance benefit and is probably better calculated with a single hardware division instead.

I feel it necessary to point out that the 3-by-2 division actually has multiple benefits which are easy to miss:

1. The quotient loop can be skipped as I mentioned.

2. The "Add back" step is less likely to be triggered.

3. Since a 2-word remainder is computed with the division, you can skip 2 iterations on the multiply+subtract step.

My reimplementation of GMP documents both the 2-by-1 and 3-by-2 divisions pretty thoroughly[1][2].

[1] https://github.com/bcoin-org/libtorsion/blob/master/src/mpi....

[2] https://github.com/bcoin-org/libtorsion/blob/master/src/mpi....