> My feeling, looking through your code is that:
>
> * It really sits *on top of* the mpz layer
> * It relies on some code for single limbs that is not abstracted
> anywhere in MPIR, but should be
>
> It should:
>
> * be implemented *in* the new mpir_n layer
> * the unsigned long portion should be abstracted out into a new long
> layer (just as there is a longlong.h, there should be a long.c and
> long.h)
>
Yesterday using binary splitting method but with zero other optimizations
I've written a code for factorial (mpz_fac_ui in gmp) in also mpz layer, but
it was slower by about only 40%. By some  optimizations it would be about
10% slower. I think that none of the uploaded 4 codes would be much faster
in mpn layer, because currently gmp is also using a binary splitting idea
for factorial, but in mpn layer.

But I'd also be interested to know, have you ever written
> anything for the mpn layer, and would you be interested in working on
> some code at that level, to help us towards our goals there.

I have written 0 code in mpn. And this is really not my plan to learn it.

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