Single limb floating point $p$-adics

[r-mb]

This PR implements a new representation for $p$-adic numbers with low precision. This new package uses the floating point representation, as detailed in #2447.

This is not meant as a replacement for the current padic package, as this new approach needs error tracking.

Currently, this PR only implements the most basic arithmetic operations.

[fredrik-johansson]

I think n_remove2_precomp is slow and shouldn't be used for removing (powers of) p.

It's better to use bit manipulation when p = 2 and n_divisible_odd_gm + multiplication by 1/p mod 2^64 when p is odd. This is done in radix (https://github.com/flintlib/flint/blob/main/src/radix/init_clear.c).

Actually I'm wondering if more code reuse between this and radix isn't possible. Hmm.

[fredrik-johansson]

By the way, I think I'm now leaning toward naming the slots u and v (and N for the error), matching padic, which I've also done in padic_radix. This is concise and mnemonic enough.

I think it would be really good to have error tracking built into this module as well.

One option is to have a pair of types (slightly verbose):

• padic_nmod_float_t / padic_nmod_t
• padic_nmod_float_t / padic_nmod_ball_t
• padic_nmod_t / padic_nmod_ball_t

Another option would be to have just one type with floating-point/ball mode selected by the context object. I think this is the right choice for padic_radix if we want to add a floating-point mode there. But for padic_nmod the overhead of 1.5x more storage is not negligible...