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Question on Barrett

Given a prime modulus p ~ 2^q, why we compute the barrett pre-conditioner using 2^{q + max_bits}/q instead of
using 2^{2 * max_bits} / q ?

For example, for the non-AVX implementation, we can store the barrett as 2^{2*64}/q so that we can lazy reduce a value
in [0, 2^{128}) back to [0, q) (which the Div64 trait seems do the same thing)

Build failure on Mac

cargo --version
cargo 1.69.0 (6e9a83356 2023-04-12)

`Plan::new` panics with invalid parameters.

When trying to construct

concrete_ntt::prime64::Plan::try_new(2048, 1024)

the programs crashes (instead of returning None, as I would have expected):

thread 'main' panicked at /Users/tlepoint/.cargo/registry/src/index.crates.io-6f17d22bba15001f/concrete-ntt-0.1.0/src/roots.rs:56:13:
assertion failed: t_pow == 1
stack backtrace:
   0: rust_begin_unwind
             at /rustc/bf9a1c8a193fc373897196321215794c8bebbeec/library/std/src/panicking.rs:597:5
   1: core::panicking::panic_fmt
             at /rustc/bf9a1c8a193fc373897196321215794c8bebbeec/library/core/src/panicking.rs:72:14
   2: core::panicking::panic
             at /rustc/bf9a1c8a193fc373897196321215794c8bebbeec/library/core/src/panicking.rs:127:5
   3: concrete_ntt::roots::sqrt_mod_ex64
             at /Users/tlepoint/.cargo/registry/src/index.crates.io-6f17d22bba15001f/concrete-ntt-0.1.0/src/roots.rs:56:13
   4: concrete_ntt::roots::find_primitive_root64
             at /Users/tlepoint/.cargo/registry/src/index.crates.io-6f17d22bba15001f/concrete-ntt-0.1.0/src/roots.rs:83:22
   5: concrete_ntt::prime64::Plan::try_new
             at /Users/tlepoint/.cargo/registry/src/index.crates.io-6f17d22bba15001f/concrete-ntt-0.1.0/src/prime64.rs:710:16
   6: bug_concrete_ntt::main
             at ./src/main.rs:4:22
   7: core::ops::function::FnOnce::call_once
             at /rustc/bf9a1c8a193fc373897196321215794c8bebbeec/library/core/src/ops/function.rs:250:5
note: Some details are omitted, run with `RUST_BACKTRACE=full` for a verbose backtrace.

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