For the field element types `FieldElement` and `Scalar`, use inherent
constants instead of (non-const) functions to return these constant
values.
It's likely the original functions predate support for inherent
constants, but now that they're available, they're a better fit for
these sort of constant values.
This was more useful at the time when we were determining, e.g., optimal lookup
table sizes and could regenerate them more easily, but it came at a massive
complexity cost. It also meant that we were unable to implement backend
autoselection. This commit removes the `build.rs` entirely. In the future, a
different `build.rs` could be added that auto-selects a backend, but it seems
like the current default-u64 setup has been working fine.
Since computation of the 0 term in reduction requires a multiplication with a
4-cycle latency, this ensures that the rest of the computation can start before
the 0 term is finished
This splits the `FieldElement51x4` type into two types:
- `F51x4Reduced` (with reduced limbs)
- `F51x4Unreduced` (with unreduced limbs)
The reduction is implemented as a `From` impl to convert one type to the other.
The output of a multiplication is now a `F51x4Unreduced`. The reason is that
the inputs to IFMA operations must be at most 52 bits, so it's not possible to
perform an addition of (51+epsilon)-bit values and still be small enough to be
used as an input to multiplication. So, it doesn't make sense to perform a
reduction at the end of a multiplication, because the reduced values will be
fed into an addition or subtraction, which then needs to be re-reduced.
