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.
This begins to attempt to restructure the source tree so that the common parts
are common and the different parts are different.
The backend is now split into two parts:
- serial (containing the implementation using serial formulas and mixed-model arithmetic).
- vector (containing the implementation using parallel formulas and single-model arithmetic).
The serial scalar_mul tree is now under backend::serial::scalar_mul.
The avx2 scalar_mul tree is now under backend::avx2::scalar_mul.
`FieldElement32` -> `FieldElement2625`
`FieldElement64` -> `FieldElement51`
`Scalar32` -> `Scalar29`
`Scalar64` -> `Scalar52`
This naming is more accurate and would let us add an ADX backend later.
This change provides a common convention for using allocator-dependent
features with:
#![cfg(feature = "alloc")]
When available, `Vec` is imported consistently as `prelude::Vec`, which
means modules that need access to `Vec` can simply do:
use prelude::*;
and if an allocator is available, `Vec` will be in the crate prelude.
This allows all `alloc` vs `std` gating to be handled in `lib.rs`,
`build.rs`, and `prelude.rs` so the rest of the codebase doesn't have to
do any gating whatsoever.
Unfortunately, Rust selects `i32` as the type for an integer literal
when the literal has no other type constraints. This means that someone
cannot write `Scalar::from(1)`, as Rust will choose `i32` as the type for
`1`, and we don't `impl From<i32> for Scalar`.
We could implement `From` conversions for signed integers, but since
`Scalar` operations should be constant-time by default, this would
require us to extract the sign bit of the integer and use it to
conditionally select between the positive and negative of Scalar
constructed from the value bits. This is more expensive than the
unsigned operation, and I don't think it's what anyone really wants.
Making API consumers specify that their literals are unsigned is
slightly annoying, but better than the above alternative.
It would also be nice to change `Scalar::from_hash` to be
`impl<D: Digest<OutputSize = U64>> From<D> for Scalar`,
but this isn't currently allowed by Rust (since that `impl` "could"
conflict with the `impl From<u8>` if someone decided that `u8` should
`impl Digest`).
