This crate uses SIMD code to achieve very fast Galois Field matrix multiplication.
I have previously implemented a version of this algorithm on a PlayStation 3. It is available here
I will implement three different SIMD engines for field multiplication across vectors:
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x86 implementation of parallel long (bitwise) multiplication
-
Arm/Aarch64 NEON implementation using hardware polynomial multiply and table-based modular reduction (vmull/tvbl)
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Arm NEON implementation of parallel long (bitwise) multiplication
-
4-way armv6 (Thumb) implementation of the long multiplication routine
Support for Arm targets requires nightly Rust build.
Before I start writing arch-specific implementations, I'm focusing on
clearly documenting how the algorithm works. I'm going to implement a
non-SIMD version that uses the same basic ideas, but using a more
rusty style (infinite iterators). That's in src/arch.rs and can be
enabled as a feature:
cargo test --features simulator --tests simulator
I'll also use this to prove that the algorithm works as intended.
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Write and test simulation of non SIMD algorithm
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Write and test simulation of SIMD algorithm
Using the simd version of the field multiplication routine, I now have:
- SIMD version of x86 matrix multiply
It needs a bit more work, but it's tested and runs around 3x faster
than the reference version. See benches/vector_mul.rs for
details. To run that with all relevant optimisations, you might need
to turn on some compile flags:
RUSTFLAGS="-O -C target-cpu=native -C target-feature=+ssse3,+sse4.1,+sse4.2,+avx" cargo bench -q "matrix"