octonion

Minimal, dependency-free, no_std octonion algebra for Rust.

This crate provides Octonion (an 8D hypercomplex number over f64) with basic arithmetic, conjugation, norms, and inversion.

Quick start

use octonion::Octonion;

let x = Octonion::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0);

// Basis elements square to -1.
assert_eq!(Octonion::E1 * Octonion::E1, -Octonion::ONE);

// Non-commutativity.
assert_eq!(Octonion::E1 * Octonion::E2, Octonion::E3);
assert_eq!(Octonion::E2 * Octonion::E1, -Octonion::E3);

// Conjugation, norm, inverse.
let _conj = x.conj();
let _norm_sq = x.norm_sqr();
let _inv = x.try_inverse().unwrap();

Notes

• Octonion multiplication is non-associative. If you need explicit grouping, enable alloc (on by default) and use Paren or OctoExpr.
• If an octonion lies in the quaternion subalgebra (its e₄..e₇ coefficients are exactly zero), you can call Octonion::as_quaternion to get a QuaternionView that supports associative multiplication.

SIMD helpers

The octonion::simd module includes a direct coefficient expansion simd::mul_direct (often easier for the compiler to auto-vectorize than the default implementation).

On x86_64 with avx, simd::mul_simd_avx is available (currently a thin wrapper around mul_direct).

Features

• alloc (default): enables [Paren], [OctoExpr], and simd::mul_batch.
• alloc (default): enables Paren, OctoExpr, and simd::mul_batch.
• e8: enables octonion::e8::IntegralOctonion (Cayley integers / E8 lattice).

To use this crate without allocation support:

octonion = { version = "0.1", default-features = false }

Examples and benches

• Colorized display demo: cargo run --example display_demo
• Benchmarks: cargo bench