geonum-0.2.0 has been yanked.
geonum
the geometric number spec in rust
use
cargo install geonum
see tests/lib_test.rs examples for scalable numerical simulation of linear and geometric algebra operations
benches
rank-3 tensor comparison
| implementation | size | time |
|---|---|---|
| tensor (O(n³)) | 2 | 1.06 µs |
| tensor (O(n³)) | 3 | 2.25 µs |
| tensor (O(n³)) | 4 | 3.90 µs |
| tensor (O(n³)) | 8 | 7.92 µs |
| tensor (O(n³)) | 16 | 69.54 µs |
| geonum (O(1)) | any | 9.83 ns |
geonum achieves constant O(1) time complexity regardless of problem size, 400× faster than tensor operations at size 4 and 7000× faster at size 16, eliminating cubic scaling of traditional tensor implementations
extreme dimension comparison
| implementation | dimensions | time | storage complexity |
|---|---|---|---|
| traditional ga | 10 | 543.40 ns (partial) | O(2^n) = 1024 components |
| traditional ga | 30 | theoretical only | O(2^n) = 1 billion+ components |
| traditional ga | 1000 | impossible | O(21000) ≈ 10301 components |
| traditional ga | 1,000,000 | impossible | O(2^1000000) components |
| geonum (O(1)) | 10 | 134.12 ns | O(1) = 2 components |
| geonum (O(1)) | 30 | 153.64 ns | O(1) = 2 components |
| geonum (O(1)) | 1000 | 2.08 µs | O(1) = 2 components |
| geonum (O(1)) | 1,000,000 | 2.94 ms | O(1) = 2 components |
geonum enables geometric algebra in million-dimensional spaces with constant time operations, achieving whats mathematically impossible with traditional implementations (requires more storage than atoms in the universe)
tests
cargo clippy # lint
cargo test --lib # unit
cargo test --test lib_test # feature
cargo bench # bench
cargo llvm-cov # coverage
docs
cargo doc --open
todo
- dot product, wedge product, geometric product
- inverse, division, normalization
- million-dimension geometric algebra with O(1) complexity
- multivector support and trivector operations
- rotations, reflections, projections, rejections
- exponential, interior product, dual operations
- meet and join, commutator product, sandwich product