6 releases
| new 0.3.1 | Apr 3, 2025 |
|---|---|
| 0.3.0 | Apr 3, 2025 |
| 0.2.1 | Apr 3, 2025 |
| 0.1.1 | Mar 29, 2025 |
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geonum
the geometric number spec in rust
features
- 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
- left-contraction, right-contraction
- anti-commutator product
- grade involution and clifford conjugate
- grade extraction
- section for pseudoscalar (extracting components for which a given pseudoscalar is the pseudoscalar)
- square root operation for multivectors
- undual operation (complement to the dual operation)
- regressive product (alternative method for computing the meet of subspaces)
- automatic differentiation through angle rotation (v' = [r, θ + π/2]) (differential geometric calculus)
use
cargo add 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(2^1000) ≈ 10^301 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)
multivector ops
| operation | dimensions | time | traditional ga complexity |
|---|---|---|---|
| grade extraction | 1,000,000 | 130.69 ns | O(2^n) |
| grade involution | 1,000,000 | 157.18 ns | O(2^n) |
| clifford conjugate | 1,000,000 | 112.90 ns | O(2^n) |
| contractions | 1,000,000 | 266.31 ns | O(2^n) |
| anti-commutator | 1,000,000 | 246.24 ns | O(2^n) |
| all ops combined | 1,000 | 826.57 ns | impossible at high dimensions |
geonum performs all major multivector operations with exceptional efficiency in million-dimensional spaces, maintaining sub-microsecond performance for grade-specific operations that would require exponential time and memory in traditional geometric algebra implementations
tests
cargo fmt --check # format
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
- blade classification (identifying geometric types like points, lines, planes)
- rotor estimation algorithms for transforming between sets of geometric objects
- conformal geometry support
- specialized projective geometric algebra (PGA) support
- broadcasting support for operating on multiple objects (point clouds)