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https://github.com/elsuizo/static-math
Safe and fast mathematical operations with static arrays in the Rust programming language
https://github.com/elsuizo/static-math
determinant dual-quaternion euler-angles linear-algebra matrix matrix-calculations matrix-computations matrix-inverse qr-decomposition quaternions rust rust-programming-language
Last synced: about 1 month ago
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Safe and fast mathematical operations with static arrays in the Rust programming language
- Host: GitHub
- URL: https://github.com/elsuizo/static-math
- Owner: elsuizo
- Created: 2020-05-31T21:31:20.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2022-03-17T03:04:34.000Z (almost 3 years ago)
- Last Synced: 2024-12-15T17:44:31.473Z (2 months ago)
- Topics: determinant, dual-quaternion, euler-angles, linear-algebra, matrix, matrix-calculations, matrix-computations, matrix-inverse, qr-decomposition, quaternions, rust, rust-programming-language
- Language: Rust
- Homepage:
- Size: 1.05 MB
- Stars: 40
- Watchers: 5
- Forks: 2
- Open Issues: 5
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
- awesome-rust-list - static-math - math?style=social"/> : Safe and fast mathematical operations with static arrays in the Rust programming language. (Scientific Computation)
- awesome-rust-list - static-math - math?style=social"/> : Safe and fast mathematical operations with static arrays in the Rust programming language. (Scientific Computation)
README
[](https://docs.rs/static-math)
[](https://crates.io/crates/static-math)
# Static Math in Rust programming language
"*Simple things should be simple, complex things should be possible*" Alan Kay.
- This crate take advantage of the static arrays in Rust for fast operations in
stack memory.
- We use a tuple to indexing elements: `m[(i, j)]` allowing nice interface with the `match` feature of Rust
- You could index the rows of the matrix with simply: `m[i]`
- No `unsafe` code :ballot_box_with_check:
- Could be optimize more with the use of SIMD
- This crate could be used in an `no-std` environment.
by enabling the feature `no-std`, for example in your `Cargo.toml`:
```toml
[dependencies.static-math]
default-features = false
version = "0.2.0"
features = ["no-std"]
```
- You can visualize the matrices
```text
inverse:
|-0.54 0.58 0.67 -0.08 -0.17 -1.18|
|2.16 -1.53 -2.44 0.44 0.32 3.77|
|0.21 -0.42 -0.39 0.15 0.20 0.62|
|0.70 -0.24 -0.53 0.20 -0.21 0.73|
|0.85 -0.47 -0.83 0.11 0.11 1.20|
|-3.91 2.47 4.17 -0.87 -0.31 -6.08|
```
- The determinant of the matrices are evaluated "in-place" without loops and code
bifurcations
- The use cases can be: Robotics, Game programming, Simulations ...etc.
The matrix types `Mnn` (where `n=2..6`) implements the Methods from the
`LinearAlgebra` trait:
- `det()`: Determinant of the matrix
- `inverse()`: Inverse of the matrix
- `qr()`: QR decomposition of the matrix
- `norm2()`: norm of the matrix
- `transpose()`: transpose of the matrix
- `trace()`: trace of the matrix
- `shape()`: shape of the matrix
- We have implemented `Quaternion`s (and all the most used methods)
- We have implemented `DualQuaternion`s (and all the most used methods in Robotics and graphics like *Screw Linear Interpolation*)
- We have implemented in the `transformations.rs` module a wide variety of functions used in Robotics (which conforms to the screw theory)
## Benchmarks
Using the criterion crate:
https://github.com/bheisler/criterion.rs
run with: `cargo bench`
Others benches comparing the performance with others crates are in this repo: https://github.com/bitshifter/mathbench-rs
*NOTE*: this is the only crate that not have unsafe code
with the following results:
| benchmark | glam | cgmath | nalgebra | euclid | vek | pathfinder | static-math | ultraviolet |
|--------------------------------|-----------------|-----------------|-----------------|----------------|-----------------|-----------------|-----------------|-----------------|
| euler 2d x10000 | 16.23 us | 16.13 us | __9.954 us__ | 16.18 us | 16.2 us | 10.42 us | __9.97 us__ | 16.17 us |
| euler 3d x10000 | __15.95 us__ | 32.11 us | 32.13 us | 32.13 us | 32.13 us | __16.27 us__ | 32.16 us | 32.11 us |
| matrix2 determinant | __2.0386 ns__ | 2.0999 ns | 2.1018 ns | N/A | 2.0997 ns | 2.0987 ns | 2.0962 ns | 2.1080 ns |
| matrix2 inverse | __2.8226 ns__ | 8.4418 ns | 7.6303 ns | N/A | N/A | 3.3459 ns | 9.4636 ns | 5.8796 ns |
| matrix2 mul matrix2 | __2.6036 ns__ | 5.0007 ns | 4.8172 ns | N/A | 9.3814 ns | __2.5516 ns__ | 4.7274 ns | 4.9428 ns |
| matrix2 mul vector2 x1 | 2.4904 ns | 2.6144 ns | 2.8714 ns | N/A | 4.2139 ns | __2.0839 ns__ | 2.8873 ns | 2.6250 ns |
| matrix2 mul vector2 x100 | 227.5271 ns | 243.3579 ns | 265.1698 ns | N/A | 400.6940 ns | __219.7127 ns__ | 267.8780 ns | 243.9880 ns |
| matrix2 return self | __2.4235 ns__ | 2.8841 ns | 2.8756 ns | N/A | 2.8754 ns | __2.4147 ns__ | 2.8717 ns | 2.8697 ns |
| matrix2 transpose | __2.2887 ns__ | 3.0645 ns | 7.9154 ns | N/A | 2.9635 ns | N/A | 3.0637 ns | 3.0652 ns |
| matrix3 determinant | 3.9129 ns | __3.8107 ns__ | __3.8191 ns__ | N/A | __3.8180 ns__ | N/A | __3.8151 ns__ | 8.9368 ns |
| matrix3 inverse | 17.5373 ns | 18.6931 ns | __12.3183 ns__ | N/A | N/A | N/A | 12.8195 ns | 21.9098 ns |
| matrix3 mul matrix3 | 9.9578 ns | 13.3648 ns | 7.8154 ns | N/A | 35.5802 ns | N/A | __6.4938 ns__ | 10.0527 ns |
| matrix3 mul vector3 x1 | 4.8090 ns | 4.9339 ns | __4.5046 ns__ | N/A | 12.5518 ns | N/A | 4.8002 ns | 4.8118 ns |
| matrix3 mul vector3 x100 | __0.4836 us__ | __0.4808 us__ | __0.4755 us__ | N/A | 1.247 us | N/A | __0.4816 us__ | __0.4755 us__ |
| matrix3 return self | __5.4421 ns__ | __5.4469 ns__ | __5.4526 ns__ | N/A | __5.4656 ns__ | N/A | __5.4718 ns__ | __5.4043 ns__ |
| matrix3 transpose | __9.9567 ns__ | __10.0794 ns__ | 10.9704 ns | N/A | __9.9257 ns__ | N/A | 10.7350 ns | 10.5334 ns |
| matrix4 determinant | __6.2050 ns__ | 11.1041 ns | 69.2549 ns | 17.1809 ns | 18.5233 ns | N/A | 16.5331 ns | 8.2704 ns |
| matrix4 inverse | __16.4386 ns__ | 47.0674 ns | 71.8174 ns | 64.1356 ns | 284.3703 ns | N/A | 52.6993 ns | 41.1780 ns |
| matrix4 mul matrix4 | __7.7715 ns__ | 26.7308 ns | 8.6500 ns | 10.4414 ns | 86.1501 ns | N/A | 21.7985 ns | 26.8056 ns |
| matrix4 mul vector4 x1 | __3.0303 ns__ | 7.7400 ns | 3.4091 ns | N/A | 21.0968 ns | N/A | 6.2971 ns | 6.2537 ns |
| matrix4 mul vector4 x100 | __0.6136 us__ | 0.9676 us | __0.627 us__ | N/A | 2.167 us | N/A | 0.7893 us | 0.8013 us |
| matrix4 return self | 7.1741 ns | __6.8838 ns__ | 7.5030 ns | N/A | 7.0410 ns | N/A | __6.7768 ns__ | 6.9508 ns |
| matrix4 transpose | __6.6826 ns__ | 12.4966 ns | 15.3265 ns | N/A | 12.6386 ns | N/A | 15.2657 ns | 12.3396 ns |
| ray-sphere intersection x10000 | 56.2 us | 55.7 us | __15.32 us__ | 55.45 us | 56.02 us | N/A | N/A | 50.94 us |
| rotation3 inverse | __2.3113 ns__ | 3.1752 ns | 3.3292 ns | 3.3311 ns | 3.1808 ns | N/A | 8.7109 ns | 3.6535 ns |
| rotation3 mul rotation3 | __3.6584 ns__ | 7.5255 ns | 7.4808 ns | 8.1393 ns | 14.1636 ns | N/A | 6.8044 ns | 7.6386 ns |
| rotation3 mul vector3 x1 | __6.4950 ns__ | 7.6808 ns | 7.5784 ns | 7.5746 ns | 18.2547 ns | N/A | 7.2727 ns | 8.9732 ns |
| rotation3 mul vector3 x100 | __0.6465 us__ | 0.7844 us | 0.7573 us | 0.7533 us | 1.769 us | N/A | 0.7317 us | 0.9416 us |
| rotation3 return self | __2.4928 ns__ | 2.8740 ns | 2.8687 ns | N/A | 2.8724 ns | N/A | 4.7868 ns | 2.8722 ns |
| transform point2 x1 | 2.7854 ns | 2.8878 ns | 4.4207 ns | 2.8667 ns | 11.9427 ns | __2.3601 ns__ | N/A | 4.1770 ns |
| transform point2 x100 | 0.3316 us | 0.3574 us | 0.4445 us | __0.3008 us__ | 1.212 us | 0.3184 us | N/A | 0.4332 us |
| transform point3 x1 | __2.9619 ns__ | 10.6812 ns | 6.1037 ns | 7.7051 ns | 13.2607 ns | 3.0934 ns | N/A | 6.8419 ns |
| transform point3 x100 | __0.6095 us__ | 1.27 us | 0.8064 us | 0.7674 us | 1.446 us | __0.6189 us__ | N/A | 0.8899 us |
| transform vector2 x1 | __2.4944 ns__ | N/A | 3.7174 ns | 2.6273 ns | 11.9424 ns | N/A | N/A | 3.0458 ns |
| transform vector2 x100 | 0.3125 us | N/A | 0.3871 us | __0.2817 us__ | 1.213 us | N/A | N/A | 0.3649 us |
| transform vector3 x1 | __2.8091 ns__ | 7.7343 ns | 5.5064 ns | 4.4810 ns | 15.4097 ns | N/A | N/A | 4.8819 ns |
| transform vector3 x100 | __0.6035 us__ | 0.9439 us | 0.7573 us | 0.6327 us | 1.63 us | N/A | N/A | 0.6703 us |
| transform2 inverse | __9.0256 ns__ | N/A | 12.2614 ns | 9.4803 ns | N/A | __8.9047 ns__ | N/A | N/A |
| transform2 mul transform2 | 4.5111 ns | N/A | 8.1434 ns | 5.8677 ns | N/A | __3.8513 ns__ | N/A | N/A |
| transform2 return self | __4.1707 ns__ | N/A | 5.4356 ns | 4.2775 ns | N/A | __4.1117 ns__ | N/A | N/A |
| transform3 inverse | __10.9869 ns__ | N/A | 71.4437 ns | 56.0136 ns | N/A | 23.0392 ns | N/A | N/A |
| transform3 mul transform3d | __6.5903 ns__ | N/A | 8.5673 ns | 10.1802 ns | N/A | 7.6587 ns | N/A | N/A |
| transform3 return self | __7.1828 ns__ | N/A | __7.2619 ns__ | __7.2407 ns__ | N/A | __7.3214 ns__ | N/A | N/A |
| vector3 cross | __2.4257 ns__ | 3.6842 ns | 3.7945 ns | 3.6821 ns | 3.8323 ns | N/A | 3.8622 ns | 3.6927 ns |
| vector3 dot | __2.1055 ns__ | 2.3179 ns | 2.3174 ns | 2.3190 ns | 2.3195 ns | N/A | 2.3204 ns | 2.3160 ns |
| vector3 length | __2.5020 ns__ | __2.5002 ns__ | 2.5986 ns | __2.5013 ns__ | __2.5021 ns__ | N/A | __2.5036 ns__ | __2.5017 ns__ |
| vector3 normalize | __4.0454 ns__ | 5.8411 ns | 8.4069 ns | 8.0679 ns | 8.8137 ns | N/A | N/A | 5.8440 ns |
| vector3 return self | __2.4087 ns__ | 3.1021 ns | 3.1061 ns | N/A | 3.1052 ns | N/A | 3.1136 ns | 3.1071 ns |
## TODOS:
- [X] `Quaternion` type and methods
- [ ] `expm()`: Exponential matrix implementation
- [X] Eigenvalues
- [X] QR decomposition