14 releases
0.2.3 | Aug 5, 2021 |
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0.2.1 | Jul 31, 2021 |
0.1.7 | Sep 13, 2020 |
0.1.1 | Jun 28, 2020 |
#300 in Math
149 downloads per month
390KB
9K
SLoC
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 thematch
feature of Rust -
No
unsafe
code ☑️ -
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 yourCargo.toml
:[dependencies.static-math] default-features = false version = "0.2.0" features = ["no-std"]
-
You can visualize the matrices
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 | 7.555 us | 7.521 us | 16.38 us | 11.86 us | 7.513 us | 9.806 us | 11.83 us | 7.499 us |
euler 3d x10000 | 16.2 us | 25.04 us | 106.3 us | 25.05 us | 25.16 us | 16.76 us | 25.03 us | 25.05 us |
matrix2 determinant | 2.0332 ns | 2.0311 ns | 2.0250 ns | N/A | 2.0209 ns | 2.0323 ns | 2.0254 ns | N/A |
matrix2 inverse | 2.6114 ns | 3.0331 ns | 2.9792 ns | N/A | N/A | 2.7550 ns | 3.0132 ns | N/A |
matrix2 mul matrix2 | 2.6047 ns | 2.5346 ns | 2.5426 ns | N/A | 8.7573 ns | 2.5381 ns | 2.6028 ns | 2.9668 ns |
matrix2 mul vector2 x1 | 2.6592 ns | 2.6104 ns | 2.6214 ns | N/A | 4.2512 ns | 2.0663 ns | 2.8674 ns | 2.6172 ns |
matrix2 mul vector2 x100 | 245.2897 ns | 233.7149 ns | 238.7395 ns | N/A | 399.3148 ns | 218.4107 ns | 260.6645 ns | 234.7099 ns |
matrix2 return self | 2.4740 ns | 2.5994 ns | 2.5968 ns | N/A | 2.5969 ns | 2.4607 ns | 2.5928 ns | 2.5974 ns |
matrix2 transpose | 2.0852 ns | 2.0814 ns | 2.3426 ns | N/A | 2.1053 ns | N/A | 2.0829 ns | N/A |
matrix3 determinant | 3.3675 ns | 3.4261 ns | 3.3780 ns | N/A | 3.4479 ns | N/A | 3.4375 ns | N/A |
matrix3 inverse | 11.4209 ns | 8.3701 ns | 9.4315 ns | N/A | N/A | N/A | 9.1710 ns | 20.1731 ns |
matrix3 mul matrix3 | 5.8501 ns | 6.5350 ns | 9.8196 ns | N/A | 47.9203 ns | N/A | 9.5170 ns | 6.5211 ns |
matrix3 mul vector3 x1 | 3.9266 ns | 4.3876 ns | 4.3333 ns | N/A | 16.0858 ns | N/A | 4.4220 ns | 4.3304 ns |
matrix3 mul vector3 x100 | 0.4372 us | 0.4416 us | 0.4594 us | N/A | 1.59 us | N/A | 0.454 us | 0.4425 us |
matrix3 return self | 4.8566 ns | 4.8401 ns | 4.8226 ns | N/A | 4.8340 ns | N/A | 4.8303 ns | 4.8383 ns |
matrix3 transpose | 5.7688 ns | 5.6980 ns | 8.1508 ns | N/A | 5.6910 ns | N/A | 5.6936 ns | 5.6766 ns |
matrix4 determinant | 8.3724 ns | 11.1604 ns | 52.8697 ns | 16.0723 ns | 17.5301 ns | N/A | 16.1402 ns | N/A |
matrix4 inverse | 21.3281 ns | 38.5833 ns | 64.5172 ns | 61.2347 ns | 275.5253 ns | N/A | 48.0641 ns | 37.1436 ns |
matrix4 mul matrix4 | 7.5043 ns | 8.3723 ns | 9.4094 ns | 10.1761 ns | 90.7185 ns | N/A | 20.6424 ns | 8.4072 ns |
matrix4 mul vector4 x1 | 3.3645 ns | 3.7273 ns | 3.7251 ns | N/A | 24.2185 ns | N/A | 6.1311 ns | 3.7524 ns |
matrix4 mul vector4 x100 | 0.6105 us | 0.6237 us | 0.6202 us | N/A | 2.402 us | N/A | 0.7044 us | 0.6202 us |
matrix4 return self | 6.8863 ns | 7.1298 ns | 6.6961 ns | N/A | 6.7079 ns | N/A | 6.6772 ns | 6.7079 ns |
matrix4 transpose | 5.7312 ns | 10.1612 ns | 14.9424 ns | N/A | 10.2015 ns | N/A | 10.1996 ns | 10.2391 ns |
rotation3 inverse | 2.1867 ns | 2.9086 ns | 2.8853 ns | 2.9092 ns | 2.8987 ns | N/A | N/A | 2.9064 ns |
rotation3 mul rotation3 | 3.3422 ns | 4.3602 ns | 7.0680 ns | 7.7111 ns | 8.9616 ns | N/A | N/A | 18.4088 ns |
rotation3 mul vector3 | 6.6977 ns | 6.7831 ns | 6.9924 ns | 6.9801 ns | 32.8778 ns | N/A | N/A | 13.5267 ns |
rotation3 return self | 2.4622 ns | 2.5983 ns | 2.6021 ns | N/A | 2.5989 ns | N/A | N/A | 2.5980 ns |
transform point2 x1 | 3.8946 ns | 2.8843 ns | 4.6543 ns | 3.2271 ns | 17.0089 ns | 2.3608 ns | N/A | N/A |
transform point2 x100 | 0.4265 us | 0.3677 us | 0.4632 us | 0.322 us | 1.712 us | 0.3206 us | N/A | N/A |
transform point3 x1 | 4.9958 ns | 6.3712 ns | 6.6426 ns | 6.1114 ns | 24.8255 ns | 3.1011 ns | N/A | N/A |
transform point3 x100 | 0.6261 us | 0.7418 us | 0.7447 us | 0.7296 us | 2.507 us | 0.6295 us | N/A | N/A |
transform vector2 x1 | 2.7159 ns | N/A | 3.9917 ns | 2.8070 ns | 16.8257 ns | N/A | N/A | N/A |
transform vector2 x100 | 0.3463 us | N/A | 0.4018 us | 0.2893 us | 1.709 us | N/A | N/A | N/A |
transform vector3 x1 | 3.9868 ns | 5.5573 ns | 8.4892 ns | 4.4068 ns | 25.0274 ns | N/A | N/A | N/A |
transform vector3 x100 | 0.5905 us | 0.6584 us | 0.8936 us | 0.6365 us | 2.513 us | N/A | N/A | N/A |
transform2 inverse | N/A | N/A | 9.4094 ns | 4.6388 ns | N/A | 3.9983 ns | N/A | N/A |
transform2 mul transform2 | N/A | N/A | 9.8173 ns | 6.2162 ns | N/A | 3.8699 ns | N/A | N/A |
transform2 return self | N/A | N/A | 4.8447 ns | 3.5091 ns | N/A | 4.1391 ns | N/A | N/A |
transform3 inverse | N/A | N/A | 65.3982 ns | 52.6160 ns | N/A | 32.0466 ns | N/A | N/A |
transform3 mul transform3d | N/A | N/A | 10.9731 ns | 9.9741 ns | N/A | 7.6754 ns | N/A | N/A |
transform3 return self | N/A | N/A | 7.1596 ns | 6.6096 ns | N/A | 7.0148 ns | N/A | N/A |
vector3 cross | 2.4542 ns | 3.5894 ns | 3.2434 ns | 3.4923 ns | 3.5150 ns | N/A | 3.2947 ns | 7.1968 ns |
vector3 dot | 2.1001 ns | 2.3025 ns | 2.2986 ns | 2.3030 ns | 2.3084 ns | N/A | 2.3072 ns | 3.7322 ns |
vector3 length | 2.1722 ns | 2.1747 ns | 2.3414 ns | 2.1716 ns | 2.2151 ns | N/A | 2.2063 ns | 3.4787 ns |
vector3 normalize | 4.4248 ns | 4.3266 ns | 8.1124 ns | 8.0704 ns | 8.0747 ns | N/A | N/A | 8.0778 ns |
vector3 return self | 2.4642 ns | 2.9591 ns | 2.9586 ns | N/A | 2.9579 ns | N/A | 2.9633 ns | 2.9572 ns |
TODOS:
-
Quaternion
type and methods -
expm()
: Exponential matrix implementation - Eigenvalues
- QR decomposition
Dependencies
~1MB
~18K SLoC